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

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Yes

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Cannot be determined

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None of these

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Solution

The correct option is A No
Given, $p (x) = x^{3} - 5 x^{2} + 4 x - 3$ ,
$g (x) = x - 2$
$=> x - 2 = 0$
$=> x = 2$
Now, $p (2)$ should be $0$ if $p (x)$ is a multiple of $g (x)$
Thus,
$p (2) = 2^{3} - 5 (2)^{2} + 4 (2) - 3$
$= 8 - 20 + 8 - 3$
$= - 7$
$= 8 - 20 + 8 - 3$
$\neq 0$
Thus, $p (x)$ is not a multiple of $g (x)$

Suggest Corrections

Similar questions

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

p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, g (x) = 2 x + 1

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

p (x) = 2 x^{3} - 11 x^{2} - 4 x + 5, g (x) = 2 x + 1

If $p (x) = x^{3} - 5 x^{2} + 4 x - 3$ and $g (x) = x - 2$ , show that p(x) is not multiple of g(x).

Check whether p(x) = $x^{3}$ + 5 $x^{2}$ + 2x - 5 is a multiple of g(x) = x + 2.

p (x)

g (x)

p (x) = x^{3} + 27 x^{2} - 8 x + 18,

g (x) = x - 1

p (x) = 2 \sqrt{2} x^{3} - 5 \sqrt{2} x^{2} + 7 \sqrt{2}, g (x) = x + 1

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