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Math Review: Expanding Polynomials & Common Factoring Concepts

Learn how to expand and simplify polynomials, factor expressions, and understand exponent laws and radicals. Practice problems included.

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Math Review: Expanding Polynomials & Common Factoring Concepts

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  1. Ma and Pa Math

  2. Expanding Polynomials And Common Factoring Review

  3. Expanding Polynomials • The product of two binomials can be found by multiplying EACH term in one binomial by EACH term in the other binomial • Then, simplify (collect like terms)

  4. Angelina and Brad go to the movies, where they meet Courtney and David. B C D A

  5. If they were to all shake hands with the people they are just meeting… who would shake hands with who? B C D A

  6. A and C B and C A and D B and D B C D A

  7. Expanding polynomials works the same way! Example 1: Expand and simplify. a) b) In this case, the 3 ‘meets’ the x and the 3 ‘meets’ the 2. In this case, the 2y is multiplied by y and the 2y is multiplied by 1.

  8. c) d)

  9. e)

  10. Common Factoring • When factoring polynomial expressions, look at both the numerical coefficients and the variables to find the greatest common factor (G.C.F.) • Look for the greatest common numerical factor and the variable with the highest degree of the variable common to each term • To check that you have factored correctly, EXPAND your answer (because EXPANDING is the opposite of FACTORING!)

  11. Example 2: Factor. a) b) c)

  12. Exponent Laws

  13. Radicals!

  14. Radicals and Exponents • A radical is a root to any degree E.g. is a squared root, is a cubed root. • A repeated multiplication of equal factors (the same number) can b expressed as a power Example: 3 x 3 x 3 x 3 = 34 34is the power  3 is the base  4 is the exponent

  15. Radicals and Exponents 53 = “5 to the three” 64 = “six to the four” Hizzo = “H to the Izzo”

  16. Radicals and Exponents 63 = 6 x 6 x 6

  17. Radicals and Exponents 52 x 55 = (5 x 5) x (5 x 5 x 5 x 5 x 5) = 57

  18. Radicals and Exponents 68 65 = = = 63

  19. Radicals and Exponents = (72) x (72) x (72) = (7 x 7) x ( 7 x 7) x (7 x 7) = (7 x 7) x ( 7 x 7) x (7 x 7) = 76

  20. Radicals and Exponents = (3 x 2) x ( 3 x 2) x (3 x 2) x (3 x 2) = (3 x 3 x 3 x 3) x (2 x 2 x 2 x 2) = (34) x (24)

  21. Radicals and Exponents = x x = =

  22. The Power of Negative Numbers • There is a difference between –32 and (–3)2 • The exponent affects ONLY the number it touches So, –32= –(3 x 3), but (–3)2 = (–3) x (–3) = –9 = 9

  23. Homework p. 399 # 1 – 3, 5 – 11 (alternating!) Challenge Pg. 401 #16 – 18

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