what is the quotient of $(x^{3}+6x^{2}+11x + 6)div(x^{2}+4x + 3)$?\n$x + 2$\n$x - 2$\n$x + 10$\n$x + 6$
what is the quotient of $(x^{3}+6x^{2}+11x + 6)div(x^{2}+4x + 3)$?\n$x + 2$\n$x - 2$\n$x + 10$\n$x + 6$
Answer
Explanation:
Step1: Factor the polynomials
First, factor (x^{3}+6x^{2}+11x + 6) and (x^{2}+4x + 3). We know that (x^{2}+4x + 3=(x + 1)(x+3)). By trial - and - error or synthetic division, (x^{3}+6x^{2}+11x + 6=(x + 1)(x + 2)(x+3)).
Step2: Perform the division
(\frac{(x + 1)(x + 2)(x+3)}{(x + 1)(x+3)}=x + 2)
Answer:
A. (x + 2)