Q4 of 86 Page 32

Classify the following as linear, quadratic and cubic polynomials

(i) 5x2 + x - 7 (ii) x - x3


(iii) x2 + x + 4 (iv) x - 1


(v) 3p (vi) πr2

(i) A quadratic polynomial is a polynomial of degree 2


∵ the degree of 5x2 + x – 7 is 2


∴ 5x2 + x – 7 is a quadratic polynomial.


(ii) A cubic polynomial is a polynomial of degree 3


∵ the degree of 5x2 + x – 7 is 3


∴ 5x2 + x – 7 is a cubic polynomial.


(iii) A quadratic polynomial is a polynomial of degree 2


∵ the degree of x2 + x + 4 is 2


∴ x2 + x + 4 is a quadratic polynomial.


(iv) A linear polynomial is a polynomial of degree 1


∵ the degree of x – 1 is 1


∴ x – 1 is a linear polynomial.


(v) A linear polynomial is a polynomial of degree 1


∵ the degree of 3p is 1


∴ 3p is a linear polynomial.


(vi) A quadratic polynomial is a polynomial of degree 2


∵ the degree of πr2 is 2


∴ πr2 is a quadratic polynomial.


More from this chapter

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2

Which of the following expressions are polynomials in one variable and which are not? Give reasons for your answer.

(i) 3x2 - 2x + 5


(ii) x2 + √2


(iii) p2 - 3p + q


(iv)


(v)


(vi) x100 + y100

3

Write the coefficient of x3 in each of the following

(i) x3 + x + 1 (ii) 2 - x3 + x2


(iii) (iv) 2x3 + 5


(v) (vi)


(vii) 2x2 + 5 (vi) 4

 5

Write whether the following statements are True or False. Justify your answer

(i) A binomial can have at the most two terms


(ii) Every polynomial is a binomial


(iii) A binomial may have degree 3


(iv) Degree of zero polynomial is zero


(v) The degree of x2 + 2xy + y2 is 2


(vi) πr2 is monomial.

 6

Give one example each of a monomial and trinomial of degree 10.