Using remainder theorem- find the remainder when-x3-6 x2-13 x-60 is divided by x-2

We have: x+2=0 #8658;x= 2 By the remainder theorem, we know that when nbsp;f(x) is divided by (x + 2), the remainder is nbsp;f( 2). Thus, we have: #160 ...

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(x³ − 6x² + 13x + 60) is divided by (x + 2)

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Solution

We have:
$x + 2 = 0 \Rightarrow x = - 2$
By the remainder theorem, we know that when f(x) is divided by (x + 2), the remainder is f( $-$ 2).
Thus, we have:
$f (x) = (x^{3} - 6 x^{2} + 13 x + 60) ∴ f (- 2) = [{(- 2)}^{3} - 6 \times {(- 2)}^{2} + 13 \times (- 2) + 60] = (- 8 - 24 - 26 + 60) = 2$

Hence, the required remainder is 2.

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Using remainder theorem, find the remainder when: (x3 − 6x2 + 13x + 60) is divided by (x + 2)

We have: x+2=0⇒x=-2 By the remainder theorem, we know that when f(x) is divided by (x + 2), the remainder is f(-2). Thus, we have: fx=x3-6x2+13x+60∴ f-2=-23-6×-22+13×-2+60 =-8-24-26+60 =2 Hence, the required remainder is 2.

Using remainder theorem, find the remainder when:
(x³ − 6x² + 13x + 60) is divided by (x + 2)