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Question 619304: (x² + x +8) (x-8)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! (x-8) * (x^2 + x + 8) is equal to:
x * (x^2 + x + 8) - 8(x^2 + x + 8) which is equal to:
x*x^2 + x*x + x*8 -8*x^2 - 8*x - 8*8 which is equal to:
x^3 + x^2 + 8x - 8x^2 - 8x - 64 which is equal to:
x^3 -7x^2 - 64
to prove this is true, do a reverse operation.
divide x^3 - 7x^2 - 64 by (x-8)
you can use synthetic division to make this easier.
you will get:
8 divided into 1 - 7 + 0 - 64 using synthetic division.
you will get an answer of:
1 + 1 + 8 + 0 which equates to:
x^2 + x + 8 with a remainder of 0
since that division by (x-8) got you back to your original expression of (x^2 + x + 8), you know that you did the multiplication right, and the result of the multiplication is:
x^3 - 7x^2 - 64
you use the distributive law of multiplication to get this answer.
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