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How do you factor this math question?

I have a couple of questions actually, I have a test tommorow on factoring from standard form PLEASE HELP ! It would be much appreciated. so here are the problems I’m having difficulties with.

a)6h^2 -17+ 12 b)24a^2b^3 + 9a^2 + b^2 + 18a^3b^2

c) 4k^2 + 36k + 81 d) 4p^2q - 8p^2 - q +2

Question 2 : 9x^2 + Kx +144 - This is a perfect square trinomial what is the value of k? explain.

Factor :

  1. a^2 - 2a + 1 - b^2 + 2bc - c^2

THANK YOU SO MUCH TO ANYONE THAT ANSWERS!!!

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Answer #1

a)6h^2 -17+ 12

6h^2 -17+ 12 = 6h^2 -5 (nothing else you can do with this, did you forget an h?)

(if you forgot the h on 17) … 6h^2 -17h+ 12 = (3h - 4) (2h - 3)

The way to get this is find what factors into 6h2 = (6h x h) or (3h x 2h) 12 = (3 x 4) (-3 x -4) (-2 x -6) (2 x 6) (1 x 12) (-1 x -12)

what adds up to -17… then I just put different pairs together to see what worked

c) 4k^2 + 36k + 81

(2k + 9) (2k + 9)

d) 4p^2q - 8p^2 - q +2

4p2q - 8p2 - q + 2

2p2 (2q - 4) - (q - 2) (not sure about this)

9x^2 + Kx +144

(3x + 12) (3x + 12)

K = 72

A perfect square = (a+b)^2

so just put it in that format

9x2 = 3x x 3x

(3x + ) (3x + )

144 = 12 x 12

(3x + 12) (3x + 12)

Now just open it

9x^2 + 72x +144

so K = 72

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