Polynomials | Class 9 | Practice Set 3.5

Polynomials | Class 9 | Practice Set 3.5

Polynomials | Class 9 | Practice Set 3.5, examples like deciding whether a divisor is a root of the given polynomial or not are solved in the article.

Practice-Set-3.5

The solutions of all the examples of this practice set are based on the following topics –

(1) Finding the value of a polynomial like P(2), P(3) and P(-2).

Also read : Sets | Class 9 | Practice Set 1.3

(2) Deciding whether the polynomial q(x) is a factor of the polynomial p(x).

(3) Finding the remainder using the remainder theorem.

(4) Use of factor theorem while deciding the factor of a polynomial.

(5) Finding the value of a given polynomial for different values of the variable.

The examples solved in this article are listed below –

Class 9 | Practice Set 3.5

(1) Find the value of the polynomial 2x – 2×3 + 7 using given values for x.
(i) x = 3 (ii) x = – 1 (iii) x = 0

(2) For each of the following polynomial, find p(1), p(0) and p(- 2).
(i) p(x) = x3 (ii) p(y) = y2 + 2y + 5 (iii) p(x) = x4 – 2×2 – x

(3) If the value of the polynomial m3 + 2m + a is 12 for m = 2, then find the value of a.

Also read : Sets | Class 9 | Practice Set 1.4

(4) For the polynomial mx2 -2x + 3 if p(- 1) = 7 then find m.

(5) Divide the first polynomial by the second polynomial and find the remainder using
remainder theorem.
(i) (x2 + 7x + 9) ; (x + 1) (ii) (2×3 – 2×2 + ax – a) ; (x – a) (iii) (54m3 + 18m2 + 27m + 5) ; (m – 3)

(6) If the polynomial y3 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.

(7) Use factor theorem to determine whether x + 3 is factor of x2 + 2x – 3 or not.

(8) If (x – 2) is a factor of x3 + mx2 + 10x – 20 then find the value of m.

(9) By using factor theorem in the following examples, determine whether q(x) is a factor p(x) or not.
(i) p(x) = x3 – x2 – x – 1, q(x) = x – 1
(ii) p(x) = 2×3 – x2 – 45, q(x) = x – 3

(10) If (x31 + 31) is divided by (x + 1) then find the remainder.

(11) Show that m – 1 is a factor of m21 – 1 and m22 – 1.

(12) If x – 2 and x – 1/2 both are the factors of the polynomial nx2 – 5x + m, then show that m = n = 2

(13) (i) If p(x) = 2 + 5x then p(2) + p(- 2) – p(1). (ii) If p(x) = 2×2 + under root 3 x + 5 then p(5 under root 3 )