Can we divide $(4 x^{4} - 5 x^{3} - 7 x + 1)$ by $(4 x - 1)$ ?

True

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False

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Solution

The correct option is B False
Solution:-
$(4 x^{4} - 5 x^{3} - 7 x + 1) \div (4 x - 1)$
Let $4 x - 1 = 0$
$\Rightarrow x = \frac{1}{4}$
Substituting the value of x in equation $4 x^{4} - 5 x^{3} - 7 x + 1 = 0$
$4 {(\frac{1}{4})}^{4} - 5 {(\frac{1}{4})}^{3} - 7 (\frac{1}{4}) + 1 = 0$
$\Rightarrow - \frac{13}{16} \neq 0$
Since $(4 x - 1)$ is not a zero of polynomial $4 x^{4} - 5 x^{3} - 7 x + 1$ , hence it cannot divide the given equation.

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