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Section 7.5

Section 7.5. Multiplying a Polynomial by a Monomial. Find the product of a monomial and a polynomial. Solve equations involving polynomials. Multiply a Polynomial by a Monomial. Find 6 y (4 y 2 – 9 y – 7). Method 1 Horizontal. 6 y (4 y 2 – 9 y – 7)

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Section 7.5

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  1. Section 7.5 Multiplying a Polynomial by a Monomial

  2. Find the product of a monomial and a polynomial. • Solve equations involving polynomials.

  3. Multiply a Polynomial by a Monomial Find 6y(4y2 – 9y – 7). Method 1 Horizontal 6y(4y2 – 9y – 7) = 6y(4y2) – 6y(9y) – 6y(7) Distributive Property = 24y3 – 54y2 – 42y Multiply. Answer: 24y3 – 54y2 – 42y

  4. 4y2 – 9y – 7 (x) 6y Distributive Property Multiply a Polynomial by a Monomial Method 2 Vertical 24y3 – 54y2 – 42y Multiply. Answer: 24y3 – 54y2 – 42y

  5. Simplify Expressions Simplify 3(2t2 – 4t – 15) + 6t(5t + 2). 3(2t2 – 4t – 15) + 6t(5t + 2) = 3(2t2) – 3(4t) – 3(15) + 6t(5t) + 6t(2) Distributive Property = 6t2 – 12t – 45 + 30t2 + 12t Product of Powers = (6t2 + 30t2) + [(– 12t) + 12t]– 45 Commutative and Associative Properties Answer: = 36t2 – 45 Combine like terms.

  6. Amountof money $3 perride regularrides superrides $2 per ride. admission + + =   A. ENTERTAINMENTAdmission 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. Sarita goes to the park and rides 15 rides, of which s of those 15 are super rides. Find an expression for how much money Sarita spent at the park. Words VariableIf s = the number of super rides, then15 – s is the number of regular rides. Let M be the amount of money Sarita spent at the park.

  7. Amountof money $3 perride regularrides superrides $2 per ride. admission + + =   Equation M = 10 + s● 3 + (15 – s) ● 2 = 10 +3s + 15(2) – s(2) Distributive Property = 10 + 3s + 30 – 2s Simplify. = 40 + s Simplify. Answer: An expression for the amount of money Saritaspent in the park is 40 + s, where s is the number of super rides she rode.

  8. B. Evaluate the expression to find the cost if Sarita rode 9 super rides. 40 + s = 40 + 9 s = 9 = 49 Add. Answer:Sarita spent $49.

  9. Polynomials on Both Sides Solve b(12 + b) – 7 = 2b + b(–4 + b). b(12 + b) – 7 = 2b + b(–4 + b) Original equation 12b + b2 – 7 = 2b – 4b + b2 Distributive Property 12b + b2 – 7 = –2b + b2 Combine like terms. 12b – 7 = –2b Subtract b2 from each side.

  10. Polynomials on Both Sides 12b = –2b + 7 Add 7 to each side. 14b = 7 Add 2b to each side. Divide each side by 14. Answer:

  11. Homework Assignment #29 7.5 Skills Practice Sheet

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