Answer:
Option (3) is correct.
The completely factored form of her polynomial [tex]4x^3+12x^2+5x + 15[/tex] is [tex](4x^2+5)(x +3)[/tex]
Step-by-step explanation:
Given : Louise begins factoring the polynomial, which has four terms.[tex]4x^3+12x^2+5x + 15[/tex]
We have to choose the completely factored form of her polynomial.
Consider the given polynomial [tex]4x^3+12x^2+5x + 15[/tex]
We will factorize the given polynomial using grouping of terms and taking common factors out.
[tex]4x^3+12x^2+5x + 15[/tex]
Taking [tex]4x^2[/tex] common from first two terms and 5 common from last two terms, we have,
[tex]4x^2(x+3)+5(x +3)[/tex]
Taking (x+3) common , we have,
[tex](4x^2+5)(x +3)[/tex]
Thus, option (3) is correct.
The completely factored form of her polynomial [tex]4x^3+12x^2+5x + 15[/tex] is [tex](4x^2+5)(x +3)[/tex]
