Math: x^2 + bx + c please help.

1) (x+6)*(x+4).

6*4 = 24

6 + 4 = 10

Can you see some pattern?

Try doing the other examples.

You have three different options to factor trinomials.
1: Find a GCF (greatest common factor) In this case none of these problems have a GCF because the first term doesnt have a number infront of it.
2: If there is no GCF look for perfect square trinomials. That means the A and the C term have to be perfect squares, if they are perfect squares then you multiply the perfect squares together and double it. (For example: c^2 + 4c + 4
C^2 is a percfect square, same with 4.
C is the P.S. of C2 and 2 is the PS of 4
C x 2 = 2c
Then you double.
4c. This is a perfect square.
Then you factor
(C + 2)(C+ 2) When you use FOIL to check, it should come out to the orrigional problem.
If there is no perfect squares. Multiply A term by C term, and find the factors of that to find numbers that add up to B.
If you cant do any of those then the trinomial is Prime!
Hope this helped!

1. X^2 + 10 x +24 take factor pair of 24 such that by adding the factors
give 10 and multiplication gives 24
factor pairs of 24 are (1,24) (2,12) (3,8) (4,6)
the only factor pair suitable is (4,6) because 4+6=10 and 4*6=24
so the expression can be rewritten x^2 +4x +6x +24
taking two terms at a time factorise using common factor method
ie x(x+4) + 6(x+4) = (x+4)(x+6)

7. x^2 - 16x +48 factor pairs of 48 =(1,48) (2,24) (3,16) (4,12) (6,8)
I choose (4,12) because -4-12=-16 and -4*-12=+48
as before rewriting x^2 -4x-12x+48=x(x-4)-12(x-4)=(x-4)(x-12)

13. f^2 +3f-28 factor pairs of 28 =(1,28) (2,14) (4,7)
I choose (4,7) because 7-4=3 and 7*-4=-28