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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?

Respuesta :

irspow
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)

Given expression : [tex]10x^3+3x^2-20x-6[/tex].

We need to factor it by grouping.

Teresa did first grouping it :[tex](10x^3 + 3x^2) + (-20x -6)[/tex]

[tex]\mathrm{Factor\:out\:}x^2\mathrm{\:from\:}10x^3+3x^2\mathrm{:\quad }x^2\left(10x+3\right)[/tex]

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

We get

[tex]=-2\left(10x+3\right)+x^2\left(10x+3\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}10x+3[/tex]

[tex]=\left(10x+3\right)\left(x^2-2\right)[/tex]

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

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


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