Question

Show that (x-4) is factor of 5x

3

-7x2

-45x-28, hence factorize it.
​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Polynomial is}$

$\mathsf{5x^3-7x^2-45x-28}$

$\underline{\textsf{To find:}}$

$\textsf{(x-4) is a factor of the given polynomial}$

$\underline{\textsf{Solution:}}$

$\textsf{Let}\;\mathsf{P(x)=5x^3-7x^2-45x-28}$

$\textsf{Put x=4}$

$\mathsf{P(4)=5(4)^3-7(4)^2-45(4)-28}$

$\mathsf{P(4)=5(64)-7(16)-45(4)-28}$

$\mathsf{P(4)=320-112-180-28}$

$\mathsf{P(4)=320-320=0}$

$\textsf{By factor theorem}$

$\therefore\textsf{(x-4) is a factor of P(x)}$

$\textsf{By Synthetic division, we get}$

$\begin{array}{r|cccc}4&5&-7&-45&-28\\&&20&52&28\\\cline{2-5}&5&13&7&\boxed{0}\end{array}$

$\implies\mathsf{5x^3-7x^2-45x-28=(x-4)(5x^2+13x+7)}$

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