Question

PLS HELP ME!!
I really need the answers to these last few questions to a practice sheet I need to turn them in ASAP.

Simplify each polynomial. Write each in standard form.
HINT: Watch for the operation! Add? Subtract? Or Multiply?
8. 4m(2m+9m^2-6)

9. q(11+8q-2q^2 )

12. (x-1)^2

13. (4y+2)^2

Factor each polynomial.
HINT: Change from x^2+bx+c to (x+p)(x+q) where p and q are the factors of c that add to b.

21. x^2-13x-30

22. d^2-18d+45

Answer 1

8. 4m(2m+9m^2-6)
Distribute Parenthesis -> 4m · 2m + 4m · 9m^2 + 4m(-6)
Multiply -> 4 · 2mm + 4 · 9m^2m - 4 · 6m
Simplify -> 36m^3 + 8m^2 - 24m

9. q(11+8q-2q^2 )
Distribute Parenthesis -> q · 11 + q · 8 + q(-2q^2)
Multiply -> 11q · + 8qq - 2q^2q
Simplify -> -2q^3 +8q^2 + 11q

12. (x-1)^2
This is a perfect square so you can just use the formula:
(a-b)^2 = a^2 -2ab + b^2 (a = x and b = 1)
(x-1)^2 = x^2 - 2(x)(1) + 1^2
Simplify: x^2 - 2x + 1

13. (4y+2)^2
This is also a perfect square formula!
See if you can solve this one using the formula I gave you.

21. x^2-13x-30
break the expression into groups -> (x^2 + 2x) + (-15x -30)
Factor out x from x^2 +2x -> x(x+2)
Factor out -15 from (-15x - 30) -> -15(x + 2)
Combine terms -> x(x + 2) - 15(x + 2)
factor out (x + 2) -> (x+2) (x-15)

22. d^2-18d+45
Break the expression into groups -> (d^2 - 3d) + (-15d + 45)
Factor out d from (d^2 - 3d) -> d(d - 3)
Factor out -15 from (-15d + 45) -> -15(d - 3)
Combine terms -> d(d - 3) - 15(d - 3)
Factor out common term d -3 -> (d - 3) (d - 15)

Hope this helps! Sorry if its not the way you're "supposed" to do it, but it's the only way I remember how to simplify these.