Question

Louise begins factoring the polynomial, which has four terms. 4x3 + 12x2 + 5x + 15 4x2(x + 3) + 5(x + 3) Which is the completely factored form of her polynomial? 4x2(x + 3)2 x(4x2 + 5) (4x2 + 5) (x + 3) (4x2 + 5) (x + 3)2

Answer 1

the answer is

(4x^2+5)(x+3) <--------------------

Answer 2

Option (3) is correct.

The completely factored form of her polynomial
`4x^3+12x^2+5x + 15` is
`(4x^2+5)(x +3)`

Explanation:

Given : Louise begins factoring the polynomial, which has four terms.
`4x^3+12x^2+5x + 15`

We have to choose the completely factored form of her polynomial.

Consider the given polynomial
`4x^3+12x^2+5x + 15`

We will factorize the given polynomial using grouping of terms and taking common factors out.

`4x^3+12x^2+5x + 15`

Taking
`4x^2` common from first two terms and 5 common from last two terms, we have,

`4x^2(x+3)+5(x +3)`

Taking (x+3) common , we have,

`(4x^2+5)(x +3)`

Thus, option (3) is correct.

The completely factored form of her polynomial
`4x^3+12x^2+5x + 15` is
`(4x^2+5)(x +3)`