Question

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

Answer 1

Given:

`3x+6x^3+9x^2`

Required:

We need to factorize the given polynomial.

Step-by-step explanation:

`3x+6x^3+9x^2=6x^3+9x^2+3x`

Take the common multiple 3x.

`3x+6x^3+9x^2=3x(2x^2+3x+1)`
`Use\text{ }3x=2x+x.`

`3x+6x^3+9x^2=3x(2x^2+2x+x+1)`
`3x+6x^3+9x^2=3x(2x(x+1)+1(x+1))`
`3x+6x^3+9x^2=3x(2x+1)(x+1)`
`3x+6x^3+9x^2=3x(x+1)\left(2x+1\right)`
`3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)`

Final answer:

`3x+6x^3+9x^2=(3x^2+3x)\left(2x+1\right)`