how would you factor 3x^2+19x+20

Question

How would you factor 3x^2+19x+20

Answer 1

3x² + 19x + 20

Here's what we know:

the three is a prime number, so when factored, one set is going to be 3x and the other x.

Also , since both signs are positive and a decent-sized middle coefficient, we're likely going to have two positive signs as well.

(3x + )(x + )

20 factors down to 2 * 2 * 5, so we're either going to have a 4 * 5 or a 2 * 10

I'm immediately thinking of 4 * 5 to get us that 19 in the center. We want a fair amount of that middle coefficient, but not too much.

(3x + 4)(x + 5)

Let's test by distributing back out:

3x * x = 3x²

3x * 5 = 15x

4 * x = 4x

4 * 5 = 20

3x² + 15x + 4x + 20 --> 3x² + 19x + 20

 

Since that is what we started out with, our factorization works out fine.

Answer 2

3x² + 19x + 20        Start with the 3, it is prime:

(3x     )(x       )

The factors of 20 are 1 & 20, 2 & 10, 4 & 5. One of these multiplied by 3 and added to the other must be equal to 19.

(3x + 4)(x + 5)