Using remainder theorem- find the remainder when-x3-6 x2-9 x-3 is divided by x-1

We know: x 1=0 #8658;x=1 By the remainder theorem, we know that when nbsp;f(x) is divided by (x nbsp; 1), the remainder is nbsp;f(1). Thus, we have: fx ...

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(x³ − 6x² + 9x + 3) is divided by (x − 1)

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Solution

We know:
$x - 1 = 0 \Rightarrow x = 1$
By the remainder theorem, we know that when f(x) is divided by (x $-$ 1), the remainder is f(1).
Thus, we have:
$f (x) = (x^{3} - 6 x^{2} + 9 x + 3) ∴ f (1) = (1^{3} - 6 \times 1^{2} + 9 \times 1 + 3) = (1 - 6 + 9 + 3) = 7$
Hence, the required remainder is 7.

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Using remainder theorem, find the remainder when: (x3 − 6x2 + 9x + 3) is divided by (x − 1)

We know: x-1=0⇒x=1 By the remainder theorem, we know that when f(x) is divided by (x - 1), the remainder is f(1). Thus, we have: fx=x3-6x2+9x+3∴ f1=13-6×12+9×1+3 =1-6+9+3 =7 Hence, the required remainder is 7.

Using remainder theorem, find the remainder when:
(x³ − 6x² + 9x + 3) is divided by (x − 1)