#5
x3 - 7x-6 divide x + 2

the quotient is 1x^2 - 2x - 3

Step-by-step explanation:

Here we're dividing the polynomial x3 - 7x-6  by the binomial  x + 2.

Synthetic division works very well here.  To use synthetic division we must write out all four (not three) terms of x^3 - 7x - 6:

Divide x^3 - 7x - 6 by x + 2 =>  Divide x^3 + 0x^2 - 7x - 6 by x + 2.

Dividing by x + 2 is equivalent to using -2 as the divisor in synthetic division.

Write out the synthetic division layout:

-2     /        1         0        -7       -6

                          -2         4       +6

                 1        -2         -3        0

Because the remainder is zero (0), we know that x + 3 divides into x^3 + 0x^2 - 7x - 6 evenly.   From the coefficients 1, -2 and -3, we know that the quotient is 1x^2 - 2x - 3.

Thus, x^3 + 0x^2 - 7x - 6 = (x + 2)(x^2 - 2x - 3)