MULTIPLYING POLYNOMIALS USING TABLES ON YOUR CALCULATOR COMMON CORE ...

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MULTIPLYING POLYNOMIALS USING TABLES ON YOUR CALCULATOR COMMON CORE ALGEBRA II HOMEWORK

FLUENCY

1. Multiply the following binomials and express each product as an equivalent trinomial. Use an area model to help find your product, if necessary.

(a) x 5 x 8

(b) 5x 22x 3

x2 8x 5x 40 x2 13x 40

10x2 15x 4x 6 10x2 19x 6

(d) x2 4 x2 10

x4 10x2 4x2 40 x4 6x2 40

(e) 2x3 15x3 4

10x6 8x3 5x3 4 10x6 13x3 4

2. Find each of the following products in equivalent form. Use an array model to help find your final answers if you find it helpful.

(a) 2x 34x2 5x 7

2x 4x2 5x 7 34x2 5x 7

8x3 10x2 14x 12x2 15x 21 8x3 2x2 29x 21

(b) 2x 53

2x 52x 52x 5

2x 5 2x 5 4x2 10x 10x 25

4x2 20x 25

2x 5 4x2 20x 25 2x 4x2 20x 25 5 4x2 20x 25

8x3 40x2 50x 20x2 100x 125 8x3 60x2 150x 125

COMMON CORE ALGEBRA II, UNIT #1 ? ESSENTIAL ALGEBRA CONCEPTS ? LESSON #5 eMATHINSTRUCTION, RED HOOK, NY 12571, ? 2015

APPLICATIONS

3. A square of an unknown side length x inches has one side length increased by 4 inches and the other increased by 7 inches.

(a) The product of x 4 and x 7

x2 11x 28

(c) If the original square had a side length of x 2 inches, then what is the area of the second rectangle? Show how you arrived at your answer.

x 4 x 7 2 42 7 69

54 square inches

REASONING

4. Think about the expression x 8 x 4 .

(a) For what values of x will this expression be equal to zero? Show how you arrived at your answer.

x80 x8 x 4 0 x 4

(d) Verify that the trinomial you found in part (b) has the same value as (c) for x 2 .

x2 11x 28 22 112 28

4 22 28 26 28 54

(b) Write this product as an equivalent trinomial.

x 8 x 4 x2 4x 8x 32

x2 4x 32

(c) Show that this trinomial is also equal to zero at the larger value of x from part (a).

x2 4x 32 82 48 32

64 32 32 32 32 0

FLUENCY

5. Use the STORE feature on your calculator to evaluate each of the following. No work needs to be shown.

(a) 7x 18 for x 8

(b) 3x2 2x 5 for x 3

(c) x3 5x2 4x 20 for x 5

38

26

0

COMMON CORE ALGEBRA II, UNIT #1 ? ESSENTIAL ALGEBRA CONCEPTS ? LESSON #5 eMATHINSTRUCTION, RED HOOK, NY 12571, ? 2015

(d) x2 2x 8 for x 1

9

5x 3 (e) 4x2 5 for x 2

1 0.3 or

3

(f) 4 x for x 5 x9

3 1.5 or

2

6. The quadratic expression x2 8x 10 has its smallest value for some integer value of x on the interval 0 x 10 . Set up a TABLE to find the smallest value of the expression and the value of x that gives this value. Show your table below.

x 0 1 2 3 4 5 6 7 8 9 10 y 10 3 -2 -5 -6 -5 -2 3 10 19 30

The smallest value of this expression is -6 at an x-value of 4.

7. Consider the complex expression x 7 x 3 x 1 x 4 .

(a) Multiply the two sets of binomials and combine like terms in order to write this expression as an equivalent trinomial in standard form. Show your work.

x 7 x 3 x2 3x 7x 21

x2 10x 21

x 1 x 4 x2 4x 1x 4

x2 5x 4

x2 10x 21 x2 5x 4 2x2 5x 25

(b) Set up a TABLE to verify that your answer in part (a) is equivalent to the original expression. Don't hesitate to point out that it is not equivalent (which means you either made a mistake in your algebra or in your table set up). Show your table.

x 0 1 2 3 4 5 6 y1 25 32 43 58 77 100 127 y2 25 32 43 58 77 100 127

COMMON CORE ALGEBRA II, UNIT #1 ? ESSENTIAL ALGEBRA CONCEPTS ? LESSON #5 eMATHINSTRUCTION, RED HOOK, NY 12571, ? 2015

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