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Transcript
Multiplying Polynomials Module VII, Lesson 3 Online Algebra VHS@PWCS Multiplying Polynomials Recall that to multiply a polynomial by a monomial, we used the distributive property. 3x(2x2 – 7x + 8) 3x(2x2) – 3x(7x) + 3x(8) 6x3 – 21x2 + 24x Multiplying Binomials We apply the distributive property when multiplying binomials using a method called FOIL. FOIL stands for: ( x + 5 )( x + 7 ) First – Multiply the first terms Outside – Multiply the outside terms Inside – Multiply the inside terms Last – Multiply the last terms x(x)+ 7x + 5x+ 5(7) x2 +12x + 35 Try these using FOIL (2x + 9)(3x – 10) (x – 8)(x + 7) First First x(x) = x2 Outside 7x Inside -8x Last -8(7) = -56 Put it all together: x2 + 7x + -8x + -56 x2 - x - 56 2x(3x) = 6x2 Outside 2x(-10) = -20x Inside 9(3x) = 27x Last 9(-10) = -56 Put it all together: 6x2 + -20x + 27x + -56 6x2 + 7x - 56 Multiplying Polynomials by Polynomials (3x2 – 2x + 3)(2x + 7) Like with adding and subtracting polynomials it is easier to multiply setting these on top of each other. 3x 2 2 x 3 2x 7 21x 14 x 21 6 x3 4 x 2 6 x In this manner we can multiply as we have always done. 2 6x3 + 17x2 – 8x + 21 1. 2. 3. Multiply everything in the first factor by 7 Multiply everything in the first factor by 2x, using a placeholder. Add the products. Try these on your own. (x – 3)(2x2 + 3x + 3) 2x2 + 3x + 3 x–3 -6x2 – 9x – 9 2x3 + 3x2 + 3x 2x3 - 3x2 - 6x - 9 (2t2 – 6t + 3)(2t – 5) 2t2 – 6t + 3 2t – 5 -10t2 + 30t – 15 4t3 – 12t2 + 6t 4t3 – 22t2 + 36t - 15 Wrap up We use FOIL to multiply 2 binomials First Outside Inside Last We can set up multiplying polynomials as we have always done and follow those rules.