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Cogito

Algebra 1 · Chapter 7 · Lesson 2

Practice Worksheet

Factoring Quadratic Trinomials

Two numbers that multiply and add correctly.

11 problems · about 24 minutes · A-SSE.A.2, A-SSE.B.3

NameDate

Figure — use these to answer the problems

A factored product is a rectangle. Its two sides are the factors.

8 + 8 + 8 + 8 + 8 = 40

5 × 8 = 40

5 × 8 = (5 × 3) + (5 × 5) = 15 + 25 = 40

One factor5
The other factor8
Cut after column3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Multiply to 18, add to 9. Larger number?

    Answer

  2. Multiply to 6, add to 5. Larger number?

    Answer

  3. Multiply to 15, add to 8. Larger number?

    Answer

  4. Multiply to 9, add to 6. Larger number?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Multiply to −12, add to 1. Positive number?

    Answer

  2. x² + 5x + 6 factors to (x + 2)(x + ?). What is the missing number?

    Answer

  3. A positive constant with a positive middle term. Are both numbers positive? 1 for yes, 0 for no.

    Answer

Stretch Yourself

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

4 problems

  1. Multiply to 20, add to 9. Larger number?

    Answer

  2. Order the steps for factoring x² + bx + c.

    Write 1 to 4 in the boxes to put these in order.

    • List pairs multiplying to c
    • Find the pair adding to b
    • Write the two brackets
    • Expand to check

  3. The Pair

    Two numbers multiply to 12 and add to 7. What is the larger?

    Answer

  4. A Negative Constant

    Two numbers multiply to −10 and add to 3. What is the positive one?

    Answer