How do you factor a trnomial as a product of two binomials

Question

How do i factor 2xsquared  + 7x + 6

 

Answer 1

2x² + 7x + 6

We know that the factors of 2x² have to be x and 2x, so we can already set up the factors as: (x ? ?)(2x ? ?) ,where question marks represent addition and subtraction signs and numbers.

Next, we can look at the sign on the constant (6) to determine what the signs inside the factors will be.  Since the sign on the constant is positive, we know that the signs in the two factors will be the same.  Since the sign on the x term (7x) is positive, we know that the signs both have to be positive.

That produces the factors as:  (x + ?)(2x + ?)

We need to determine factors of 6.  These factors can either be 1X6 or 2X3.  Also, the factors need to line up so that one is multiplied by 1 and the other by 2 so that they add up to 7.

The correct factor is 2X3, because 1 X 3 + 2 X 2 = 7.

The factors are (x + 2)(2x + 3)