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Factorisation Class 8 MCQs Questions with Answers
Factorisation Class 8 MCQ Question 1.
The common factor of x²y² and x³y³ is
(a) x²y²
(b) x³y³
(c) x²y³
(d) x³y².
Answer
Answer: (a) x²y²
Hint:
x2y2 = x × x × y × y
x3y3 = x × x × x × y × y × y
Class 8 Maths Chapter 14 MCQ Question 2.
The common factor of x3y2 and x4y is
(a) x43y2
(b) x4y
(c) x3y2
(d) x3y.
Answer
Answer: (d) x3y.
Hint:
x3y2 = x × x × x × y × y
x4y = x × x × x × x × y
Class 8 Factorisation MCQ Question 3.
The common factor of a2 m4 and a4m2 is
(a) a4m4
(b) a2m2
(c) a2m4
(d) a4m2
Answer
Answer: (b) a2m2
Hint:
a2m4 = a × a × m × m × m × m
a4m2 = a × a × a × a × m × m
MCQ Of Factorisation Class 8 Question 4.
The common factor of p3q4 and p4q3 is
(a) p4q4
(b) p4q3
(c) p3q3
(d) p3q4
Answer
Answer: (c) p3q3
Hint:
p3q4 = p × p × p × q × q × q × q
p4q3 = p × p × p × p × q × q × q
MCQ On Factorisation Class 8 Question 5.
The common factor 12y and 30 is
(a) 6
(b) 12
(c) 30
(d) 6y.
Answer
Answer: (a) 6
Hint:
12y = 2 × 2 × 3 × y
30 = 2 × 3 × 5.
MCQ On Factorization For Class 8 Question 6.
The common factor of 2x, 3x3, 4 is
(a) 1
(b) 2
(c) 3
(d) 4.
Answer
Answer: (a) 1
Hint:
2x = 2 × x
3x3 = 3 × x × x × x
4 = 2 × 2.
Factorization Class 8 MCQ Question 7.
The common factor of 10ab, 30bc, 50ca is
(a) 10
(b) 30
(c) 50
(d) abc.
Answer
Answer: (a) 10
Hint:
10ab = 2 × 5 × a × b
30bc = 2 × 3 × 5 × b × c
50ca = 2 × 5 × 5 × c × a.
MCQ Questions For Class 8 Maths Factorisation Question 8.
The common factor of 14a2b and 35a4b² is
(a) a4b²
(b) 35a4b²
(c) 14a²b
(d) 7a²b.
Answer
Answer: (d) 7a²b.
Hint:
14a²b = 2 × 7 × a × a × b
35a4b2 = 5 × 7 × a × a × a × a × b × b.
Factorisation Class 8 Extra Questions Question 9.
The common factor of 8a2b4c2, 12a4bc4 and 20a3b4 is
(a) a4b4
(b) a2b2
(c) 4a2b2
(d) 4a2b.
Answer
Answer: (d) 4a2b.
Hint:
8a2b4c2 = 2 × 2 × 2 × a × a × b × b × b × b × c × c
12a4bc2 = 2 × 2 × 3 × a × a × a × a × b × c × c
20a3b4 = 2 × 2 × 5 × a × a × a × b × b × b × b
Class 8 Maths Factorisation MCQ Question 10.
The common factor of 6a3b4c2, 21a2b and 15a3 is
(a) 3a2
(b) 3a3
(c) 6a3
(d) 6a2
Answer
Answer: (a) 3a2
Hint:
6a3b4c2 = 2 × 3 × a × a × a × b × b × b × b × c × c
21a2b = 3 × 7 × a × a × a
15a364c4 = 3 × 5 × a × a × a
MCQ Factorisation Class 8 Question 11.
The common factor of 2a2b4c2, 8a4b3c4 and 6a3b4c2 is
(a) 2a2b3c2
(b) 6a2b3c2
(c) 8a2b3c2
(d) a4b4c4.
Answer
Answer: (a) 2a2b3c2
Hint:
6a2b4c2 = 2 × a × a × b × b × b × b × c × c × c × c
8a4b3c4 = 2 × 2 × 2 × a × a × a × a × b × b × b × c × c × c × c
6a3b4c2 = 2 × 3 × a × a × a × b × b × b × b × c × c.
Factorisation MCQ Class 8 Question 12.
The common factor of 3a2b4c2, 12b2c4 and 15a3b4c4 is
(a) b4c4
(b) 3b2c2
(c) 15b2c4
(d) 12b2c4
Answer
Answer: (b) 3b2c2
Hint:
3a²b4c² = 3 × a × a × b × b × b × b × c × c
12b²c4 = 2 × 2 × 3 × b × b × c × c × c × c.
15a³b4c4 = 3 × 5 × a × a × a × b × b × b × b × c × c × c × c.
Factorisation Of Algebraic Expressions Class 8 MCQ Question 13.
The common factor of 24x3y4, 36x4z4 and 48x3y2z is
(a) 12x3
(b) 24x3
(c) 36x3
(d)48x3
Answer
Answer: (a) 12x3
Hint:
24x³y4 = 2 × 2 × 2 × 3 × x × x × x × y × y × y × y.
36x4z4 = 2 × 2 × 3 × 3 × x × x × x × x × z × z × z × z.
48x3y2z = 2 × 2 × 2 × 2 × 3 × x × x × x × y × y × z
Class 8 Maths Ch 14 MCQ Question 14.
The common factor of 72x3y4z4, 120z2d4x4 and 96y3z4d4 is
(a) 96z3
(b) 120z3
(c) 72z3
(d) 24z2.
Answer
Answer: (d) 24z2
Hint:
72x3y4z4 = 2 × 2 × 2 × 3 × 3 × x × x × x × y × y × y × y × z × z × z × z.
120z²d4x4 = 2 × 2 × 2 × 3 × 5 × z × z × d × d × d × d × x × x × x × x
96y3z4d4 = 2 × 2 × 2 × 2 × 2 × 3 × y × y × z × z × z × z × d × d × d × d
MCQ Questions On Factorisation Class 8 Question 15.
The common factor of 36p2q3x4, 48pq3x2 and 54p3q3x4 is
(a) 6pq3x2
(b) 36pq3x2
(c) 54pq3x2
(d) 48pq3x2
Answer
Answer: (a) 6pq3x2
Hint:
36p2q3x4 = 2 × 2 × 3 × 3 × p × p × q × q × q × x × x × x × x
48pq³x² = 2 × 2 × 2 × 2 × 3 × p × q × q × q × x × x
p3q3x4 = p × p × p × q × q × q × x × x × x × x
Question 16.
The factorisation of 12a2b + 15ab2 is
(a) 3ab (4a + 5b)
(b) 3a2b (4a + 5b)
(c) 3ab2 (4a + 5b)
(d) 3a2b2 (4a + 5b).
Answer
Answer: (a) 3ab (4a + 5b)
Hint:
12a²b + 15ab² = 3ab(4a + 5b).
Question 17.
The factorisation of 10x2 – 18x3 + 14x4 is
(a) 2x2 (7x2 – 9x + 5)
(b) 2x (7x2 – 9x + 5)
(c) 2 (7x2 – 9x + 5)
(d) 2x3 (7x2 – 9x + 5).
Answer
Answer: (a) 2x2 (7x2 – 9x + 5)
Hint:
10x² – 18x³ + 14x³ = 2x²(5 – 9x + 7x²).
Question 18.
The factorisation of 6x – 42 is
(a) 6(x – 7)
(b) 3(x – 7)
(c) 2(x – 7)
(d) 6(x + 7)
Answer
Answer: (a) 6(x – 7)
Hint:
6x – 42 = 6(x – 7)
Question 19.
The factorisation of 6x + 12y is
(a) 6(x + 2y)
(b) 3(x + 4y)
(c) 2(3x + 12y)
(d) none of these.
Answer
Answer: (a) 6(x + 2y)
Hint:
6x + 12y = 6(x + 2y)
Question 20.
The factorisation of 28a3b5 – 42a5b3 is
(а) 14a3b3(2b2 – 3a2)
(b) 14a2b3(2b2 – 3a2)
(c) 14a3b2(2b2 – 3a2)
(d) none of these.
Answer
Answer: (а) 14a3b3(2b2 – 3a2)
Hint:
28a³ b5 – 42a5b3 = 14a3b3(2b² – 3a²)
Question 21.
The factorisation of a3 + a2b + ab2 is
(a) a(a2 + ab + b2)
(b) 6(a2 + ab + b2)
(c) ab(a2 + ab + b2)
(d) none of these.
Answer
Answer: (a) a(a2 + ab + b2)
Hint:
a³ + a²b + ab² = a(a² + ab + b²)
Question 22.
The factorisation of x2yz + xy2z + xyz2 is
(a) xyz(x + y + z)
(b) x2yz(x + y + z)
(c) xy2z(x + y + z)
(d) xyz2(x + y + z).
Answer
Answer: (a) xyz(x + y + z)
Hint:
x²yz + xy²z + xyz² = xyz (x + y + z)
Question 23.
The factorisation of ax2y + bxy2 + cxyz is
(a) xy(ax + by + cz)
(b) axy(ax + by + cz)
(c) bxy(ax + by + cz)
(d) cxy(ax + by + cz).
Answer
Answer: (a) xy(ax + by + cz)
Hint:
ax²y + bxy² + cxyz = xy (ax + by + cz)
Question 24.
The factorisation of
a (x + y + z) + b(x + y + z) + c(x + y + z) is
(a) (a + b + c)(x + y + z)
(b) (ab + bc + ca)(x + y + z)
(c) (xy + yz + zx)(a + b + c)
(d) none of these.
Answer
Answer: (a) (a + b + c)(x + y + z)
Hint:
a(x + y + z) + b(x + y + z) + c(x + y + z)
= (x + y + z) (a + b + c).
Question 25.
The factorisation of 6xy – 4y + 6 – 9x is
(a) (3x – 2)(2y – 3)
(b) (3x + 2)(2y – 3)
(c) (3x – 2)(2y + 3)
(d) (3x + 2)(2y + 3).
Answer
Answer: (a) (3x – 2)(2y – 3)
Hint:
6xy – 4y + 6 – 9x
= 2y(3x – 2) – 3(- 2 + 3x)
= (3x – 2)(2y – 3)
Question 26.
The factorisation of x2 + xy + 2x + 2y is
(a) (x + 2)(x + y)
(b) (x + 2)(x – y)
(c) (x – 2)(x + y)
(d) (x – 2)(x – y).
Answer
Answer: (a) (x + 2)(x + y)
Hint:
x² + xy + 2x + 2y
= x(x + y) + 2(x + y)
= (x + 2) (x + y).
Question 27.
The factorisation of ax + bx – ay – by is
(a) (x – y)(a + b)
(b) (x + y)(a + b)
(c) (x – y)(a – b)
(d) (x + y)(a – b).
Answer
Answer: (a) (x – y)(a + b)
Hint:
ax + bx – ay – by
= x(a + b) – y(a + b)
= (x – y)(a + b).
Question 28.
The factorisation of ab – a – b + 1 is
(a) (a – 1)(b – 1)
(b) (a + 1)(b + 1)
(c) (a – 1)(b + 1)
(d) (a + 1)(b – 1).
Answer
Answer: (a) (a – 1)(b – 1)
Hint:
ab – a – b + 1
= a(b – 1) – 1(b – 1)
= (a – 1)(b – 1).
Question 29.
The factorisation of
x2 + x + xy + y + zx + z is
(a) (x + y + z)(x + 1)
(b) (x + y + z)(x + y)
(c) (x + y + z)(y + z)
(d) (x + y + z)(z + x).
Answer
Answer: (a) (x + y + z)(x + 1)
Hint:
x² + x + xy + y + zx + z
= x(x + 1) + y(x + 1) + z(x + 1)
= (x + 1)(x + y + z).
Question 30.
The factorisation of x2y2 + xy + xy2z + yz + x2yz + xz is
(a) (xy + yz + zx)(xy + 1)
(b) (xy + yz + zx)(yz + 1)
(c) (xy + yz + zx)(zx + 1)
(d) none of these.
Answer
Answer: (a) (xy + yz + zx)(xy + 1)
Hint:
x²y² + xy + xy²z + yz + x²yz + xz
= xy(xy + 1) + yz(xy + 1) + zx(xy + 1)
= (xy + yz + zx)(xy + 1).
Question 31.
The factorisation of x2 + 8x + 16 is
(a) (x + 2)2
(b) (x + 4)2
(c) (x – 2)2
(d) (x – A)2
Answer
Answer: (b) (x + 4)2
Hint:
x² + 8x + 16
= (x)² + 2 (x)(4) + (4)²
= (x + 4)².
Question 32.
The factorisation of 4y2 – 12y + 9 is
(a) (2y + 3)2
(b) (2y – 3)2
(c) (3y + 2)2
(d) (3y – 2)2
Answer
Answer: (b) (2y – 3)2
Hint:
4y² – 12y + 9
= (2y)² – 2(2y)(3) + (3)²
= (2y – 3)²
Question 33.
The factorisation of 49p2 – 36 is
(a) (7p + 6)(7p – 6)
(b) (6p + 7)(6p – 7)
(c) (7p + 6)2
(d) (7p – 6)2
Answer
Answer: (a) (7p + 6)(7p – 6)
Hint:
49p² – 36
= (7p)² – (6)² = (7p – 6)(7p + 6).
Question 34.
The factorisation of y2 – 7y + 12 is
(a) (y + 3)(y + 4)
(b) (y + 3)(y – 4)
(c) (y – 3)(y + 4)
(d) (y – 3)(y – 4).
Answer
Answer: (d) (y – 3)(y – 4)
Hint:
y² – 7y + 12
= y² – 3y – 4y + 12
= y(y – 3) – 4(y – 3)
= (y – 3)(y – 4).
Question 35.
The factorisation of z2 – 4z – 12 is
(a) (z + 6)(z + 2)
(b) (z – 6)(z – 2)
(c) (z – 6)(z + 2)
(d) (z + 6)(z – 2).
Answer
Answer: (c) (z – 6)(z + 2)
Hint:
z³ – 4z – 12
= z² – 6z + 2z — 12
= z(z – 6) + 2(z – 6)
= (z – 6)(z + 2).
Question 36.
The factorisation of am2 + bm2 + bn2 + an2 is
(a) (a + b)(m2 – n2)
(b) (a + b)(m2 + n2)
(c) (a – b)(m2 + n2)
(d) (a – b)(m2 – n2).
Answer
Answer: (b) (a + b)(m2 + n2)
Hint:
am² + bm² + bn² + an²
= m²(a + b) + n²(b + a)
= (a + b)(m² + n²).
Question 37.
The factorisation of (lm + l) + m + 1 is
(a) (l + 1)(m + 1)
(6) (l – 1)(m – 1)
(c) (l + 1)(m – 1)
(d) (l – 1)(m + 1).
Answer
Answer: (a) (l + 1)(m + 1)
Hint:
lm + l + m + 1
= l(m + 1) + 1 (m + 1)
= (l + 1 )(m + 1).
Question 38.
The factorisation of (l + m)2 – 4lm is
(a) (l – m)2
(b) (l + m – 2)2
(c) (l + m + 2)2
(d) none of these.
Answer
Answer: (a) (l – m)2
Hint:
(1 + m)² – 4lm
= l² + m² + 2lm – 4lm
= l² – 2lm + m² = (l – m)²
Question 39.
The factorisation of
1 + p + q + r + pq + qr + pr + pqr is
(a) (1 + p)(1 + q)(1 + r)
(b) (1 – p)(1 – q)(1 – r)
(c) (1 – p)(1 – q)(1 + r)
(d) (1 + p)(1 – q)(1 – r).
Answer
Answer: (a) (1 + p)(1 + q)(1 + r)
Hint:
1 + p + q + r + pq + qr+pr + pqr
= 1 + p + q + pq + r(1 + p + q + pq)
= (1 + r)(1 + p + q + pq)
= (1 + r)(1 + p)(1 + q).
Question 40.
The value of
0.645 × 0.645 + 2 × 0.645 × 0.355 + 0.355 × 0.355 is
(a) 1
(b) 0
(c) -1
(d) 2.
Answer
Answer: (a) 1
Hint:
Value = (0.645 + 0.355)² = (1)² = 1.
Question 41.
The factorisation 1 + 16x + 64x² is
(a) (1 – 8x)2
(b) (1 + 8x)2
(c) (8 – x)2
(d) (8 + x)2
Answer
Answer: (b) (1 + 8x)2
Hint:
1 + 16x + 64x²
= (1)2 + 2(1) (8x) + (8x)² = (1 + 8x)²
Question 42.
The factorisation x2 + x + \(\frac{1}{4}\) is
(a) (\(\frac{x}{2}\) – 1)²
(b) (\(\frac{x}{2}\) + 1)²
(c) (x + \(\frac{1}{2}\))²
(d) (x – \(\frac{1}{2}\))²
Answer
Answer: (c) (x + \(\frac{1}{2}\))²
Hint:
x² + x + \(\frac{1}{4}\) = x² + 2(x)(\(\frac{1}{2}\)) + (\(\frac{1}{2}\))2
= (x + \(\frac{1}{2}\))2
Question 43.
The value of 992 is
(a) (90)2 + 2(90)(9) + (9)2
(b) (90)2 – 2(90)(9) + (9)2
(c) (90)2 + (9)2
(d) none of these.
Answer
Answer: (a) (90)2 + 2(90)(9) + (9)2
Hint:
99² = (90 + 9)²
= (90)² + 2(90)(9) + (9)²
Question 44.
The value of 492 is
(a) (50)2 – 2(50)(1) + (1)2
(b) (50)2 + 2 (50) (1) + (1)2
(c) (50)2 – (1)2
(d) (50)2 + (1)2
Answer
Answer: (a) (50)2 – 2(50)(1) + (1)2
Hint:
49² = (50 – 1)²
= (50)² – 2(50)(1) + (1)²
Question 45.
The factorisation of (\(\frac{x^2}{y^2}\) -2+\(\frac{y^2}{x^2}\)) x ≠ 0, y ≠ 0 is
(a) (\(\frac{x}{y}\)+\(\frac{y}{x}\))2
(b) (\(\frac{x}{y}\)–\(\frac{y}{x}\))2
(c) (\(\frac{x}{y}\)-1)2
(d) (\(\frac{x}{y}\)+1)2
Answer
Answer: (b) (\(\frac{x}{y}\)–\(\frac{y}{x}\))2
Hint:
\(\frac{x^2}{y^2}\) – 2 + \(\frac{y^2}{x^2}\)
= (\(\frac{x}{y}\))2 – 2(\(\frac{x}{y}\))(\(\frac{y}{x}\)) + (\(\frac{y}{x}\))2
= (\(\frac{x}{y}\) – \(\frac{y}{x}\))2
Question 46.
The value of \(\frac{0.73×0.73×-0.27×0.27}{0.73-0.27}\) is
(a) 1
(b) 0
(c) 0.73
(d) 0.27.
Answer
Answer: (a) 1
Hint:
Value = \(\frac{(0.73+0.27)(0.73-0.27)}{0.73-0.27}\) = 1
Question 47.
The factorisation of x2 – 9 is
(a) (x – 3)2
(b) (x + 3)2
(c) (x + 3)(x – 3)
(d) none of these.
Answer
Answer: (c) (x + 3)(x – 3)
Hint:
x² – 9 = (x)² – (3)² = (x – 3) (x + 3).
Question 48.
The factorisation of 36x2y2 – 1 is
(a) (6xy – 1)(6xy + 1)
(b) (6xy – 1)2
(c) (6xy + 1)2
(d) (6 + xy)2
Answer
Answer: (a) (6xy – 1)(6xy + 1)
Hint:
36x²y² – 1 = (6xy)² – (1)²
= (6xy – 1)(6xy + 1).
Question 49.
The value of \(\frac{0.564×0.564×-0.436×0.436}{0.564-0.436}\) is
(a) 0
(b) 1
(c) -1
(d) none of these.
Answer
Answer: (b) 1
Hint:
Value = \(\frac{(0.564+0.436)(0.564-0.436)}{0.564-0.436}\) = 1
Question 50.
The value of (0.68)2 – (0.32)2 is
(a) -1
(b) 0
(c) 1
(d) 0.36.
Answer
Answer: (d) 0.36.
Hint:
Value = (0.68 + 0.32) (0.68 – 0.32) = 0.36.
Question 51.
The factorisation of 3x² + 10x + 8 is
(a) (3x + 4)(x + 2)
(b) (3x – 4)(x – 2)
(c) (3x + 4)(x – 2)
(d) (3x – 4)(x + 2).
Answer
Answer: (a) (3x + 4)(x + 2)
Hint:
3x² + 10x + 8 = 3x² + 6x + 4x + 8
= 3x(x + 2) + 4(x + 2)
= (x + 2)(3x + 4).
Question 52.
The factorisation of 3x2 – 16x + 16 is
(a) (x – 4)(3x – 4)
(b) (x + 4)(3x + 4)
(c) (x – 4)(3x + 4)
(d) (x + 4)(3x – 4).
Answer
Answer: (a) (x – 4)(3x – 4)
Hint:
3x² – 16x + 16
= 3x² – 12x – 4x + 16
= 3x(x – 4) – 4(x – 4)
= (x – 4) (3x – 4).
Question 53.
The factorisation of 6x2 – 5x – 6 is
(a) (2x – 3)(3x + 2)
(b) (2x + 3)(3x + 2)
(c) (2x – 3)(3x – 2)
(d) (2x + 3)(3x – 2).
Answer
Answer: (a) (2x – 3)(3x + 2)
Hint:
6x² – 5x – 6
= 6x² – 9x + 4x – 6
= 3x(2x – 3) + 2(2x – 3)
= (2x – 3)(3x + 2).
Question 54.
The factorisation of 6 – x – 2x2 is
(a) (2 + x)(3 – 2x)
(b) (2 + x)(3 + 2x)
(c) (2 – x)(3 – 2x)
(d) (2 – x)(3 + 2x).
Answer
Answer: (a) (2 + x)(3 – 2x)
Hint:
6 – x – 2x²
= 6 + 3x – 4x – 2x²
= 3(2 + x) – 2x (2 + x)
= (2 + x)(3 – 2x).
Question 55.
If x2 – x – 42 = (x + k)(x + 6), then k =
(a) 6
(b) -6
(c) 7
(d) -7.
Answer
Answer: (d) -7
Hint:
x² – x – 42
= x² – 7x + 6x – 42
= x(x – 7) + 6(x – 7)
= (x – 7)(x + 6) ∴ k = – 7.
Question 56.
The value of 3.5 × 3.5 – 2.5 × 2.5 is
(a) -6
(b) 6
(c) 60
(d) 1.
Answer
Answer: (b) 6
Hint:
Value = (3.5 + 2.5)(3.5 – 2.5) = 6.
Question 57.
If (x – \(\frac{1}{x}\))² = x² + a + \(\frac{1}{x^2}\) then a =
(a) -2
(b) 2
(c) 2x
(d) -2x
Answer
Answer: (a) -2
Hint:
(x – \(\frac{1}{x}\))2 = x² – 2 + \(\frac{1}{x^2}\) ∴ a = -2.
Question 58.
If x = 2, y = -1 then the value of x² -+ 4xy + 4y² is
(a) 0
(b) 1
(c) -1
(d) 2
Answer
Answer: (a) 0
Hint:
x² + 4xy + 4y² = (x)² + 2(x)(2y) + (2y)²
= (x + 2y)² = {2 + 2(- 1)}² = 0.
Question 59.
The quotient of 28x² + 14x is
(a) 2
(b) 2x
(c) x
(d) x²
Answer
Answer: (b) 2x
Hint:
\(\frac{28x^21}{14x}\) = \(\frac{2×2×7×x×x}{2×7×x}\) = 2x
Question 60.
The quotient of 12a8b8 + (- a6b6) is
(a) 3a2b2
(6) 3a2b
(c) 3ab2
(d) -3a2b2
Answer
Answer: (d) -3a2b2
Hint:
= -3a²b²
Question 61.
The factorisation of 12a2b +15ab2 gives:
(a) 3ab(4ab + 5)
(b) 3ab(4a + 5(b)
(c) 3a(4a + 5(b)
(d) 3b(4a + 5(b)
Answer
Answer: (b) 3ab(4a + 5(b)
Hint:
12a2b+15ab2
12a2b = 3 x 4 x a x a x b
15ab2 = 3 x 5 x a x b x b
The common factors are 3ab.
12a2b + 15ab2 = 3ab(4a +5b)
Question 62.
The factorisation of 12x + 36 is
(a) 12(x + 3)
(b) 12(3x)
(c) 12(3x + 1)
(d) x(12 + 36x)
Answer
Answer: (a) 12(x + 3)
Hint:
12x + 36
12 x + 12 . 3
= 12(x + 3)
Question 63.
On factorising 14pq + 35pqr, we get:
(a) pq(14 + 35r)
(b) p(14q + 35qr)
(c) q(14p + 35pr)
(d) 7pq(2 + 5r)
Answer
Answer: (d) 7pq(2 + 5r)
Hint:
14pq + 35pqr
= 2.7.p.q + 5.7.p.q.r
= 7pq(2 + 5r)
Question 64.
The factors of 6xy – 4y + 6 – 9x are:
(a) (3x + 2) (2y + 3)
(b) (3x – 2) (2y – 3)
(c) (3x – 2) (2y + 3)
(d) (3x + 2) (2y – 3)
Answer
Answer: (b) (3x – 2) (2y – 3)
Hint:
6xy – 4y + 6 – 9x
= 6xy – 4y – 9x + 6
= 2y (3x – 2) – 3 (3x – 2)
= (3x – 2) (2y – 3)
Question 65.
The factors of x2 + xy + 8x + 8y are:
(a) (x +y) (x + 8)
(b) (2x + y) (x + 8)
(c) (x + 2y) (x + 8)
(d) (x + y) (2x + 8)
Answer
Answer: (a) (x +y) (x + 8)
Hint:
x2 + xy + 8x + 8y
= x(x + y) + 8(x + y)
=(x + y)(x + 8)
Question 66.
The factors of 4y2 – 12y + 9 is:
(a) (2y + 3)2
(b) (2y – 3)2
(c) (2y – 3)(2y + 3)
(d) None of the above
Answer
Answer: (b) (2y-3)2
Hint:
4y2 – 12y + 9
4y2 = (2y)2 & 9 = 32 & 12y = 2.3.2y
4y2 – 12y + 9 = (2y)2 – 2 × 3 × (2y) + (3)2
= (2y – 3)2 [By algebraic identities: (a-(b)2 = a2+b2-2ab
Question 67.
The factors of 49p2 – 36 are:
(a) (7p + 6)2
(b) (7p – 6)2
(c) (7p – 6 ) ( 7p + 6)
(d) None of the above
Answer
Answer: (c) (7p – 6 ) ( 7p + 6)
Hint:
49p2 – 36 = (7p)2 – ( 6 )2 = (7p – 6 ) ( 7p + 6)
Question 68.
The factors of m2 – 256 are:
(a) (m + 4)2
(b) (m – 4)2
(c) (m – 4) (m+4)
(d) None of the above
Answer
Answer: (d) None of the above
Hint:
m4 = (m2)2 and 256 = (16)2
m4 – 256 = (m2)2 – (16)2 = (m2 – 16) (m2 + 16)
m2 – 16 = m2 – 42 = (m – 4) (m + 4)
m4 – 256 = (m – 4) (m + 4) (m2 + 16)
Question 69.
When we factorise x2 + 5x + 6, then we get:
(a) (x + 2) (x + 3)
(b) (x – 2) (x – 3)
(c) (x × 2) + (x × 3)
(d) (x × 2) – (x × 3)
Answer
Answer: (a) (x + 2) (x + 3)
Hint:
The factors of a form:
(x + (a) (x + (b) = x2 + (a + (b) x + ab
x2 + 5x + 6
a + b = 5 and ab = 6
x2 + 5x+6 = (x + 2) (x + 3)
Question 70.
The factors of 3m2 + 9m + 6 are:
(a) (m + 1) (m + 2)
(b) 3(m + 1) (m + 2)
(c) 6(m + 1) (m + 2)
(d) 9(m + 1) (m + 2)
Answer
Answer: (b) 3(m + 1) (m + 2)
Hint:
3m2 + 9m + 6 = 3(m2 + 3m + 2)
= 3 [m2 + m + 2m + 2]
= 3 [m(m + 1)+ 2( m + 1)]
= 3 [(m + 1) (m + 2)]
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