In order to solve the product of polynomials simplify the numerator and denominator following those steps
we have
[tex](\frac{x^{2}-16}{2x+8})*( \frac{x^{3}-2x^{2}+x}{x^{2}+3x-4})[/tex]
Step 1
Using difference of squares and complete squares in the numerator
[tex]({x^{2}-16})*({x^{3}-2x^{2}+x)=[(x+4)(x-4)]*[x(x^{2}-2x+1)][/tex]
[tex][(x+4)(x-4)]*[x(x^{2}-2x+1)]=[(x+4)(x-4)]*[x(x-1)^{2}][/tex]
Step 2
Complete squares in the denominator
[tex](2x+8)*(x^{2}+3x-4)=[2(x+4)]*[(x+4)(x-1)][/tex]
Step 3
Substitute
[tex]\frac{[(x+4)(x-4)]*[x(x-1)^{2}]}{[2(x+4)]*[(x+4)(x-1)]}[/tex]
[tex]=\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
therefore
the answer is the option A
[tex]\frac{x(x-4)(x-1)}{2(x+4)}[/tex]
