Figuring out the remainder

The remainder of the division of a polynomial $P(x)$ by $x-1$ is 6, and the remainder of the division of $P (x)$ by $x + 2$ is 4.Then the remainder of the division of $P (x)$ by $(x-1 ) (x + 2)$ is:

(a): $R (x) = 2x / 3 + 16/3$ .

(b): $R (x) = 2x / 3 - 16/3$ .

(c): $R (x) = 2x / 3 + 8/3$ .

#Algebra

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
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Comments

Consder P(x)=(x-1)(x+2)Q(x)+ax+b;P(1)=6=>a+b=6;P(-2)=4=>-2a+b=4.solve for a,b giving option (a) as remainder.

Deepak Kumar - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$