18.1 & 18.2: multiplying polynomialsteachers.dadeschools.net/sdaniel/multiplying polynomials...
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18.1 & 18.2: Multiplying Polynomials
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Multiplying Polynomials
Each term in the first polynomial, must be multiplied by each term in the second polynomial.
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Distribute!
1. a2(4 +5a3)
2. 4k2(6k – 3k4)
3. -2b2a(5b3 + 7a – 2ab3 + 4)
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Method 1: Distribute
First
Outer
Inner
Last
• Multiply!!!
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For Example:
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Method 2: Box
Multiply (3x – 5)(5x + 2)
1. Draw a box.
2. Write a polynomial on the top and side of a box.
3. Multiply.
4. Combine like terms.
3x -5
5x
+2
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Pick Your Method: (7p - 2)(3p - 4)
7p -2
3p
-4
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Let’s Practice #1
1. (7x – 10)(3x + 8)
2. (2x – 3)(4x - 8)
3. (5x -10)(2x +8)
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4. Trina is building a garden. She designs a rectangular garden with length (x + 4) feet and width (x + 1) feet. When x = 4, what is the area of the garden?
Let’s Practice #1
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5. Orik has desiged a rectangular mural that measures 20 feet in width and 30 feet in length. Laura has also designed a rectangular mural, but it measure x feet shorter on each side. When x = 6 what is the area of Laura’s mural?
Let’s Practice #1
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Multiplying Terms with Exponents
• When FOILing, add the exponents and multiply coefficients.
• Add the little numbers and multiply the big numbers!!!
Example:
(3x2 + 10x)(5x3 – 7x2)
15x5 - 21x4 + 50x4 – 70x3
15x5 + 29x4 – 70x3
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Let’s Practice #2
1. (7x2 – 10x)(3x3 + 8x2)
2. (2x4 – 3x2)(4x - 8)
3. (5x3 + 2x2)(8x - 7)
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Multiplying Larger Polynomials
Each term in the 1st polynomial must be multiplied by each term in the 2nd.
Example:
(7x2 + 2x + 8)(4x3 – 9x2)
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x2 -5x +4
2x
-5
Method 2:
Multiply: (2x - 5)(x2 - 5x + 4)
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Let’s Practice #3
1. (5x2 + 7) (2x3 – 5x2 +9)
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Let’s Practice #3
2. (10x4 – 5x2 + 8) (8x3 -3x -6)
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3. Mr. Silva manages a manufacturing plant. The number of units produced (in thousands) can by modeled by N(x) = 0.02x2 + 0.2x + 3, where x is the number of years. The average cost per unit (in dollars) can be modeled by C(x) = - 0.002x2 – 0.1x + 2, where x is the number of years. Write a polynomial T(x) that can be used to model Mr. Silva’s total manufacturing cost.
Let’s Practice #3
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4. Brent runs a small toy store specializing in wooden toys. The number of toys made can be modeled by N(x) = – 0.7x2 – 2x + 23 and the average cost can be modeled by C(x) = -0.004x2 – 0.08x +25, where x is the number of years. Write a polynomials that can be used to model Brent’s total cost of making toys, T(x).
Let’s Practice #3