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Review for Algebra Test over Polynomials…

Review for Algebra Test over Polynomials… Use laws of exponents, Distributive Property, CLT, addition, subtraction, multiplication, and division of polynomials. Also, find and use GCF. The 2nd power mean… WRITE THE PARENTHESIS TWICE! ( 3p + 4 ) ( 3p + 4 ). + 16. + 12p. + 12p.

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Review for Algebra Test over Polynomials…

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  1. Review for Algebra Test over Polynomials… Use laws of exponents, Distributive Property, CLT, addition, subtraction, multiplication, and division of polynomials. Also, find and use GCF.

  2. The 2nd power mean… WRITE THE PARENTHESIS TWICE! ( 3p + 4 ) ( 3p + 4 ) + 16 + 12p + 12p 9p2 CLT + 24p + 16 9p2

  3. “subtracted from” means… (2q + 6 ) goes first! (2q + 6 ) – ( 7q – 3 ) 2q + 6 Distribute the minus sign. + 3 – 7q C.L.T. + 9 – 5q

  4. To find the degree… ADD all the powers in the term. 3 + 5 + 1 = 9 Ninth degree

  5. We are given the perimeter: 12x + 1 To find the missing side, first, look at the x-terms . 4x + 5x + ( ? ) = 12x 3x Now look at the numbers: +5 + (– 8) + ( ? ) = 1 positive 4 3x + 4

  6. Area of a triangle: Do the Power to a Power FIRST! (multiply the powers…) 50 w7 Multiply & Divide numbers: 25 • 4 ÷ 2 = When you multiply w6 times w… add the powers! 50

  7. Perimeter means… ADD ALL SIDES! Label them. 2m – 5 3m + 4 C.L.T. Add all the m-terms… 2m + 3m + 2m + 3m = – 2 10m Combine the numbers: +4 + 4 – 5 – 5 = – 2

  8. Binomial (2 terms) times a Trinomial (3 terms) means… 6 multiplications 3b2 3 • b2 = b3 b • b2 = 6b 3 • 2b= 2b2 b • 2b= –15 3 • (–5)= –5b b • (–5)= CLT – 5b + 2b2 b3 – 15 + 3b2 + 6b Highest power first! – 15 + 1b + 5b2 b3

  9. = x12 = x12 Multiply the powers! Add the powers! = x12 = x12 Subtract the powers! The zero power means… 1 The negative power means… the reciprocal. (the x12 moves to the numerator)

  10. Area of square: A = length • width c + 6 ( c + 6 ) ( c + 6 ) c2 + 6c + 6c + 36 CLT c2 + 12c + 36

  11. – 2xy + 3xy 2x2 – 3y2 CLT + xy – 3y2 2x2

  12. – 6n + 6n 4n2 – 9 CLT – 9 4n2

  13. Volume of a rectangular prism: V = Bh (B is the area of the base) The “base” is a rectangle… length • width V = l•w•h (2xy4)(3x2y)( x + y ) Multiply the first 2 monomials… Multiply #’s and ADD the Powers! Distributive Property ( x + y ) 6x3y5 + 6x3y6 6x4y5

  14. 1y2 + 1y2 2y2 Sum means ADD. CLT

  15. Product means MULTIPLY! + 5n + 4n n2 + 20 CLT + 9n + 20 n2

  16. Perimeter means ADD ALL SIDES! Label them. 6p + 1 Do not use the 5p. That’s the height. p2– 2p + 3 CLT Start with the highest power. (-2p) + (-2p) + 6p + 6p + 8p p2 + p2 2p2 + 8 +3 + 3 + 1 + 1

  17. 2 3 4 c d The GCF consists of: The biggest number that will divide into 8 and 12… and the common/shared variables… c and d Take the lowest power. c2 and d3

  18. = 24x7 b. Multiply #’s and… Add the powers. a. NOT Like Terms… Cannot be simplified! = 24 d. NOT Like Terms… Cannot be simplified! c. Power to a power… Multiply the powers. (x0)7 = x0 Anything to the 0 power equals 1. 24 • 1 =

  19. 10y6 10y6 y(8–6) GCF consists of: The biggest number that will go into 20 and 30… 10 AND, the common variable(s) with the LOWEST POWER… y6 10y6 ( ) + 3 2 y2 Divide both terms by 10y6 and put the results in the parentheses.

  20. TRUE Trinomial  3 terms Quadratic  2nd power FALSE Binomial  2 terms Cubic  3rd power TRUE Monomial  1 term 5th degree  5th power TRUE Binomial  2 terms linear  1st power

  21. Distributive Property Multiply the #’s and add the powers! 6x2 15x4 +

  22. m–2 Multiply #’s and Add the powers: 6 n0 equals 1… GOES AWAY! m–2 means… the reciprocal. (It goes in the bottom)

  23. Distributive Property Distribute the minus sign. d2 – 4d + 3 – 7d2 – d + 5 CLT + 8 – 6d2 – 5d

  24. TRUE a2– 5a + 5a – 25 FALSE ADD… CLT a + a + 5 2a + 5 FALSE ( a + 5 ) ( a + 5 ) a2 + 5a + 5a + 25 a2 + 10a + 25

  25. 12x2 + 18x – 10x – 15 CLT + 8x 12x2– 15

  26. Area of a rectangle: A = bh We know A and b. To solve for h… divide! 12 ÷ 12 x(2 – 1) 36 ÷ 12 x(3 – 1) + x x2 3

  27. 28 ÷ 4 g(3– 3) = g0 = 1 20 ÷ 4 g(10 – 3) 5g7 – g4 + 7 – 1g4 5g7 + 7 –4 ÷ 4 g(7 – 3)

  28. Power-to-a-Power: Multiply powers! a6•3 = ? 43 = ? 64 The power outside the parentheses applies to everything in parentheses. b5•3 = ? a18 b15

  29. – 5k2 – 6k + 9 6k3 + 4k – 10 CLT – 1 – 2k 6k3 – 5k2

  30. STUDY!

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