Cogito
Algebra 1 · Chapter 7 · Lesson 1
Multiplying and Factoring
The same picture, read in two directions.
10 problems · about 20 minutes · A-APR.A.1, A-SSE.A.2, A-SSE.B.3
What this lesson teaches
The student multiplies binomials and factors quadratic expressions.
- Multiplying binomials is an area model with four pieces.
- Factoring runs the same picture backwards.
- Take out a common factor first, and watch for a difference of squares.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Comparing Linear and Exponential Growth: 3, 12, 48. Common ratio?
Answer 4
Why 4.
Review — Laws of Exponents: x⁷ · x². Exponent?
Answer 9
Why 9.
Warm Up
Straightforward practice. Get the method working first.
4 problemsx² + 11x + 24 = (x + 3)(x + ?). Missing number?
Answer 8
Why 8.
What should you always look for first when factoring?
Answer A common factor.
Why Take out the common factor first.
(x + 2)(x + 6) = x² + ?x + 12. Middle coefficient?
Answer 8
Why 2 + 6.
x² + 10x + 21 = (x + 3)(x + ?). Missing number?
Answer 7
Why 3 × 7 = 21.
Build It Up
The same ideas with more to keep track of.
2 problemsx² − 25 = (x + 5)(x − ?). Missing number?
Answer 5
Why Difference of squares.
3x² + 12x = 3x(x + ?). Missing number?
Answer 4
Why 12 ÷ 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsExpanding: (x + 3)(x + 4) = x² + ?x + 12. What is the middle coefficient?
Answer 7
Why 7.
Factoring: x² + 8x + 15 factors as (x + 3)(x + ?). What is the missing number?
Answer 5
Why 5.