Question

Using complete sentences, explain how to completely factor 3x2 − 3x − 60

Answer 1

1. you need two factors, whose sum is equivalent to the middle term of the expression (-3x) and whose product is equal to the the product of first and last terms (3x^2 * -60)
you follow upto there?

Answer 2

it might be easier if you rewrite the problem -3x + 3*2 - 60
you want to pull out the common factor (3)
3(-x + 2 - 20) or -3(x -2 + 20)
does this answer it or do i need to break it down more?

Answer 3

a little more

Answer 4

take 3 out as a common factor

\[3(x^2 - x - 20) \]

next find the factors of 20 that add to -1.... the larger factor is negative...

-20 x 1 -20 + 1 = -19
-10 x 2 -10 + 2 = -8
- 5 x 4 -5 + 4 = -1

the factors are -5 and 4

then its

\[3(x - 5)(x + 4) = 3x^2 - 3x - 60\]

Answer 5

2. those factors are 12x and -15x (note -15x+12x = -3x and -15x * 12x = -180x^2)
so now substitute this two factors for the middle term and your expression now becomes:
\[3x ^{2} +12x - 15x -60\]

Answer 6

thank you!

Answer 7

divide the whole equation by three (3(-x + 2 - 20))/3
this will give you -x + 2/3 - 20/3
= -x -18/3 or -1(x + 18/3)
...it has been a while since i've done math but i didn't know if in your original equation if that was supposed to be an "x" or a times symbol

Answer 8

@simplybeyoutiful \[3x(x+4)-15(x+4)\]
=\[(3x-15)(x+4)\] that's how to completely factor