Warm Up 3-9
Add
1. 𝑥 2 + 2𝑥 − 12 +
𝑥 3 − 8𝑥 2 + 10
Multiply the polynomials
3. 3𝑥 2 4𝑥 3 + 5𝑥 2 −
2𝑥 + 3
Subtract
2. 𝑥 2 + 2𝑥 − 12
− (−8𝑥 2 + 4𝑥 + 10)
4. (𝑥 − 3)(2𝑥 + 5)
Factor the Difference of Squares
5. 𝑥 2 − 16
6. 9𝑥 2 − 36
Unit 7 Day 6: Factoring
Trinomials When a is 1
Essential Question: How do you factor a
trinomial when the leading coefficient is 1?
Vocabulary Review
• Standard form: when the terms are
written in descending order of the
powers (exponents)
• Leading Coefficient: the coefficient of
the variable with the highest power
• Constant: the number not connected to a
variable
Factoring Process
**Make sure trinomial is in standard form**
example: x2 - 1x - 12
For a trinomial with a leading coefficient of 1:
1. Find two numbers that multiply to give you the
constant and add to give you the middle term
• -4 and 3
2. Write as a product of two binomials
• (x + 3)(x - 4) or (x - 4)(x + 3)
Examples
1. x2 + 5x + 6
x2 + 5x + 6
Constant
Middle Term
What two numbers multiply to give
you 6 and add to give you 5?
(3)(2) = 6
3 + 2 = 5
Answer: (x + 3)(x + 2)
2. x2 + 2x - 8
x2 + 2x - 8
Constant
Middle Term
What two numbers multiply to give
you -8 and add to give you 2?
(4)(-2) = -8
4 + -2 = 2
Answer: (x + 4)(x – 2)
Practice!
Factor the following polynomials:
x2 + 5x + 4
x2 + 9x + 20
Factors of 4:
2 and 2
4 and 1
Which ones add to 5???
(x + 4)(x + 1)
Proof: Distribute back out with FOIL!
x2 + 1x + 4x + 4
x2 + 5x + 4
Factors of 20:
1 and 20
2 and 10
4 and 5
Which ones add to 9???
(x + 4)(x + 5)
Practice!
Factor the following polynomials:
x2 + 12x - 28
x2 - 2x - 48
Factors of -28:
1 and -28
-1 and 28
2 and -14
-2 and 14
4 and -7
-4 and 7
Factors of -48:
1 and -48
-1 and 48
2 and -24
-2 and 24
3 and -16
-3 and 16
4 and -12
-4 and 12
-6 and 8
6 and -8
Which ones add to 12???
Which ones add to -2???
(x - 2)(x + 14)
(x + 6)(x - 8)
Practice on your own!
x2 − 7x + 10
x2 − 5x + 6
x2 − 13x + 40
(x - 5)(x - 2)
(x - 3)(x - 2)
(x - 5)(x - 8)
x2 + 8x + 7
x2 − x - 56
x2 + 3x - 10
(x + 7)(x + 1)
(x - 8)(x + 7)
(x + 5)(x - 2)
Summary
In the summary portion of your notes,
answer the essential questions and any
other questions in your notes.
Essential Question: How do you factor a
trinomial when the leading coefficient is 1?