Question

Factorise the expressions and then divide them as directed.

( 5x^2 + 70x – 160) ÷ ( 5x – 10)​

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{5x^2+70x-160}{5x-10}}$

$\textbf{To find:}$

$\textsf{Simplified form of}\mathsf{\dfrac{5x^2+70x-160}{5x-10}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{5x^2+70x-160}{5x-10}}$

$\mathsf{=\dfrac{5(x^2+14x-32)}{5(x-2)}}$

$\mathsf{=\dfrac{x^2+14x-32}{x-2}}$

$\textsf{Factorize the numerator}$

$\mathsf{=\dfrac{x^2+16x-2x-32}{x-2}}$

$\mathsf{=\dfrac{x(x+16)-2(x+16)}{x-2}}$

$\mathsf{=\dfrac{(x+16)(x-2)}{x-2}}$

$\mathsf{=\dfrac{x+16}{------}}$

$\implies\mathsf{\dfrac{5x^2+70x-160}{5x-10}=x+16}$

Answer 2

Step-by-step explanation:

$\textbf{Given:}$

$\mathsf{\dfrac{5x^2+70x-160}{5x-10}5x−10 5x 2 +70x−160$

$\textbf{To find:}$

$\textsf{Simplified form of}\mathsf{\dfrac{5x^2+70x-160}{5x-10}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{5x^2+70x-160}{5x-105x−105x 2 +70x−160$

$\mathsf{=\dfrac{5(x^2+14x-32)}{5(x-2)}}=5(x−2)5(x 2 +14x−32)$

$\mathsf{=\dfrac{x^2+14x-32}{x-2}}=x−2x 2 +14x−32$

$\textsf{Factorize the numerator}$

$\mathsf{=\dfrac{x^2+16x-2x-32}{x-2}}=x−2x 2 +16x−2x−32$

$\mathsf{=\dfrac{x(x+16)-2(x+16)}{x-2}}=x−2x(x+16)−2(x+16)$

$\mathsf{=\dfrac{(x+16)(x-2)}{x-2}}=x−2(x+16)(x−2)$

$\mathsf{=\dfrac{x+16}{------}}</p><p>{{−−−−−−x+16}}$

$\implies\mathsf{\dfrac{5x^2+70x-160}{5x-10}=x+16}$$⟹ 5x−105x 2 +70x−160 =x+16$