How do you factor the trinomial 2x^2 + 9x + 4?

1 Answer
Jan 3, 2016

2x^2+9x+4=(2x+1)(x+4)

Explanation:

2x^2+9x+4
First multiply the constant 4 with the coefficient of x^ which is 2

The result is 8

Now find factors of 8 such that they add up to the coefficient of x here it is +9.

Let us list out the pairs which multiply to give 8
These are 1,8, 2,4, -1,-8 and -2,-4

Let us check if these add up to +9

1xx8=8 and 1+8 =9 this works. Using this we shall split the middle term. 9x = 1x+8x

2x^2+9x+4
=2x^2+1x+8x+4 This is called splitting the middle term.
Now we would do factor by grouping.

=(2x^2+1x)+(8x+4)

GCF from each group is taken out.

=x(2x+1) + 4(2x+1)

Now we have (2x+1) as the common factor, so it is factored out.

=(2x+1)(x+4) Answer