# Warm-ups 04-10-14 Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial. 4. x 2 + 12x + 355. x 2 + 2x – 63 6. x 2.

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Warm-ups 04-10-14 Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial. 4. x 2 + 12x + 355. x 2 + 2x – 63 6. x 2 – 10x + 167. 2x 2 – 16x + 32 x 2 + 9x + 14x 2 – 6x – 55 x 2 – 20x + 100 (x + 5)(x + 7)(x – 7)(x + 9) (x – 2)(x – 8)2(x – 4 )2 or (x-4)(2x-8)

Quadratic Equations A quadratic equation is an equation that can be written in the standard form: ax² + bx + c = 0 Quadratic equations will have zero, one, or two solutions.

Ways to Solve Quadratic Equations Graphing Factoring Square Root Method 3x 2 = 108 Completing the Square Quadratic Formula 3x 2 – 2x + 3 = 0

Solving by Factoring x 2 + 5x = -6 Make it equal zero (also called the Zero Product Property) x 2 + 5x + 6 = 0 Factor the left side (use the box or one of the short cuts). (x + 2)(x + 3) = 0 Set ALL FACTORS (including both sets of parentheses) equal to zero.

Solving by Factoring (cont.) x + 2 = 0x + 3 = 0 Solve. x = -2 and x = -3

Example 2 x 3 + x 2 – 6x = 0 Factor: x(x 2 + x – 6) = 0 x(x – 2)(x + 3)= 0 Set each factor equal to zero: x = 0 x – 2 = 0 x + 3 = 0 Solve: x = 0, 2, -3

Word Problem You are building a rectangular wading pool. You want the area of the bottom to be 90 ft 2. You want the length of the pool to be 3 ft longer than twice its width. What will be the dimensions of pool?

Word Problem (cont) Draw a picture. w(2w + 3) = 90 Distribute 2w 2 + 3w = 90 Make it equal zero 2w 2 + 3w – 90 = 0 Factor (2w + 15)(w – 6) = 0 w 2w + 3

Word Problem (cont) Set each factor equal to zero 2w + 15 = 0 w – 6 = 0 Solve: W = -7.5 w = 6 The width cannot be negative so it cannot be -7.5. It must be 6 feet. The length is 3 more than twice 6 Dimensions are 6 feet by 15 feet

Try these… x 2 + 11x + 30 = 0 2x 2 – 5x = 88 x 2 – 5 = 4 3x 2 + 4x = 2x 2 – 2x – 9 x 3 – 10x 2 + 24x = 0 x = -5, -6 x = -5.5, 8 x = 3, -3 x = -3 x = 0, 6, 4

Try these (cont)… You are building a rectangular wading pool. You want the area of the bottom to be 105 ft 2. You want the length of the pool to be 1 ft longer than twice its width. What will be the dimensions of pool? 7 feet by 15 feet

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