How do I factor this equation?

\(3x^2+5x+2\)

I tried, but the answer I came up with didn't match with my teacher's answers, so I want a second opinion.

AdamTaurus
Sep 26, 2017

#1**+2 **

\(3x^2+5x+2\\ \)

First you need to find two numbers that multiply to give 3*2=6

Obviously they need to be of the same sign (positive or negative)

They also need to add to 5. Since 5 is positive both numbers must be positive.

2 and 3 work

2+3=5

2*3=6

so now you need to write 5x as 3x+2x

\(3x^2+5x+2\\ =3x^2+3x+2x+2\\ =3x^2+3x\quad+\quad2x+2\\ \text{Now factor in pairs}\\ =3x(x+1)\quad + \quad 2(x+1)\\ =(3x+2)(x+1) \)

Melody
Sep 26, 2017

#2**+2 **

Ohhhh. Okay. I see what I did wrong. I was only thinking about adding to 5 so I tried -1 and 6. Thanks!

AdamTaurus
Sep 26, 2017