Question

10x3 + 3x2 – 20x – 6 (10x3 + 3x2) + (–20x – 6) x2(10x + 3) + (_______)(10x + 3) Teresa is factoring this polynomial by grouping. Which number goes in the blank to complete the step?

Answer 1

Given expression : $10x^3+3x^2-20x-6$.

We need to factor it by grouping.

Teresa did first grouping it :$(10x^3 + 3x^2) + (-20x -6)$

$\mathrm{Factor\:out\:}x^2\mathrm{\:from\:}10x^3+3x^2\mathrm{:\quad }x^2\left(10x+3\right)$

$\mathrm{Factor\:out\:}-2\mathrm{\:from\:}-20x-6\mathrm{:\quad }-2\left(10x+3\right)$

We get

$=-2\left(10x+3\right)+x^2\left(10x+3\right)$

$\mathrm{Factor\:out\:common\:term\:}10x+3$

$=\left(10x+3\right)\left(x^2-2\right)$

We got another factor in shown factors (10x + 3) .

Therefore, $\left(x^2-2\right)$ should come in the blank to complete the step.

Answer 2

10x^3-20x+3x^2-6

10x(x^2-2)+3(x^2-2)

(10x+3)(x^2-2)  ←  that's what they are looking for...but if you want to go further

(10x+3)(x+√2)(x-√2)