Question

divide.
$(12x^{3}+20x^{2}-10x-15)\div(3x+2)$
your answer should give the quotient and the remainder.
quotient: $square$
remainder: $square$

Explanation:

Step1: Divide leading terms

$\frac{12x^3}{3x} = 4x^2$

Step2: Multiply divisor by $4x^2$

$4x^2(3x+2) = 12x^3 + 8x^2$

Step3: Subtract from dividend

$(12x^3+20x^2-10x-15)-(12x^3+8x^2) = 12x^2-10x-15$

Step4: Divide new leading terms

$\frac{12x^2}{3x} = 4x$

Step5: Multiply divisor by $4x$

$4x(3x+2) = 12x^2 + 8x$

Step6: Subtract from new polynomial

$(12x^2-10x-15)-(12x^2+8x) = -18x-15$

Step7: Divide new leading terms

$\frac{-18x}{3x} = -6$

Step8: Multiply divisor by $-6$

$-6(3x+2) = -18x-12$

Step9: Subtract to find remainder

$(-18x-15)-(-18x-12) = -3$

Answer:

Quotient: $4x^2 + 4x - 6$
Remainder: $-3$