(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Su

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(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Substituting $x = 1$ into the polynomial:$p(1) = (1)^{2} + 1 + k$$p(1) = 1 + 1 + k$$p(1) = 2 + k$Since $p(1) = 0$,we have:$2 + k = 0$$k = -2$

Class 9 Mathematics Polynomials Factorisation of Polynomials

Medium

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

A
$0$
B
$3$
C
$2$
D
$-2$

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Factorisation of Polynomials

Factorise: $6x^2 + 5x - 6$

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

Similar Questions

Factorise: $6x^2 + 5x - 6$

From the following polynomials,find out which of them has $(x-1)$ as a factor:$x^{3}+4x^{2}+x-6$

Determine whether $(x+1)$ is a factor of the polynomial $p(x) = x^{3} - 2x^{2} - 5x + 6$.

With the help of the remainder theorem,examine whether $x+2$ is a factor of the polynomial $x^{3}+9x^{2}+26x+24$ or not.

Is $x+1$ a factor of $4x^3 + 7x^2 - 2x - 5$ or not?

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From the following polynomials,find out which of them has $(x-1)$ as a factor:
$x^{3}+4x^{2}+x-6$