When px-x3-3 x2-4 x-32 is divided by x-2- the remainder isa 0b 32c 36d 4

(d) 4 x+2=0 #8658;x= 2 By the remainder theorem, we know that when nbsp;p(x) is divided by (x + 2), the remainder is nbsp;p( 2). Now, we have: p 2= 23 3 ...

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Byju's Answer

Standard IX

Mathematics

Remainder Theorem

When px=x3-3 ...

Question

When p(x) = x³ − 3x² + 4x + 32 is divided by (x + 2), the remainder is
(a) 0
(b) 32
(c) 36
(d) 4

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Solution

(d) 4

$x + 2 = 0 \Rightarrow x = - 2$
By the remainder theorem, we know that when p(x) is divided by (x + 2), the remainder is p( $-$ 2).
Now, we have:
$p (- 2) = {(- 2)}^{3} - 3 \times {(- 2)}^{2} + 4 \times (- 2) + 32 = - 8 - 12 - 8 + 32 = 4$

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When p(x) = x3 − 3x2 + 4x + 32 is divided by (x + 2), the remainder is (a) 0 (b) 32 (c) 36 (d) 4

(d) 4 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). Now, we have: p-2=-23-3×-22+4×-2+32 =-8-12-8+32 =4

When p(x) = x³ − 3x² + 4x + 32 is divided by (x + 2), the remainder is
(a) 0
(b) 32
(c) 36
(d) 4

(d) 4

$x + 2 = 0 \Rightarrow x = - 2$
By the remainder theorem, we know that when p(x) is divided by (x + 2), the remainder is p( $-$ 2).
Now, we have:
$p (- 2) = {(- 2)}^{3} - 3 \times {(- 2)}^{2} + 4 \times (- 2) + 32 = - 8 - 12 - 8 + 32 = 4$