SOLUTION: Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. x^3+2x^2-5x-6, x+3 Elementary and Intermediate Algebra Chapter 5 - Facto

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. x^3+2x^2-5x-6, x+3 Elementary and Intermediate Algebra Chapter 5 - Facto      Log On


   

Question 134593: Factor each polynomial completely, given that the binomial following it is a factor of the polynomial.
x^3+2x^2-5x-6, x+3
Elementary and Intermediate Algebra
Chapter 5 - Factoring
Found 2 solutions by solver91311, vleith:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Use polynomial long division to divide x%2B3 into x%5E3%2B2x%5E2-5x-6

x goes into x%5E3 x%5E2 times, so x%5E2 is the first term of the quotient.

x%5E2 times x%2B3 is x%5E3%2B3x%5E2.

Subtract x%5E3%2B3x%5E2 from x%5E3%2B2x%5E2 and get -x%5E2

Bring down the -5x to form -x%5E2-5x

x goes into -x%5E2 -x times, so -x becomes the second term of the quotient.

-x times x%2B3 is -x%5E2-3x

Subtract -x%5E2-3x from -x%5E2-5x and get -2x

Bring down the -6 to form -2x-6

x goes into -2x -2 times, so -2 becomes the third term of the quotient.

-2 times x%2B3 is -2x-6

Subtract -2x-6 from -2x-6 and get 0. So you have verified that x%2B3 is a factor. Now put the quotient together:

x%5E2-x-2

-2%2A1=-2 and -2%2B1=-1, so the trinomial quotient factors to:

%28x-2%29%28x-1%29

Therefore: x%5E3%2B2x%5E2-5x-6=%28x%2B3%29%28x-2%29%28x-1%29

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: x%5E3%2B2x%5E2-5x-6 and %28x%2B3%29 is a factor
Divide just the same way you would using arithmetic
Ask How many times does the (x+3) go into (x^3 +2x^2) ?? x^2 times
x^3 + 2x^2 - 5x -6
x^3 + 3x^2
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-x^2 - 5x - 6 How many times does (x+3) go into -x^2 - 5x? -x
-x^2 - 3x
---------------
-2x - 6 How many times does (x+3) go into this? -2
-2x - 6
------
0
%28x%2B3%29%28x%5E2+-+x+-2%29
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