Using remainder theorem- find the remainder when-x3-7 x2-6 x-4 is divided by x-6

We have: x 6=0 #8658;x=6 By the remainder theorem, we know that when nbsp;f(x) is divided by (x 6), the remainder is nbsp;f(6). Thus, we have: fx=x3 7x2 ...

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Standard IX

Mathematics

Remainder Theorem

Using remaind...

Question

Using remainder theorem, find the remainder when:
(x³ − 7x² + 6x + 4) is divided by (x − 6)

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Solution

We have:
$x - 6 = 0 \Rightarrow x = 6$
By the remainder theorem, we know that when f(x) is divided by (x $-$ 6), the remainder is f(6).
Thus, we have:
$f (x) = (x^{3} - 7 x^{2} + 6 x + 4) ∴ f (6) = (6^{3} - 7 \times 6^{2} + 6 \times 6 + 4) = (216 - 252 + 36 + 4) = 4$
Hence, the required remainder is 4.

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Using remainder theorem, find the remainder when: (x3 − 7x2 + 6x + 4) is divided by (x − 6)

We have: x-6=0⇒x=6 By the remainder theorem, we know that when f(x) is divided by (x - 6), the remainder is f(6). Thus, we have: fx=x3-7x2+6x+4∴f6=63-7×62+6×6+4 =216-252+36+4 =4 ​Hence, the required remainder is 4.

Using remainder theorem, find the remainder when:
(x³ − 7x² + 6x + 4) is divided by (x − 6)