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Factor the polynomial.3x + 6x³ +9x²A. 3x³(x+2)+9x²B. x²(2x³+3x²+2x)C. (3x² + 3x) (x²+2x)D. 3x²(x²+2x+3)

Sagot :

Given:

[tex]3x+6x^3+9x^2[/tex]

Required:

We need to factorize the given polynomial.

Explanation:

[tex]3x+6x^3+9x^2=6x^3+9x^2+3x[/tex]

Take the common multiple 3x.

[tex]3x+6x^3+9x^2=3x(2x^2+3x+1)[/tex][tex]Use\text{ }3x=2x+x.[/tex]

[tex]3x+6x^3+9x^2=3x(2x^2+2x+x+1)[/tex][tex]3x+6x^3+9x^2=3x(2x(x+1)+1(x+1))[/tex][tex]3x+6x^3+9x^2=3x(2x+1)(x+1)[/tex][tex]3x+6x^3+9x^2=3x(x+1)\left(2x+1\right)[/tex][tex]3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)[/tex]

Final answer:

[tex]3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)[/tex]