Q5 of 64 Page 30

Examine the validity of the following statements:

(x + 1) is a factor of p(x) = 3x3 + 2x2 + 7 x + 8

Given, p(x) = 3x3 + 2x2 + 7 x + 8


For (x + 1) to be a factor of p(x), the condition: p(–1) = 0; should be satisfied.


p(–1) = 3(–1)3 + 2(–1)2 + 7(–1) + 8


= 3(–1) + 2(1) + 7(–1) + 8


= –3 + 2 – 7 + 8


= 0


Thus, (x + 1) is a factor of the given polynomial.


⇒ The given statement is valid.


More from this chapter

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3

Find the coefficients of the underlined terms:

(1) p(x) = 10x3+ 7 x2 — 3x + 5


(2) p(x) = 7 — 5x5+ 3x4 + x2 — x


(3) p(x) = 25 — 125x


(4) p(x) = x3 — x2 + x + 7

 4

Obtain the value of the following polynomials at the given values of x:

(1) p(x) = 2x3 + 3x2 + 7x + 9 ; at x = 0, 1


(2) p(x) = 3x2 + 10x + 7 ; at x = —3, 1


(3) p(x) = x2 — 2x + 5 ; at x = —1, 5


(4) p(x) = 2x4 — 3x3 + 7x + 5 ; at x = —2, 2

 5

Examine the validity of the following statements:

(x + 2) is a factor of p(x) = x3 + x2 + x + 2

 5

Examine the validity of the following statements:

(x — 1) is a factor of p(x) = x4 — 2x3 + 3x —2