the binomial (x + 5) is a factor of x² + 8x + 15. what is the other factor?\n(x + 3)\n(x + 7)\n(x + 12)\n(x…

the binomial (x + 5) is a factor of x² + 8x + 15. what is the other factor?\n(x + 3)\n(x + 7)\n(x + 12)\n(x + 13)

the binomial (x + 5) is a factor of x² + 8x + 15. what is the other factor?\n(x + 3)\n(x + 7)\n(x + 12)\n(x + 13)

Answer

Explanation:

Step1: Set up the factoring form

Let (x^{2}+8x + 15=(x + 5)(x + a)). Expand the right - hand side: ((x + 5)(x + a)=x^{2}+ax+5x + 5a=x^{2}+(a + 5)x+5a).

Step2: Equate the coefficients

We know that (x^{2}+(a + 5)x+5a=x^{2}+8x + 15). So we have the system of equations: (\begin{cases}a + 5=8\5a=15\end{cases}). From (a + 5=8), we can solve for (a) by subtracting 5 from both sides: (a=8 - 5=3).

Answer:

A. ((x + 3))