# LT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.

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1 LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1. (4x x 2 ) + (3x 3 + 7x 2-1) 2. (14x 5 2x 3 ) + (7x 5 2x 3 ) 3. (4x 4 + 2x 3 ) (2x 4 + x 3 ) 4. (8x 4 + 3x 2 ) (3x 4 + x 2 ) 5. (14x 5 + 9x 3 + 8) (10x 5 + 7x 3-5) LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1. (4x x 2 ) + (3x 3 + 7x 2-1) 2. (14x 5 2x 3 ) + (7x 5 2x 3 ) 3. (4x 4 + 2x 3 ) (2x 4 + x 3 ) 4. (8x 4 + 3x 2 ) (3x 4 + x 2 ) 5. (14x 5 + 9x 3 + 8) (10x 5 + 7x 3-5)

2 LT2: The Distributive Property _ *Multiply the outside term by each term inside the parentheses. Combine like terms when possible. 1. 3(4x² + 5x 7) 2. 5x(x² - 4x + 3x 1) 3. -2x(3x 5 + x²) 4. x²(x² + 3x x) LT2: The Distributive Property _ *Multiply the outside term by each term inside the parentheses. Combine like terms when possible. 1. 3(4x² + 5x 7) 2. 5x(x² - 4x + 3x 1) 3. -2x(3x 5 + x²) 4. x²(x² + 3x x)

3 LT3: The Distributive Property with Binomials _ *Use FOIL or the rectangle method to multiply the polynomials. Remember that when you multiply variables the exponent changes. 1. (x + 3)(2x 5) 2. (3w + 4)(2w 1) 3. (c + 9)(c 11) 4. (4x 7)(2x 5) LT3: The Distributive Property with Binomials _ *Use FOIL or the rectangle method to multiply the polynomials. Remember that when you multiply variables the exponent changes. 1. (x + 3)(2x 5) 2. (3w + 4)(2w 1) 3. (c + 9)(c 11) 4. (4x 7)(2x 5)

4 LT4: Greatest Common Factor _ *Find the greatest number, variable, or both that can divide each term. Factor out the GCF and put it in front of the parentheses x² + 6x x² - 20x x³ - 4x² + 2x 4. 9x 4-18x³ - 6x² LT4: Greatest Common Factor _ *Find the greatest number, variable, or both that can divide each term. Factor out the GCF and put it in front of the parentheses x² + 6x x² - 20x x³ - 4x² + 2x 4. 9x 4-18x³ - 6x²

5 LT5: Factoring Polynomials *Use the diamond puzzle to find the factors. Be sure to write your factors in parentheses. 1. x² - 15x x² - 7x x² + 11x x² + 3x 18 LT5: Factoring Polynomials *Use the diamond puzzle to find the factors. Be sure to write your factors in parentheses. 1. x² - 15x x² - 7x x² + 11x x² + 3x 18

6 LT6: Graphing Quadratic Equations Name Find the following for the equation. Then graph. a. factored form (use the diamond to find the factors) b. opens up or down? c. y-intercept (plug zero in for x in the equation) d. line of symmetry (x = b 2a e. vertex (plug the value from the line of symmetry into the equation) f. x intercepts (set each of the factors equal to zero and solve for x) 1. y = x² - 5x + 4 LT6: Graphing Quadratic Equations Name Find the following for the equation. Then graph. g. factored form (use the diamond to find the factors) h. opens up or down? i. y-intercept (plug zero in for x in the equation) j. line of symmetry (x = b 2a k. vertex (plug the value from the line of symmetry into the equation) l. x intercepts (set each of the factors equal to zero and solve for x) 2. y = x² - 5x + 4

7 LT7: Interpreting Graphs of Quadratic Equations _ Answer the following questions about the given graph. It represents the path of a ball thrown into the air. a. What is the starting height of the ball? b. What is the highest point the ball reaches? When does it reach that height? c. For how many seconds is the ball in the air? d. What is the line of symmetry? e. Does this equation have a +x² or -x²? How do you know? LT7: Interpreting Graphs of Quadratic Equations _ Answer the following questions about the given graph. It represents the path of a ball thrown into the air. a. What is the starting height of the ball? b. What is the highest point the ball reaches? When does it reach that height? c. For how many seconds is the ball in the air? d. What is the line of symmetry? e. Does this equation have a +x² or -x²? How do you know?

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