‘(x-1) is a factor of 4×3+3×2-4x-3’.State true or false.

# $\text{'}\left(x-1\right)$ is a factor of $4{x}^{3}+3{x}^{2}-4x-3$’.State true or false.

1. A
true
2. B
false

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### Solution:

The given expression is $4{x}^{3}+3{x}^{2}-4x-3.$
We know that the factor theorem states, if $f\left(x\right)$ is a polynomial of degree $n\ge 1$ and a be a real number,then $\left(x-a\right)$ is a factor of $f\left(x\right)$ , if $f\left(a\right)=0$.
Let $\left(x-1\right)$ is the factor of a given polynomial.

$⇒x=1$
Checking whether the value of x satisfies the given polynomial or not.
Therefore, substituting the values of x in the given polynomial, we get,
At $x=1,$
$f\left(2\right)=4{\left(1\right)}^{3}+3{\left(1\right)}^{2}-4\left(2\right)-3$
$=4+3-4-3$
$f\left(1\right)=0$
Clearly, this value of x satisfies the given polynomial.
Hence, $\left(x-1\right)$ is the factor of a given polynomial.
Therefore, the given statement is true i.e, $\text{'}\left(x-1\right)$ is a factor of $4{x}^{3}+3{x}^{2}-4x-3$.
Hence, option 1 is  correct.

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