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

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)

Answer 2

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.