Question

1. 5(x^2 +2x-6) - 3(2+x-x^2)

2. 2x^4-5x(x^3 -y) + 2y(5x)

3.Factor 2x^5+6x4+4x^3+12x^2

4. Factor 9y^2-18y +8

Please help. Thank you!!

Answer 1

1.
5x^2+10x-30 - (6+3x-3x^2)
5x^2+10x-30+3x^2-3x-6
8x^2+7x-36

2. do this the same way

3.
2x^5+6x^4+4x^3+12x^2
2x^2(x^3+3x^2 + 2x+6)
now, by inspection, we have
2x^2(x^2(x+3) + 2(x+3))
to wind up with
2x^2(x^2+2)(x+3)

4. Looks like a difference of squares, but it's one off. So, tweak it a bit:
9(y^2-2y+1)-1
9(y-1)^2 - 1^2
(3(y-1)-1)(3(y-1)+1)
(3y-4)(3y-2)