Answer:
Option (3) is correct.
The completely factored form of her polynomial \(4x^3+12x^2+5x + 15\) is \((4x^2+5)(x +3)\)
Step-by-step 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 \((4x^2+5)(x +3)\)
