SOLUTION: Factor the polynomial f(x)=x^3+5x^2-2x-10 into linear factors using two methods: Grouping method and rational zeros

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Question 1130007: Factor the polynomial f(x)=x^3+5x^2-2x-10 into linear factors using two methods: Grouping method and rational zeros
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
"Grouping" Method
x%5E3%2B5x%5E2-2x-10
x%5E3%2B5x%5E2-%282x%2B10%29
x%5E3%2B5x%5E2-2%28x%2B5%29
x%5E2%28x%2B5%29-2%28x%2B5%29
%28x%5E2-2%29%28x%2B5%29


Synthetic Division, Check for Possible Roots:
A few roots to try, but...

-5    |    1    5    -2    -10
      |
      |        -5     0     10
      |______________________________
          1    0    -2      0

Shows that -5 works so x%2B5 is one factor, and the resulting quotient shows x%5E2-2 is a the other factor.