Answer:
-3/8 -69/(64x -56)
Explanation:
You want the result of dividing (3x+6) by (-8x+7).
Polynomial long division
The steps in polynomial long division are substantially identical to the steps in numerical long division. The quotient term at any step is the ratio of the leading terms of the dividend and divisor. The new dividend is found by subtracting the product of the quotient and divisor from the dividend.
First quotient term
The first quotient term is (3x)/(-8x) = -3/8.
Remainder
The remainder is the difference of the dividend and the product of the quotient and divisor:
remainder = (3x +6) -(-3/8)(-8x +7) = 3x +6 -3x +21/8 = 8 5/8 = 69/8
The degree of this remainder is less than the degree of the divisor, so the division is finished.
Result
We often like to have the polynomials have positive leading coefficients, so we will express the result that way:
