Question

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

Answer 1

Answer:

v

x

5

−

2

v

x

4

−

8

x

4

+

3

v

x

3

+

24

x

3

−

4

v

x

2

−

40

x

2

+

v

x

+

56

x

+

8

x

−

40

v

x

5

-

2

v

x

4

-

8

x

4

+

3

v

x

3

+

24

x

3

-

4

v

x

2

-

40

x

2

+

v

x

+

56

x

+

8

x

-

40

Step-by-step explanation:

Answer 2

Answer:

Step-by-step 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)