Factoring Trinomials

What happens when we multiply the
binomials below?
(𝑥 − 4)(𝑥 + 1)



Form: 𝑥 2 + 𝑏𝑥 + 𝑐
(Notice that the leading coefficient is 1)
Steps:
1. Find integers that multiply to be 𝑐.
2. Of those, choose the pair that adds to be 𝑏.
If no such integers exist, then it’s prime.
Factor the trinomial.
𝑣 2 + 2𝑣 − 63
Factor the trinomial.
𝑡 2 + 11𝑡 + 30
Factor the trinomial.
𝑣 2 − 5𝑣𝑦 − 14𝑦 2
Factor the trinomial.
2 2
a. 𝑥 𝑦 + 11𝑥𝑦 + 18
b.
𝑥 2 𝑦 2 + 10𝑥𝑦 + 18

What happens when we multiply the
binomials below?
(2𝑥 − 5)(3𝑥 + 1)



Form: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, 𝑎 ≠ 1
(Notice that the leading coefficient is not 1)
Use the 𝑎𝑐 method:
1. Multipy 𝑎 and 𝑐 together.
2. Find integers that multiply to be 𝑎𝑐 .
3. Of those, choose the pair that adds to be 𝑏.
4. Substitute those for 𝑏𝑥 above.
5. Factor by grouping.
If no such integers exist, then it’s prime.
Factor the trinomial.
−3𝑥 2 − 17𝑥 + 56
Factor the trinomial.
15𝑥 2 + 17𝑥𝑦 − 18𝑦 2
Factor the trinomial.
15𝑥 2 𝑦 2 + 7𝑥𝑦 − 2

Our first step in factoring is always the same.

Factor out a GCF if possible.
Factor the trinomial.
−11𝑥 3 + 66𝑥 2 − 88𝑥
Factor the trinomial.
𝑎4 𝑏 3 − 8𝑎3 𝑏 2 + 12𝑎2 𝑏
Special Factoring
Factor the polynomial.
32𝑥 2 − 98𝑦 2
Factor the polynomial.
𝑦 3 − 64
Factor the polynomial.
9𝑦 2 + 6𝑦𝑧 + 𝑧 2
Factor the polynomial.
𝑦 + 𝑧 3 + 64
Factor the polynomial.
𝑝4 − 256
Factor the polynomial.
𝑥+𝑦 2+6 𝑥+𝑦 +9
Factor the polynomial.
24𝑛3 + 81𝑝3
Factor the polynomial.
9𝑛2 − 24𝑛 + 16 − 𝑚2
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