Question

Divide the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x.

9x 2 - 18x - 7 ÷ (3x + 1)

Answer 1

well the quadratic can be factored it makes the division easier

for a quadratic \[ax^2 + bx +c\]

multiply a and c so in your question a = 9 and c = -7

so a*c = -63

find the factors of -63 that add to -18 the coefficient of b

the larger factor will be negative

then use

\[\frac{(ax + factor ~1)(ax + factor ~2)}{a}\]

or in your question

\[\frac{(9x + factor~1)(9x + factor ~2)}{9}\]

then remove common factors in the numerator... and you'll find they cancel with the denominator