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Remainder Theorem

When px=x4+2x...

Question

When $p (x) = x^{4} + 2 x^{3} - 3 x^{2} + x - 1$ is divided by (x-2), the remainder is
(a) 0
(b) -1
(c) -15
(d) 21

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Solution

ANSWER:
(d) 21
x-2=0⇒x=2
By the remainder theorem, we know that when p(x) is divided by ( x - 2), the remainder is p(2).
Thus, we have:
$p (2) = 2^{4} + 2 \times 2^{3} - 3 \times 2^{2} + 2 - 1 = 16 + 16 - 12 + 1 = 21$

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Q. When p(x) = x³ + ax² + 2x + a is divided by (x + a), the remainder is
(a) 0
(b) −1
(c) −15
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Q. When p(x) = x³ − 3x² + 4x + 32 is divided by (x + 2), the remainder is
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x^{4} + 2 x^{3} - 3 x^{2} + x - 1

x - 2

. then the remainder is

Q. The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by

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19

.
Find the value of

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Q. Question 2
The polynomial

p (x) = x^{4} - 2 x^{3} + 3 x^{2} - a x + 3 a - 7

when divided by x + 1 leaves the remainder 19. Find the value of a. Also , find the remainder when p(x) is divided by x + 2.

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