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What is the product? x^2-16/2x+8 times x^3-2x^2+x/x^2+3x-4

User Shuang
by
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1 Answer

6 votes

Answer:

Explanation:

Rewrite x^2-16/2x+8 as

x^2 - 16

-------------

2(x + 8)

and rewrite x^3-2x^2+x/x^2+3x-4 as

x^3-2x^2+x

-----------------

x^2+3x-4

Next, write "x^2-16/2x+8 times x^3-2x^2+x/x^2+3x-4" as

x^2 - 16 x^3-2x^2+x

--------------- * -------------------

2(x+8) x^2+3x-4

Now factor both numerators and both denominators. We get:

(x - 4)(x + 4)(x)(x^2 - 2x + 1)

--------------------------------------

2(x + 8)(x + 4)(x - 1)

Now begin cancelling wherever possible. The x + 4 factors cancel, leaving us with:

(x - 4)(x)(x - 1)(x - 1)

---------------------------

2(x + 8)(x - 1)

Cancelling the x - 1 factors yields:

(x - 4)(x)(x - 1) x(x - 4)

--------------------- = -------------------

2(x + 8) 2(x + 8)

User Elddenmedio
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