SOLUTION: I need help with this problem. Can someone write out the steps if possible. Thank you. Factor the polynomial into two polynomials of lesser degrees given one of its factors:

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this problem. Can someone write out the steps if possible. Thank you. Factor the polynomial into two polynomials of lesser degrees given one of its factors:       Log On


   

Question 53491: I need help with this problem. Can someone write out the steps if possible. Thank you.
Factor the polynomial into two polynomials of lesser degrees given one of its factors:
((x^3+2x^2-5x-6; factor: x-2))))))))))
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E3%2B2x%5E2-5x-6%29; factor: x-2 [Use synthetic division or regular division to solve]
.
Since (x-2) is one of the factors, divide the polynomial by (x-2):
.
x-2=0
x=2 [Divisor]
.
.
1+2-5-6 [Use only the coefficients for the dividend]
.
________________________
1 [Bring down the very first coefficient of "1"]
.
1+2-5-6 [Dividend]
0+2
________________________
1+4 [Begin to "divide" by 2 by multiplying [(1*2) + 2)=4]
.
.
1+2-5-6 [Dividend]
0+2+8
________________________
1+4+3 [Continue to "divide" by 2 by multiplying [(4*2)+(-5)=3]
.
.
1+2-5-6 [Dividend]
0+2+8+6
________________________
1+4+3+0 [Continue to "divide" by 2 by multipling [(3*2) + (-6)=0][Quotient]

[Re-apply the coefficents to the "x"terms minus one. For example you started with x^3, so the quotient will start with x^2]
.
So, the factors are %28x-2%29%28x%5E2%2B4x%2B3%29
Check by multiplying the factors to get the original polynomial.