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Algebra Final Review

Polynomials. Algebra Final Review. Adding & Subtracting Polynomials. Steps: Write the first polynomial in standard form If subtracting, change the signs on the polynomial that follows the subtraction sign Line up the other polynomial under the first by lining up like terms

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Algebra Final Review

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  1. Polynomials Algebra Final Review

  2. Adding & Subtracting Polynomials Steps: • Write the first polynomial in standard form • If subtracting, change the signs on the polynomial that follows the subtraction sign • Line up the other polynomial under the first by lining up like terms • Add or Subtract according to the rules of integers

  3. Example: Add or subtract the polynomials. 1. (2k2 – 3 + k) + (3k + 5k2 – 7)

  4. 2. (-6w4 + w2) – (-2w3 + 4w2 – w)

  5. Distributive Property • a(b + c) = ab + ac • a(b – c) = ab – ac

  6. Example: Use the distributive property. 1. 9(x – 8)

  7. 2. -4x3y2(-3x2y + 9xy2 + 7x)

  8. FOIL • A method of multiplying a binomial by a binomial • Firsts • Outer • Inner • Lasts

  9. FOIL Example • F: x2 • O: -9x • I: +2x • L: -18 • x2 – 7x - 18 F L (x + 2)(x – 9) -7x I O

  10. Punnett Square • a method for multiplying polynomials that are larger than a binomial by binomial.

  11. Example x + 7 (x – 9)(x + 7) x2 +7x – 9x – 63 x2 – 2x – 63 x x2 + 7x - 9 - 9x - 63

  12. Example: Find each product. Use any method. 1. (x – 7)(2x + 4)

  13. 2. (x – 4)(3x2 + 2x – 7)

  14. Dividing Polynomials Steps: • Rewrite the first polynomial so that each term is divided by the second polynomial. • Divide each term • When dividing variables, subtract the exponents.

  15. Example: Divide the polynomials. 1. (4x2 + 8x) ÷ 2x

  16. Factoring Algebra Final Review

  17. Factoring ax2+bx + c Steps: 1. Multiply the leading coefficient (a) and the constant (c) 2. List the factors of this product (ac) 3. Follow the sign on the number to determine the operation • Negative – subtraction • Then subtract the factors • Positive – addition • Then add the factors

  18. 4. Place the correct signs on the factors • If you added in step 3 • Both signs are the same and take the middle sign and put on both numbers • If you subtracted in step 3 • Signs are different and bigger factor gets the middle sign. 5. Rewrite the polynomials a. Bring down the first term and last term b. Place the circled factors in the middle

  19. 6. Group the first two terms and the last two terms with parentheses. 7. Find the GCF of each of these groups 8. Pull out the common factor in the parentheses and write the remaining terms as a factor in the other parentheses

  20. Example: Factor the polynomials completely. 1. 2x2 – 9x + 4

  21. 2. 18x3– 32x

  22. Steps for solving by factoring 1. Write the polynomial correctly • Make sure the polynomial is equal to zero • Make sure the polynomial is in standard form 2. Factor the polynomial completely 3. Set each factor equal to zero 4. Solve each equation for the variable

  23. Example: Solve each equation by factoring. 1. 2x2 + 15x – 8 = 0

  24. Quadratics Algebra Final Review

  25. Discriminate/Quadratic Formula • Discriminate • b2 – 4ac • Quadratic Formula

  26. Number of Solutions b2 – 4ac > 0 2 Real Solutions b2 – 4ac = 0 1 Real Solution b2 – 4ac < 0 No Real Solutions

  27. Example: Find the value of the discriminate and determine the number of real solutions. 1. 2x2 – 8x + 9 = 0

  28. Simplifying Square Roots 1. Factor each number using prime factor trees • Cross off a number once it is factored 2. Circle any two numbers that are the same 3. Any circled number comes out of the square root 4. Any number not circled stays in the square root

  29. Example: Simplify each square root. 1.

  30. Use the quadratic formula to solve each equation. Round your answer to the nearest hundredth when necessary. 1. -x2 – 4x + 7 = 0

  31. Graphing Quadratics 1. Find the axis of symmetry 2. Make a table put this value in the middle 3. Give two number bigger and two numbers smaller 4. Plug in each x into the equation and solve for y 5. Graph all 5 points to make a parabola

  32. Example: Find the axis of symmetry and vertex of the following function. Then graph the function using a table. 1. y = -2x2 – 8x – 5

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