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SECTION 5.4 Multiplying Polynomials MULTIPLYING POLYNOMIALS We just extend the distributive property. First terms Last terms Inner terms Outer terms In the case of two binomials, its usually called the FOIL method. EXAMPLE 1 Find each product. 4 a. −3𝑎 4 + 𝑎 b. (2𝑚 + 6)(5𝑚 − 3) EXAMPLE 2 2𝑦 5 (𝑦 − 8)(𝑦 + 2) EXAMPLE 3 (4𝑧 + 2)(𝑧 2 − 3𝑧 − 5) DIFFERENCE OF TWO SQUARES PATTERN What happens below? 𝑥+𝑦 𝑥−𝑦 = EXAMPLE 4 a. b. 𝑦+2 𝑦−2 (5𝑟 + 4𝑠)(5𝑟 − 4𝑠) DIFFERENCE OF TWO SQUARES PATTERN What happens below? (𝑥 + 𝑦)2 = EXAMPLE 5 (5𝑟 − 7𝑠)2 SECTION 5.5 Dividing Polynomials THINK BACK TO FRACTIONS . . . What happens below? 1 4 + = 6 6 EXAMPLE 1 27𝑚4 −18𝑚3 +9𝑚 a. 9 12𝑎𝑏2 𝑐 + 10𝑎2 𝑏𝑐 +18𝑎𝑏𝑐 2 b. 6𝑎2 𝑏𝑐 THINK BACK TO LONG DIVISION . . . 24 33482 EXAMPLE 2 (𝑥2 + 14𝑥 + 45) ÷ (𝑥 + 9) EXAMPLE 3 8𝑚3 − 18𝑚2 + 37𝑚 − 13 2𝑚2 − 3𝑚 + 6 WHAT HAPPENS IF WE HAVE MISSING TERMS? What happens with 1001 ÷ 5? Write the polynomial in standard form. If any power is missing, use a zero to hold the place of that term. EXAMPLE 4 2𝑥4 + 3𝑥3 – 7𝑥 − 10 𝑥2 – 2𝑥 EXAMPLE 5 9𝑘4 + 12𝑘3 – 4𝑘 − 1 3𝑘2 – 1 QUESTIONS??? Be working hard in MyMathLab!!!