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Cogito

Algebra 1 · Chapter 7 · Lesson 1

Practice Worksheet

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

NameDate

Figure — use these to answer the problems

Four pieces, exactly as when multiplying two two-digit numbers.
102
105
  • 10 × 10100
  • 2 × 1020
  • 10 × 550
  • 2 × 510
  • 12 × 15180
First number12
Second number15
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Comparing Linear and Exponential Growth”

    3, 12, 48. Common ratio?

    Answer

  2. From “Laws of Exponents”

    x⁷ · x². Exponent?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. x² + 11x + 24 = (x + 3)(x + ?). Missing number?

    Answer

  2. What should you always look for first when factoring?

    • A common factor.
    • The quadratic formula.

  3. (x + 2)(x + 6) = x² + ?x + 12. Middle coefficient?

    Answer

  4. x² + 10x + 21 = (x + 3)(x + ?). Missing number?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. x² − 25 = (x + 5)(x − ?). Missing number?

    Answer

  2. 3x² + 12x = 3x(x + ?). Missing number?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. Expanding

    (x + 3)(x + 4) = x² + ?x + 12. What is the middle coefficient?

    Answer

  2. Factoring

    x² + 8x + 15 factors as (x + 3)(x + ?). What is the missing number?

    Answer