how do you solve this algebra 2 problem (4x^3+13x^2+12x+4)/(x+2)

Question

I need step by step help with this.!

Answer 1

Synthetic division is easiest. Change x+2 into -2 as a zero of the polynomial, then divide:

-2 | 4 13  12     4 (coefficients in descending degree order)

  +  4  -8 -10 | -4 (copy leading coefficient; multiply result of previous column by -2)

(Add the two rows)

      4   5    2 |   0 remainder. The vertical bar separates the quotient from the remainder.

Insert the powers of x: 4x²+5x+2 is the quotient.