Cogito
Integrated Math 2 · Chapter 2 · Lesson 1
Solving by Factoring
A product is zero only when a factor is.
12 problems · about 21 minutes · A-SSE.B.3, A-REI.B.4
What this lesson teaches
The student solves quadratic equations by factoring using the zero product property.
- A product is zero only when a factor is zero.
- Rearrange to equal zero, then factor.
- Take out a common factor first and watch for a difference of squares.
Warm Up
Straightforward practice. Get the method working first.
5 problemsx² − 6x + 8 = 0. What is the larger solution?
Answer 4
Why 4.
Why must the equation equal zero before factoring helps?
Answer The zero product property applies only to a product of zero.
Why Only zero forces a factor to be zero.
(x − 7)(x + 1) = 0. Larger solution?
Answer 7
Why Set each factor to zero.
x² − 9 = 0. Positive solution?
Answer 3
Why Difference of squares.
x² + 5x + 6 = 0. Larger solution?
Answer -2
Why (x + 2)(x + 3).
Build It Up
The same ideas with more to keep track of.
3 problemsx² − 7x = 0. Non-zero solution?
Answer 7
Why Take out x.
x² − 16 = 0. Positive solution?
Answer 4
Why Difference of squares.
x² − 4x + 4 = 0. What is the repeated solution?
Answer 2
Why (x − 2)².
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich expressions are a difference of squares?
Answer x squared minus 25; 9x squared minus 4
Why It needs two squares with a subtraction between them.
x² − 8x + 15 = 0. Larger solution?
Answer 5
Why (x − 3)(x − 5).
The Factors: (x − 4)(x + 2) = 0. What is the positive solution?
Answer 4
Why 4.
The Trinomial: x² − 5x + 6 = 0. What is the larger solution?
Answer 3
Why 3.