Lesson 10 – Perfect Square Trinomials
Specific Outcome:
- Model the factoring of a trinomial, concretely or pictorially, and record the process symbolically (5.2).
- Generalize and explain strategies used to factor a trinomial (5.7).
- Express a polynomial as a product of its factors (5.8).
Investigate:
Given the following square with a side length of 𝑥 + 3, determine the area of the square.
How does the middle term relate to the original expression?
Perfect Square Trinomial:
To factor a perfect square trinomial:
1. Square root the first term of the trinomial
2. Square root the third term of the trinomial
3. Check to see if the middle term is 2 times the two square roots
Example 1: Factor each trinomial.
a) x2 + 12x + 36
b) x2 – 8x + 16
c) 4x2 – 12x + 9
d) 9x2 + 30x + 25
Example 2: Find an integer to replace _____ so that each trinomial is a perfect square.
a) x2 + ____x + 49
b) a2 – ____a + 81
c) x2 + 12x + _____
d) a2 – 10a + _____
Example 3: The polynomial expression 9x2 + 6x + 1 can be written in the form of
(ax + b)2. The value of 𝑎 + 𝑏 is __________.
Guidelines for Factoring a polynomial Expression
Factoring
Question
Is there a
common
factor?
Yes
Factor out the common
factor
No
How many
terms are there?
2
4
3
Could be a
difference of squares
Could be a
factoring by grouping
Is a = 1
(ax + bx + c )?
2
Yes
This is a simple trinomial. Factor
using sum/product method.
No
This is a complex trinomial.
Factor using method of
decomposition.
Note: Always check to see if further factoring is possible
Example 4: Factor the following,
𝑎) 3𝑥 + 12
𝑏) 5𝑥 2 𝑦 − 𝑥 2 + 5𝑦 − 1
𝑐) 𝑥 2 − 81
𝑑) 4𝑥 2 − 1
𝑒) 𝑥 2 + 7𝑥 + 12
𝑓) 𝑥 2 − 2𝑥 − 15
𝑔) 6𝑥 2 + 11𝑥 + 3
ℎ) 3𝑥 2 − 4𝑥 − 4
𝑖) 𝑥 2 + 24𝑥 + 144
𝑗) 8𝑧 2 + 8𝑦𝑧 + 2𝑦 2
Practice Questions: Page 194 # 5, 7a(iii, iv), 8(a, c, e), 15(a)