Question

Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation.


2x2 + 13x + 15
2x2 + 27x + 13
5x2 − 2x − 7
10x2 − 7x − 3
8x2 − 11x + 3

Answer 1

pick the 1st one...

so for a quadratic

\[ax^2 + bx + c = 0\]

multiply a and c

so for

\[2x^2 + 13x + 15 = 0\]

2 * 15 = 30

next find the factors of 30 that add to 30

10 + 3

so then write (ax + factor 1)(ax + factor 2)
----------------------------- =0
2

(2x + 10)(2x + 3)
---------------- =0
2

now look for common factors in either binomial

so you get

2(x + 5)(2x + 3)
----------------- = 0
2

cancel the common factor of 2 leaves

(x + 5)(2x + 3) = 0

now solve

x + 5 = 0 and 2x + 3 = 0

for your solution.