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Algebra I Name Unit #1: Linear Equations & Inequalities Period Lesson # 4 : Multiplying Polynomials Date
Day 1
Review – Distributive Property
Multiplying a polynomial by a monomial is rather easy- In fact, we JUST DID THIS ON MONDAY!!! All we need to do is to distribute the monomial over each term in the polynomial and write our answer in standard form. Give it a try…. a.) 5(x^2 – 3x + 11) b.) x(x^2 + 3x – 8) c.) 2x(x^2 – 4x + 5) d.) - 3x(2x^2 – 5x + 3)
Lesson
One way to think about multiplying binomials is to use the distributive property twice. Some people call this ‘double distributing’ and others might call it FOILing. FOIL is an acronym that helps you remember which terms need to be multiplied.
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Directions : Use the distributive property to multiply the following binomials. Write your answer in standard form! a.) (x + 5)(x – 2) b.) (2x – 3)(x + 6)
c.) (x – 5)(x – 1) d.) (3x + 1)(2x – 7) e.) (c + 4)(c – 4) f.) (2x + 1)(2x – 1) Try these… 1.) (x + 8)(x – 3) 2.) (d – 7)(d – 6) 3.) (2x + 1)(x – 4) 4.) (3b – 1)(b + 4) 5.) (x – 5)(x + 5) 6.) (2x + 3)(2x – 3)
Example #2: Use a geometric diagram to find the product of (x + 5) and (x – 3).
Product means we need to. So, what we’re asked to find is (x +5)(x – 3). Ask yourself: How many terms are in (x + 5)? How many terms are in (x – 3)? That means we need to draw a rectangle that has rows and columns. Label each side with the terms from each binomial. It is SUPER IMPORTANT that you do NOT FORGET the subtraction signs when you label your diagram!!! Example #3: Use a geometric diagram to multiply the following polynomials. Write your answer in standard form! a.) (x + 5)(x – 2) b.) (x – 3)(x + 6) c.) ( 3 x + 2)(x – 7) d.) (2x – 5 )( 3 x – 2 )
Try these… a.) (x + 7)(x + 4) b.) (x – 8)(x – 3) c.) ( 4 x – 5)(x + 7) d.) ( 5 x – 2)(x + 11) e.) (2b + 5)( 3 b – 8) f.) ( 2 d – 11)( 3 d – 10)
c.) (d – 3)(d^2 + 2d + 4) d.) (x – 1)(x^2 – 3x – 2) Try these…. a.) (m + 4)(m^2 – 3m + 7) b.) (d – 3)(d^2 + 5d + 2) Example #2: Use a geometric diagram to multiply the following polynomials. Write your answer in standard form! a.) (x^2 + 5x – 2)(x^2 + 4x – 2) b.) (x^2 – 3x – 1)(x^2 + 5x + 3)
c.) (x^2 – 2x + 3)(x^2 + 4x – 1) d.) (x^2 + 5x + 3)(x^2 – 2x + 8) Try this… a.) (m^2 – 3m + 5)(m^2 + 8m + 11)
