Which of the following is a factor of 2[tex]x^{4}[/tex] + 22x[tex]x^{3}[/tex] + 60x[tex]x^{2}[/tex]?


[tex]x^{3}[/tex]

[tex]x^{4}[/tex]

x + 4

x + 5

Respuesta :

gmany

[tex]2x^4+22x^3+60x^2=2x^2(x^2+11x+30)=2x^2(x^2+6x+5x+30)\\\\=2x^2[x(x+6)+5(x+6)]=2x^2(x+6)(x+5)\\\\Answer:\ x+5[/tex]

Answer:

(x+5) is the final answer.

Step-by-step explanation:

We have to find the factors of [tex]2x^4+22x^3+60x^2[/tex]

Then select correct choice or choices from the given options.

[tex]2x^4+22x^3+60x^2[/tex]

[tex]=2x^2(x^2+11x+30)[/tex]

[tex]=2x^2(x^2+6x+5x+30)[/tex]

[tex]=2x^2(x(x+6)+5(x+6))[/tex]

[tex]=2x^2((x+5)(x+6))[/tex]

[tex]=2x^2(x+5)(x+6)[/tex]

From above factors, we see that only (x+5) is correct.

Hence (x+5) is the final answer.

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