Question

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

a. x(x-4)(x-1)/2(x+4)
b.x(x-1)/2
c.(x+4)(x-4)/2x(x-1)
d.(x-4)(x-1)/2x(x+4)

Answer 1

In order to solve the product of polynomials simplify the numerator and denominator following those steps

we have

`((x^(2)-16)/(2x+8))*( (x^(3)-2x^(2)+x)/(x^(2)+3x-4))`

Step 1

Using difference of squares and complete squares in the numerator

`({x^(2)-16})*({x^(3)-2x^(2)+x)=[(x+4)(x-4)]*[x(x^(2)-2x+1)]`

`[(x+4)(x-4)]*[x(x^(2)-2x+1)]=[(x+4)(x-4)]*[x(x-1)^(2)]`

Step 2

Complete squares in the denominator

`(2x+8)*(x^(2)+3x-4)=[2(x+4)]*[(x+4)(x-1)]`

Step 3

Substitute

`([(x+4)(x-4)]*[x(x-1)^(2)])/([2(x+4)]*[(x+4)(x-1)])`

`=(x(x-4)(x-1))/(2(x+4))`

therefore

the answer is the option A

`(x(x-4)(x-1))/(2(x+4))`

Answer 2

the answer is (a) i just took the test