Question

What is the quotient of (x3 + 6x2 + 11x + 6) ÷ (x2 + 4x + 3)? x + 2 x – 2 x + 10 x + 6

Answer 1

Answer:

x + 2

Step-by-step explanation:

If we know one of the factors, we should be able to use long division.

We can divide the trinomial by the binomial and find the other factor.

                 x  +  2                  

x² + 4x + 3)x³ + 6x² + 11x + 6

                  x³ + 4x² + 3x

                         2x² + 8x + 6

                         2x² + 8x + 6

                                           0

Thus,

$\dfrac{x^{3} + 6x^2 + 11x + 6} {x^{2} + 4x + 3} = \mathbf{x + 2}$