Multiplying Polynomials flashcards

Card 1

Multiply (6a²)(−3a⁴).

−18a⁶. Multiply the coefficients (6 × (−3) = −18) and add the exponents (2 + 4 = 6).

Card 2

Multiply (5a²b)(−2ab³).

−10a³b⁴. The coefficients give 5 × (−2) = −10. For a: 2 + 1 = 3. For b: 1 + 3 = 4.

Card 3

Expand 4x(x − 7).

4x² − 28x

Card 4

Expand (x + 4)(x + 9).

x² + 13x + 36. The middle term is 9x + 4x = 13x.

Card 5

Expand (x − 5)(x + 2).

x² − 3x − 10. The middle term is 2x − 5x = −3x.

Card 6

Expand (x − 4)(x − 7).

x² − 11x + 28. The middle term is −7x − 4x = −11x, and (−4)(−7) = +28.

Card 7

Expand (3x + 1)(2x − 5).

6x² − 13x − 5. The products are 6x², −15x, 2x and −5, and −15x + 2x = −13x.

Card 8

How many products do you write before combining like terms when you multiply a binomial by a trinomial? A trinomial by a trinomial?

6 and 9: the number of terms in one factor times the number of terms in the other (2 × 3 and 3 × 3).

Card 9

In this lesson’s FOIL memory aid, what do the letters stand for, and when does it apply?

First, Outer, Inner, Last: the four products of two binomials. It applies only to two binomials.

Card 10

In this lesson’s PACE plan, what do the letters stand for?

Pair every term with every term and multiply, Add the products, Combine like terms (standard form), Evaluate a test value such as 3.

Card 11

What is the degree of the product of a degree-6 polynomial and a degree-3 polynomial?

9. The degrees add (for nonzero polynomials), so it is 6 + 3 = 9, not 18.

Card 12

Why avoid x = 0, 1 and 2 as test values?

At 0 every term with x vanishes, so a missing x-term hides. At 1 every power equals 1, so a wrong exponent hides. At 2, x² and 2x are equal, so mixing up squaring and doubling hides. Use 3 or 4.

Card 13

Write (m + 4)² as a product, then expand it.

(m + 4)(m + 4) = m² + 4m + 4m + 16 = m² + 8m + 16. It is not m² + 16.