Using remainder theorem- find the remainder when-3 x4-5 x2-9 x-8 is divided by x-3

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

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(3x⁴ − 5x² + 9x − 8) is divided by (x − 3)

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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:
$f (x) = (3 x^{4} - 6 x^{2} - 8 x + 2) ∴ f (2) = (3 \times 2^{4} - 6 \times 2^{2} - 8 \times 2 + 2) = (48 - 24 - 16 + 2) = 10$
Hence, the required remainder is 10.

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Using remainder theorem, find the remainder when: (3x4 − 5x2 + 9x − 8) is divided by (x − 3)

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=3x4-6x2-8x+2∴ f2=3×24-6×22-8×2+2 =48-24-16+2 =10 ​Hence, the required remainder is 10.

Using remainder theorem, find the remainder when:
(3x⁴ − 5x² + 9x − 8) is divided by (x − 3)