Question

Factorize the expression and divide them as directed:
$(2x^3-12x^2+16x)÷(x-2)(x-4)$

Answer 1

Step 1: Factorize the expression
$2x^3-12x^2+16x$
$=2x[x^2-6x+8]$
$=2x[x^2-(4+2)x+8]$
$=2x[x^2-4x-2x+8]$
$=2x\left[x\right(x-4)-2(x-4\left)\right]$
$=\left(2x\right)(x-2)(x-4)$

Step 2: Perform division of the given expression
$\frac{2x^3-12x^2+16x}{(x-2)(x-4)}=\frac{2x(x-2)(x-4)}{(x-2)(x-4)}$
$=2x$
$\therefore (2x^3-12x^2+16x)÷(x-2)(x-4)=2x$