Can you please help me factor these expressions?

Question

Completely factor the following expressions.
Please show work.

4x^2 - 8x - 12 + 6x

144 - 9p^2

5c^2 - 24cd - 5d^2

w^2 - 17w + 42

256z^2 - 4 - 192z^2 + 3

2a^2 c^3 - 14bc^3 + 32c^3 d^2

35g^2 + 6g - 9

3j^3 - 51j^2 + 210j

Thank you so much for your help!

Answer 1

4x^2 - 8x - 12 + 6x , looks like grouping works nicely
= 4x^2- 8x+ 6x - 12
= 4x(x-2) + 6(x-2)
= (x-2)(4x+6)
= 2(x-2)(2x+3)

144 - 9p^2 , should have recognized difference of squares
= (12-3p)(12+3kp)

5c^2 - 24cd - 5d^2
if it factors it must start with (5c ...)(c...)
and end with (... 5c)(.... c)
should have been obviously
(5c + 1)(c - 5c)

w^2 - 17w + 42
really ? what 2 numbers multiply to get +42 and have a sum of -17
They must obviously be both negative.
how about -3 and -14 ?
form the factors.

256z^2 - 4 - 192z^2 + 3 , wants to be simplified first
= 64z^2 - 1
you do it !

2a^2 c^3 - 14bc^3 + 32c^3 d^2
common factor first ...
= 2c^3( a^2 - 7b + 16d^2)
nothing else to do here

3j^3 - 51j^2 + 210j
again, common factor first
= 3j(j^2 - 17j + 70)

mmmh,, can you think of 2 numbers which when multiplied give you 70 , and when added will give you -17 ?

let me know what you get for this one

Answer 2

Ok... I tried to figure these out. This is what I got. Will you check my work?
1).
4x^2 - 8x - 12 + 6x
= 4x^2 - 2x -12
= 2(2x + 3)(x - 2)

2).
144 - 9p^2
= 9(16 - p^2)
= -9(p^2 - 4^2)
= -9(p + 4)(p - 4)

3).
5c^2 - 24cd - 5d^2
= (5c + d)(c - 5d)

4).
w^2 - 17w + 42
= (w - 3)(w + 14)

5).
256z^2 - 4 - 192z^2 + 3
= 64z^2 - 1
= (8z + 1)(8z - 1)

6).
2a^2 c^3 - 14bc^3 + 32c^3 d^2
= 2c^3(a^2 - 7b + 16d^2)

7).
35g^2 + 6g - 9
= (7g - 3)(5g + 3)

8).
3j^3 - 51j^2 + 210j
= 3j(j - 7)(j - 10)

Answer 3

Yeahhh!
you got it