### Factoring Trinomials

```Factoring Trinomials
ο½
What happens when we multiply the
binomials below?
(π₯ β 4)(π₯ + 1)
ο½
ο½
ο½
Form: π₯ 2 + ππ₯ + π
(Notice that the leading coefficient is 1)
Steps:
1. Find integers that multiply to be π.
2. Of those, choose the pair that adds to be π.
If no such integers exist, then itβs prime.
Factor the trinomial.
π£ 2 + 2π£ β 63
Factor the trinomial.
π‘ 2 + 11π‘ + 30
Factor the trinomial.
π£ 2 β 5π£π¦ β 14π¦ 2
Factor the trinomial.
2 2
a. π₯ π¦ + 11π₯π¦ + 18
b.
π₯ 2 π¦ 2 + 10π₯π¦ + 18
ο½
What happens when we multiply the
binomials below?
(2π₯ β 5)(3π₯ + 1)
ο½
ο½
ο½
Form: ππ₯ 2 + ππ₯ + π, π β  1
(Notice that the leading coefficient is not 1)
Use the ππ method:
1. Multipy π and π together.
2. Find integers that multiply to be ππ .
3. Of those, choose the pair that adds to be π.
4. Substitute those for ππ₯ above.
5. Factor by grouping.
If no such integers exist, then itβs prime.
Factor the trinomial.
β3π₯ 2 β 17π₯ + 56
Factor the trinomial.
15π₯ 2 + 17π₯π¦ β 18π¦ 2
Factor the trinomial.
15π₯ 2 π¦ 2 + 7π₯π¦ β 2
ο½
Our first step in factoring is always the same.
ο½
Factor out a GCF if possible.
Factor the trinomial.
β11π₯ 3 + 66π₯ 2 β 88π₯
Factor the trinomial.
π4 π 3 β 8π3 π 2 + 12π2 π
Special Factoring
Factor the polynomial.
32π₯ 2 β 98π¦ 2
Factor the polynomial.
π¦ 3 β 64
Factor the polynomial.
9π¦ 2 + 6π¦π§ + π§ 2
Factor the polynomial.
π¦ + π§ 3 + 64
Factor the polynomial.
π4 β 256
Factor the polynomial.
π₯+π¦ 2+6 π₯+π¦ +9
Factor the polynomial.
24π3 + 81π3
Factor the polynomial.
9π3 β 24π + 16 β π2
Be sure to stay on top of your MyMathLab
assignments!!!
```