Question

I'm going to post two questions in one here!

I'm really stuck on these questions about factorising quadratics.
the two questions are:
3x^2 + 5x + 2
and
3x^2 + 5x - 12.

any help would be much appreciated.

Answer 1

To factor quadratics, you multiply a and c, and find the factors that when added equal b...

3x^2+5x+2

3(2)=6

Factors of 6 are
-1 and -6
-2 and -3
1 and 6
2 and 3

2 +3= 5(which is the b value)

Then you split 5x into 3x and 2x

3x^2+3x+2x+2

Group them together

(3x^2+3x) + (2x+2)

Take out anything in common

3x(x+1)+2(x+1)

Since the equations in the parentheses are the same, you can combine the terms on the outside to be 1

(x+1)(3x+2)

That is 3x^2+5x+2 factored out.

For the other equation you follow the same steps.

3(-12)=-36

-36
-1 and 36
-2 and 18
-3 and 12
-4 and 9

3x^2+9x-4x-12
(3x^2+9x)+(-4x-12)
3x(x+3)-4(x+3)

(3x-4)(x+3)

That is 3x^2+5x-12 factored.