Q5 of 64 Page 30

Examine the validity of the following statements:

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

Given, p(x) = x3 + x2 + x + 2


For (x + 2) to be a factor of p(x), the condition: p(–2) = 0; should be satisfied.


p(–2) = (–2)3 + (–2)2 + (–2) + 2


= (–8) + (4) + (–2) + 2


= – 8 + 4 – 2 + 2


= –4 ≠ 0


Thus, (x + 2) is not a factor of the given polynomial.


⇒ The given statement is invalid.


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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

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Examine the validity of the following statements:

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

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Examine the validity of the following statements:

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

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Examine the validity of the following statements:

(x — 3) is a factor of p(x) = x2 — 2x — 3