Find the value of k, if $x – 1$ is a factor of $4x^3 + 3x^2 – 4x + k$.

Given:

$x - 1$ is a factor of $4x^3+3x^2-4x+k$.

To do:

We have to find the value of k.

Solution:

Factor Theorem:

The factor theorem states that if p(x) is a polynomial of degree n > or equal to 1 and ‘a’ is any real number, then $x-a$ is a factor of p(x) if $p(a)=0$.

Therefore,

$x-1$ is a factor of $P(x)=4x^3+3x^2-4x+k$.

$P(1) = 4x^3+3x^2-4x+k= 0$

$4(1)^3+3(1)^2-4(1)+k = 0$

$4+3-4+k=0$

$k = -3$.

The value of k is $-3$.

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Updated on: 10-Oct-2022

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