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Cogito

Integrated Math 2 · Chapter 2 · Lesson 1

Practice Worksheet

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

NameDate

Figure — use these to answer the problems

The roots are where the curve meets the axis. Factoring finds those crossings algebraically.
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y = 1x² − 5x + 6
a1
b-5
c6
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. x² − 6x + 8 = 0. What is the larger solution?

    Answer

  2. Why must the equation equal zero before factoring helps?

    • The zero product property applies only to a product of zero.
    • It makes the factoring easier.

  3. (x − 7)(x + 1) = 0. Larger solution?

    Answer

  4. x² − 9 = 0. Positive solution?

    Answer

  5. x² + 5x + 6 = 0. Larger solution?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x² − 7x = 0. Non-zero solution?

    Answer

  2. x² − 16 = 0. Positive solution?

    Answer

  3. x² − 4x + 4 = 0. What is the repeated solution?

    Answer

Stretch Yourself

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

4 problems

  1. Which expressions are a difference of squares?

    • x squared minus 25
    • 9x squared minus 4
    • x squared + 16
    • x squared minus 5x
    • Tick every box that applies.

  2. x² − 8x + 15 = 0. Larger solution?

    Answer

  3. The Factors

    (x − 4)(x + 2) = 0. What is the positive solution?

    Answer

  4. The Trinomial

    x² − 5x + 6 = 0. What is the larger solution?

    Answer