Factoring Trinomials
Name: ___________________________________________
I.
Date: ______________
Trinomials of the Form: ___________________________ (not perfect square trinomials).
Recall (
)(
),
Factoring “Easy” Trinomials
Quadratic
Term
Linear
Term
Constant
Term
“Easy” Trinomials: The Leading Coefficient is __________.
Method
1. Write down two pairs of parentheses.
2. Determine the factors of C.
3. Find the combination of factors that will add/subtract to equal B.
4. Place the values into the parentheses
5. Check using FOIL.
1
Factoring Trinomials (A=1)
Name: ____________________________________________
Date: ______________
Factor each trinomial (rewrite as a product of two binomials).
1.
2.
3.
7.
8.
9.
x2 + 6x + 5
(
)(
x2 + 4x + 3
(
)(
x2 + 12x + 11
(
)(
x2 – 2x – 3
(
)(
x2 – 12x – 13
(
)(
)
)
)
)
)
x2 – 6x – 7
(
)(
General Form is Ax2 + Bx + C.
4.
5.
6.
10.
11.
12.
)
x2 – 8x + 7
(
)(
x2 – 24x + 23
(
)(
x2 – 12x + 11
(
)(
x2 + 2x – 3
(
)(
x2 + 12x – 13
(
)(
)
)
)
)
)
x2 + 6x – 7
(
)(
)
On this page, C is _______________________.
2
Factor each trinomial (rewrite as a product of two binomials).
General Form is Ax2 + Bx + C.
1.
x2 + 5x + 6
(
2.
)(
5.
)
)(
)
)
x2 + 6x – 16
(
)(
)
)
)(
)
x2 – 3x – 18
(
8.
)(
x2 – 7x + 12
(
7.
)(
x2 – 11x + 10
(
4.
x2 + x – 20
(
6.
3.
x2 + 6x + 8
(
On this page, C is _______________________.
)(
)
x2 – 10x – 24
(
)(
)
3
E) Always check for common monomials FIRST! (GCF stuff)
Factor:
2x2 + 8x + 8
3x2 - 27
You try:
1. 2v - 50
2. 3w2 – 30w + 75
3. x2 + 9x
4. 2m2 + 24m - 26
5. 24p2 – 16p
6. 9r2 + 30r + 24
2
4
Leading
Coefficient
“Hard” Trinomials:
Quadratic
Term
Linear
Term
Constant
Term
The leading coefficient is ____________________.
METHOD 1: GROUPING
Steps for factoring “Hard” Trinomials
1.
Decide your signs for the parentheses.
2. Multiply
3. Find 2 #’s that multiply to equal
and add to the linear term (B).
4. Rewrite Bx as a sum of the two factors. There will be 4 terms.
5. Factor by grouping:
Group the first two terms and the last two terms
Factor the GCF out of each group {the parentheses should match}
Use distributive property to write as two binomials
6. Check your answer - FOIL!!!
Example 1: Factor
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
5
METHOD 2: TRIAL AND ERROR
Steps for factoring “Hard” Trinomials:
I.
Method
1.
Find the factors of A and C.
2.
Determine which combination of factors will yield the middle term when
multiplied and added.
3.
Check.
Ex 1: 2x2 + 11x + 5
Ex 2: 3x2 – 4x – 7
6
Factoring Trinomials Practice, A = 1
Factor the trinomial, if possible. If it cannot be factored, write “prime.”
1.
3t2 + 16t + 5
2.
3c2 – 37c + 44
3.
3x2 – 17x – 6
4.
2x2 – 3x – 2
5.
6b2 – 11b – 2
6.
6y2 – 11y – 10
7