Answer:
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)
