Question

Can anybody help me with factoring trinomials that do not have a greatest common factor?
Ex. 2x^2+7x+5

Answer 1

Quadratic formula! For a trinomial of the form ax^2+bx+c, use \[\frac{-b \pm \sqrt{b^2-4ac}}{ 2a }\]

Answer 2

I have to factor it into this form (2x+5) (x+1)
I used mathway to get that answer but I can't figure out how to actually work it out.

Answer 3

What you want to do is split up the middle term so that you can factor 2 terms at a time.

Answer 4

Well, you can do the quadratic formula, but I think this way would be faster.

Answer 5

To figure out how to split up the middle term to help you the most, multiply the a (the coefficient of the x^2 term) and the c (the constant term).

Answer 6

This number gives you the number that your two terms need to both multiply and add to get.

Answer 7

For example, in this problem, the a is 2 and the c is 5.

Answer 8

So, the product of these 2 numbers is 10.

Answer 9

Ok, I left out a very important letter. The previous comment should read "This number gives you the number that your two terms need to both multiply to get and add to get b."

Answer 10

Sorry!

Answer 11

So, for this question, you need to find two numbers that multiply to get 10 and add to get 7.

Answer 12

These 2 numbers are 2 and 5.
2*5=10
2+5=7

Answer 13

Rewrite the equation with the middle term split up into these coefficients.
\[2x^{2}+2x+5x+5\]

Answer 14

now you can take the common factors from first 2 terms and last 2 terms in brackets..