(A) According to the Factor Theorem,$g(x) = x - a$ is a factor of $p(x)$ if $p(a) = 0$.Here,$g(x) = x + 1$,which can be written as $x - (-1)$. So,$a =

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Yes,$g(x)$ is a factor of $p(x)$.

(A) According to the Factor Theorem,$g(x) = x - a$ is a factor of $p(x)$ if $p(a) = 0$.Here,$g(x) = x + 1$,which can be written as $x - (-1)$. So,$a = -1$.We evaluate $p(-1)$:$p(-1) = 2(-1)^3 + (-1)^2 - 2(-1) - 1$$p(-1) = 2(-1) + 1 + 2 - 1$$p(-1) = -2 + 1 + 2 - 1$$p(-1) = 0$Since $p(-1) = 0$,by the Factor Theorem,$g(x)$ is a factor of $p(x)$.

Class 9 Mathematics Polynomials Factorisation of Polynomials

Medium

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.

A
Yes,$g(x)$ is a factor of $p(x)$.
B
No,$g(x)$ is not a factor of $p(x)$.
C
Cannot be determined.
D
None of these.

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Polynomials

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Factorisation of Polynomials

Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = x^{2} + x + k$.

Medium

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Factorise the following:
$1-64 a^{3}-12 a+48 a^{2}$

Easy

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Determine which of the following polynomials has $(x + 1)$ as a factor: $x^{3} - x^{2} - (2 + \sqrt{2})x + \sqrt{2}$

Difficult

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$x-1$ is one of the factors of $p(x) = x^3 - 3x^2 + 7x - 5$. Which of the following is a factor of $p(x) = x^3 - 3x^2 + 7x - 5$?

Easy

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Factorise: $x^{3}+13x^{2}+32x+20$

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Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.

Similar Questions

Find the value of $k$,if $x - 1$ is a factor of $p(x)$ in this case: $p(x) = x^{2} + x + k$.

Factorise the following:$1-64 a^{3}-12 a+48 a^{2}$

Determine which of the following polynomials has $(x + 1)$ as a factor: $x^{3} - x^{2} - (2 + \sqrt{2})x + \sqrt{2}$

$x-1$ is one of the factors of $p(x) = x^3 - 3x^2 + 7x - 5$. Which of the following is a factor of $p(x) = x^3 - 3x^2 + 7x - 5$?

Factorise: $x^{3}+13x^{2}+32x+20$

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Factorise the following:
$1-64 a^{3}-12 a+48 a^{2}$