Check whether p(x) is a multiple of g(x) or not : p(x)=x^{3}-5 x^{2}+4 x-3, quad g(x)=x-2

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2. Polynomials

easy

Check whether $p(x)$ is a multiple of $g(x)$ or not :

$p(x)=x^{3}-5 x^{2}+4 x-3, \quad g(x)=x-2$

Option A

Option B

Option C

Option D

Solution

$p ( x )$ will be a multiple $g ( x )$ if $g ( x )$ divides $p ( x )$

Now, $g(x)=x-2$ gives $x=2$

Remainder $=p(2)=(2)^{3}-5(2)^{2}+4(2)-3$

$=8-5(4)+8-3=8-20+8-3$

$=-7$

since remainder $\neq 0,$

So $p ( x )$ is not a multiple of $g ( x )$

Standard 9

Mathematics

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