How do I factor these trinomials?

Question

1. 3x^2 + 5x + 2

2. 5x^2 - 18x -8

Answer 1

1.  3x² + 5x + 2 =

replace 5x with 3x + 2x:

3x² + 3x + 2x + 2 =

group the terms as:

(3x² + 3x) + (2x + 2) =

factor out the common terms from each group:

3x(x + 1) + 2(x + 1) =

having got the common term (x + 1) (note that the initial replacement has been made just in order to make the common factor (x + 1) come out) factor it out, yielding:



(x + 1)(3x + 2)

the trinomial is completely factored

2. 5x² - 18x - 8 =

replace - 18x with - 20x + 2x:

5x^2 - 20x + 2x - 8 =

group the terms as:

(5x^2 - 20x) + (2x - 8) =

factor out 5x from the first group and 2 from the second group:

5x(x - 4) + 2(x - 4) =

having got the common term (x - 4) (note that the initial replacement has been made just in order to make the common factor (x - 4) come out) factor it out as:

(x - 4)(5x + 2)

the trinomial is completely factored

I hope it helps...

Bye!