RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1

Other Exercises

Question 1.
Write the degree of each of the following polynomials :
(i) 2x³+5x²-7
(ii) 5x² – 3x +7 ’
(iii) 2x + x² –-8
(iv) \(\frac { 1 }{ 2 }\) y⁷ -12y⁵ + 48y⁶ – 10
(v) 3x³ + 1
(vi) 5
(vii) 20x³ + 12x²y²– 10y² + 20
Solution:
(i) 2x³ + 5x²-7: The degree of this polynomial is 3.
(ii) 5x² – 3x + 2 : The degree of this polynomial is 2.
(iii) 2x + x² – 8 : The degree of this polynomial is 2.
(iv) \(\frac { 1 }{ 2 }\) y⁷ – 12y⁶ + 48y⁵ – 10 : The degree of this polynomial is 7.
(v) 3x³ + 1 : The degree of this polynomial is 3.
(vi) 5 : The degree of this polynomial is 0 as it is only constant term
(vii) 20x³ + 12x²y² – 10y² + 20: The degree of this polynomial is 2 + 2 = 4.

Question 2.
Which of the following expressions are not polynomials :
(i) x² + 2x²
(ii) √a x + x²-x³(iii) 3y³ – √5y + 9
(iv) ax^1/2+ ax + 9x² + 4
(v) 3x² + 2x^-1 + 4x + 5
Solution:
(i) x² + 2x^-2 = x² + 2x \(\frac { 1 }{ { x }^{ 2 } }\) =x² + \(\frac { 1 }{ { x }^{ 2 } }\)
: It is not xx polynomial as it has negative integral power.
(ii) √ax + x² – x³: It is polynomial.
(iii) 3y³ √5y + 9 : It is a polynomial.
(iv) ax^1/2+ ax + 9x² + 4: It is not a polynomial as the degree of \(\frac { 1 }{ { x }^{ 2 } }\) is an integer.
(v) 3x² + 2x^-1 + 4x + 5 : It is not a polynomial as the degree of x^–², x^-1 are negative.

Question 3.
Write each of the following polynomials in the standard form. Also write their degree.
(i) x² + 3 + 6x + 5x⁴
(ii) a¹ + 4 + 5a⁶(iii) (x³ – 1) (x³ – 4)
(iv) (y³ – 2) (y³ + 11)
(v) \(\left( { a }^{ 3 }-\frac { 3 }{ 8 } \right)\) \(\left( { a }^{ 3 }-\frac { 16 }{ 17 } \right)\)
(vi) \(\left( { a }+\frac { 3 }{ 4 } \right)\) \(\left( { a }+\frac { 3 }{ 4 } \right)\)
Solution:
Polynomial in standard form is the polynomial in ascending order or descending order.
RD Sharma Class 8 Solutions Chapter 8 Division of Algebraic Expressions Ex 8.1 1

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