Name: ___________________________________
Algebra 1
Factoring Special Products – Solve Means “Set = 0, Factor, Solve”
Perfect Square Trinomials
(𝒂𝒙)𝟐 + 𝟐𝒂𝒃𝒙 + 𝒃𝟐 = (𝒂𝒙 + 𝒃)(𝒂𝒙 + 𝒃) = (𝒂𝒙 + 𝒃)𝟐
(𝒂𝒙)𝟐 − 𝟐𝒂𝒃𝒙 + 𝒃𝟐 = (𝒂𝒙 − 𝒃)(𝒂𝒙 − 𝒃) = (𝒂𝒙 − 𝒃)𝟐
***Difference of Two Squares
(𝒂𝒙)𝟐 − 𝒃𝟐 = (𝒂𝒙 + 𝒃)(𝒂𝒙 − 𝒃)
1. Factor the expressions below completely.
x2 + 4x + 4
x2 – 6x + 9
x2 – 16
49x2 – 25
81x4 – 100
64x6 – 9y8
2. Solve the equations below. (Find the zeros of the function.)
x2 + 5x = -3x – 16
f(x) = 36x2 – 25
144x2 = 49
Name: ___________________________________
Algebra 1
Factoring Completely – Solve Means “Set = 0, Factor, Solve”
1. Factor the expressions below completely.
-x3 + 8x2 – 15x
-x2 + 12x – 27
5x5 – 80x
2x3 + 20x2 + 42x
5x2 + 25x + 20
16x3 – 25x2
2. Solve each equation below. (Find the zeros of the function.)
f(x) = -2x2 + 14x + 60
3x2 = 21x + 54
4x2 + 12x = 160
18x2 = 30x
2x2 – 50 = 0
8x2 = 98