Algebra I Part 2
Unit 2 Day 5 - Multiplying a Polynomial by a Monomial, Multiplying Polynomials (7-6, 7-7)
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Objective:
Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials.
Multiply polynomials by using the Distributive Property. Multiply polynomials using the FOIL method.
Polynomial Multiplied by Monomial:
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To find the product of a polynomial and a monomial, you can use the _________________ Property.
Example 1: Find 6y(4y2 – 9y – 7).
Check Your Progress: Choose the best answer for the following.
Find 3x(2x2 + 3x + 5).
A. 6x2 + 9x + 15
B. 6x3 + 9x2 + 15x
C. 5x3 + 6x2 + 8x
D. 6x2 + 3x + 5
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We can use this same method more than once to simplify large expressions.
Example 2: Simplify 3(2t2 – 4t – 15) + 6t(5t + 2).
Check Your Progress: Choose the best answer for the following.
Simplify 5(4y2 + 5y – 2) + 2y(4y + 3).
A. 4y2 + 9y + 1
B. 8y2 + 5y – 6
C. 20y2 + 9y + 6
D. 28y2 + 31y – 10
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We can use the Distributive Property to multiply monomials by polynomials and solve real world problems.
Example 3: Admission to the Super Fun Amusement Park is $10. Once in the park, super rides are an
additional $3 each, and regular rides are an additional $2. Wyome goes to the park and rides 15
rides, of which s of those 15 are super rides. Find the cost in dollars if Wyome rode 9 super
rides.
Algebra I Part 2
Unit 2 Day 5 - Multiplying a Polynomial by a Monomial, Multiplying Polynomials (7-6, 7-7)
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Check Your Progress: Choose the best answer for the following.
The Fosters own a vacation home that they rent throughout the year. The rental rate during peak season is
$120 per day and the rate during the off-peak season is $70 per day. Last year they rented the house 210
days, p of which were during peak season. Determine how much rent the Fosters received if p is equal to
130.
A. $120,000
B. $21,200
C. $70,000
D. $210,000
Solve Equations with Polynomial Expressions:
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We can use the Distributive Property to solve equations that involve the products of monomials and
polynomials.
Example 4: Solve b(12 + b) – 7 = 2b + b(-4 + b).
Check Your Progress: Choose the best answer for the following.
Solve x(x + 2) + 2x(x – 3) + 7 = 3x(x – 5) – 12.
A. -19/11
B. -2
C. 21/11
D. 0
Multiply Binomials:
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To multiply two binomials such as h – 32 and ½h + 11, the Distributive Property is used.
Binomials can be multiplied horizontally or by the box method.
Example 5: Find each product.
a. (y + 8)(y – 4)
b. (2x + 1)(x + 6)
Algebra I Part 2
Unit 2 Day 5 - Multiplying a Polynomial by a Monomial, Multiplying Polynomials (7-6, 7-7)
Check Your Progress: Choose the best answer for the following.
A. Find (c + 2)(c – 4).
A. c2 – 6c + 8
B. c2 – 4c – 8
C. c2 – 2c + 8
D. c2 – 2c – 8
B. Find (x + 3)(4x – 1).
A. 4x2 – 11x – 3
B. 4x2 + 11x – 3
C. 4x2 + 13x – 3
D. 4x2 + 12x – 3
FOIL Method:
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A shortcut version of the Distributive Property for multiplying binomials is called the _________
method.
To multiply two binomials, find the sum of the products of F the __________ terms, O the
__________ terms, I the __________ terms, and L the _________ terms.
(x + 4)(x – 2) =
Example 6: Find each product.
a. (z – 6)(z – 12)
b. (5x – 4)(2x + 8)
Check Your Progress: Choose the best answer for the following.
A. Find (x + 2)(x – 3).
A. x2 + x – 6
B. x2 – x – 6
C. x2 + x + 6
D. x2 + x + 5
B. Find (3x + 5)(2x – 6).
A. 5x2 – 8x + 30
B. 6x2 + 28x – 1
C. 6x2 – 8x – 30
D. 6x – 30
Real-World Examples:
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Notice that when two linear expressions are multiplied, the result is a ______________ expression.
A quadratic expression is an expression in one variable with a degree of _____.
When three linear expressions are multiplied, the result has a degree of _____.
The FOIL method can be used to find an expression that represents the area of an object when the
lengths of the sides are given as binomials.
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Algebra I Part 2
Unit 2 Day 5 - Multiplying a Polynomial by a Monomial, Multiplying Polynomials (7-6, 7-7)
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Example 7: A patio in the shape of the triangle shown below is being built in Lavali’s backyard. The
dimensions given are in feet. The area A of the triangle is one half the height h times the base
b. Write an expression for the area of the patio.
Check Your Progress: Choose the best answer for the following.
The area of a rectangle is the measure of the base times the height. Write an expression for the area of
the rectangle.
A. 7x + 3 units2
B. 12x2 + 11x + 2 units2
C. 12x2 + 8x + 2 units2
D. 7x2 + 11x + 3 untis2