Question

match each polynomial expression with its factored form. pairs $x^2 - 36$ $x^3 - x^2 + 3x - 3$ $2x^3 + 2x^2 - 12x$ $x^2 - 6x + 8$ tiles $2x(x + 3)(x - 2)$ $(x - 4)(x - 2)$ $(x - 6)(x + 6)$ $(x^2 + 3)(x - 1)$

Explanation:

Step1: Factor difference of squares

$x^2 - 36 = x^2 - 6^2 = (x-6)(x+6)$

Step2: Factor by grouping

$x^3 - x^2 + 3x - 3 = x^2(x-1) + 3(x-1) = (x^2+3)(x-1)$

Step3: Factor out then quadratic

$2x^3 + 2x^2 -12x = 2x(x^2+x-6) = 2x(x+3)(x-2)$

Step4: Factor quadratic trinomial

$x^2 -6x +8 = (x-4)(x-2)$

Answer:

$x^2 - 36
ightarrow (x - 6)(x + 6)$
$x^3 - x^2 + 3x - 3
ightarrow (x^2 + 3)(x - 1)$
$2x^3 + 2x^2 - 12x
ightarrow 2x(x + 3)(x - 2)$
$x^2 - 6x + 8
ightarrow (x - 4)(x - 2)$