Using remainder theorem- find the remainder when-2 x4-6 x3-2 x2-x-8 is divided by x-3

We have: x+3=0 #8658;x= 3 By the remainder theorem, we know that when nbsp;f(x) is divided by (x + 3), the remainder is nbsp;f( 3). Thus, we have: fx=2x4+ ...

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(2x⁴ + 6x³ + 2x² + x − 8) is divided by (x + 3)

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Solution

We have:
$x + 3 = 0 \Rightarrow x = - 3$
By the remainder theorem, we know that when f(x) is divided by (x + 3), the remainder is f( $-$ 3).
Thus, we have:
$f (x) = (2 x^{4} + 6 x^{3} + 2 x^{2} + x - 8) ∴ f (- 3) = [2 \times {(- 3)}^{4} + 6 \times {(- 3)}^{3} + 2 \times {(- 3)}^{2} + (- 3) - 8] = (162 - 162 + 18 - 11) = 7$
Hence, the required remainder is 7.

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Similar questions

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $2 x^{4} - 6 x^{3} + 2 x^{2} - x + 2$ , g(x) = x + 2

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Q. Using remainder theorem, find the remainder when:
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Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
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Using remainder theorem, find the remainder when: (2x4 + 6x3 + 2x2 + x − 8) is divided by (x + 3)

We have: x+3=0⇒x=-3 By the remainder theorem, we know that when f(x) is divided by (x + 3), the remainder is f(-3). Thus, we have: fx=2x4+6x3+2x2+x-8∴ f-3=2×-34+6×-33+2×-32+-3-8 =162-162+18-11 =7 ​Hence, the required remainder is 7.

Using remainder theorem, find the remainder when:
(2x⁴ + 6x³ + 2x² + x − 8) is divided by (x + 3)