Answer:
Step-by-step explanation:
hg(x) means you multiply h(x) times g(x) and then we will set it equal to [tex]3x^2+x-1[/tex].
hg(x) = [tex]x^2(x+2)[/tex] which simplifies to
[tex]x^3+2x^2[/tex]. Now set that equal to [tex]3x^2+x-1[/tex]:
[tex]x^3+2x^2=3x^2+x-1[/tex] and get everything on the same side and factor:
[tex]x^3-x^2-x+1=0[/tex]. Factor by grouping:
[tex](x^3-x^2)-(x+1)=0[/tex] and factor out what's common in each set of ( ):
[tex]x^2(x-1)-1(x-1)=0[/tex] which factors out to
[tex](x^2-1)(x-1)=0[/tex]. But [tex]x^2-1[/tex] factors somoe to:
(x + 1)(x - 1)(x - 1) = 0 So the solutions for this are
x = -1, 1
