SOLUTION: Find each product. (x³+x²+1)(x²-x-5)

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Question 118729: Find each product.

(x³+x²+1)(x²-x-5)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E3%2Bx%5E2%2B1%29%28x%5E2-x-5%29 Start with the given expression



x%5E3%28x%5E2-x-5%29%2Bx%5E2%28x%5E2-x-5%29%2B1%28x%5E2-x-5%29 Expand the expression. Remember for something like %28a%2Bb%2Bc%29%28d%2Be%2Bf%29 it expands to a%28d%2Be%2Bf%29%2Bb%28d%2Be%2Bf%29%2Bc%28d%2Be%2Bf%29


%28x%5E3%29%2A%281x%5E2%29%2B%28x%5E3%29%2A%28-1x%29%2B%28x%5E3%29%2A%28-5%29%2B%28x%5E2%29%2A%281x%5E2%29%2B%28x%5E2%29%2A%28-1x%29%2B%28x%5E2%29%2A%28-5%29%2B%281%29%2A%281x%5E2%29%2B%281%29%2A%28-1x%29%2B%281%29%2A%28-5%29 Distribute


x%5E5-x%5E4-5x%5E3%2Bx%5E4-x%5E3-5x%5E2%2Bx%5E2-x-5 Multiply


-4x%5E2-6x%5E3-x%2Bx%5E5-5 Combine like terms



x%5E5-6x%5E3-4x%5E2-x-5 Now rearrange the terms in descending order


So %28x%5E3%2Bx%5E2%2B1%29%28x%5E2-x-5%29 expands and simplifies to x%5E5-6x%5E3-4x%5E2-x-5.

In other words, %28x%5E3%2Bx%5E2%2B1%29%28x%5E2-x-5%29=x%5E5-6x%5E3-4x%5E2-x-5




If you need more help with multiplying polynomials, check out this Long Multiplication Calculator