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MJ2A

MJ2A. Ch 13.4 – Multiplying a Polynomial by a Monomial. Bellwork. Simplify each expression (x)(3x) (2y)(4y) (t 2 )(6t) (4m)(m2). Solutions. 3x 2. 8y 2. 6t 3. 4m 3. Assignment Review. Text p. 680 # 10 – 25. Before we begin…. Please take out your notebook and get ready to work…

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MJ2A

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  1. MJ2A Ch 13.4 – Multiplying a Polynomial by a Monomial

  2. Bellwork • Simplify each expression • (x)(3x) • (2y)(4y) • (t2)(6t) • (4m)(m2) Solutions 3x2 8y2 6t3 4m3

  3. Assignment Review • Text p. 680 # 10 – 25

  4. Before we begin… • Please take out your notebook and get ready to work… • In the last two lessons we looked at adding and subtracting polynomials… • In today’s lesson we will look at multiplying a polynomial by a monomial… • We will use the distributive property here…you are required to recognize and know how to work with the distributive property!

  5. Objective 13.4 • Students will multiply polynomials by monomials

  6. Background Knowledge • At this point you should all know that the rules for multiplying are not the same as adding… • For example you cannot add polynomials unless you have like terms… • That doesn’t apply to multiplying… • I can multiply a ● b to get ab • Also, at this point you should know that if you multiply a ● a you get a2

  7. Strategy • When multiplying monomials and polynomials a good strategy is to segment the parts… • What that means is you do a step by step process doing the coefficients first, then the variables, then the exponents, and finally the sign of the terms… • This strategy is effective because it minimizes errors… • Let’s look at an example…

  8. Example Multiply -2a2 (-3a) • Multiply the coefficients to get 6 2. Multiply the variables to get a3 6 a3 + 3. Multiply the signs – negative times negative = positive In this example the solution is +6a3

  9. Distributive Property • When multiplying a polynomial by a monomial you will use the distributive property… • That is you will multiply what on the outside of the parenthesis with EACH term on the inside of the parenthesis • Let’s look at an example…

  10. Example #1 (2x – 6)(3x) 1. Multiply 3x times 2x to get 6x2 2. Then multiply 3x times – 6 to get – 18x 6x2 – 18x 6x2 – 18x is the solution

  11. Example #2 1. Multiply 3a ● a2 to get 3a3 (3a)(a2 + 2ab -4b2) 2. Then multiply 3a ● 2ab to get + 6a2b 3a3 +6a2b -12ab2 3. Then multiply 3a ● -4b2 to get -12ab2 3a2 + 6a2b – 12ab2 is the solution

  12. Your Turn • In the notes section of your notebook write and multiply the polynomial by the monomial. • (5y – 4)3 • (3x – 7)4x • -5( 3x2 – 7x + 9) Solutions 15y - 12 12x2 – 28x -15x2 + 35x - 45

  13. Summary • In the notes section of your notebook summarize the key concepts covered in today’s lesson • Today we discussed: • Multiplying polynomials by monomials • What methodology will you use? • What strategy will you use?

  14. Assignment • Text p. 685 # 11 – 24 Reminder • This assignment is due tomorrow • I do not accept late assignments • You must show how you got your answer (no work = no credit)

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