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5.3 Factoring Quadratic Function

5.3 Factoring Quadratic Function. 11/15/2013. To multiply 2 Binomials (expression with 2 terms) use FOIL. Multiplying Binomials:. FOIL First, Outside, Inside, Last. F. L. Ex. (x + 3)(x + 5). ( x + 3)( x + 5). I. F irst: x •x = x 2 O utside: x • 5 = 5x

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5.3 Factoring Quadratic Function

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  1. 5.3Factoring Quadratic Function 11/15/2013

  2. To multiply 2 Binomials (expression with 2 terms) use FOIL. Multiplying Binomials: FOIL First, Outside, Inside, Last F L Ex. (x + 3)(x + 5) ( x + 3)( x + 5) I First: x •x = x2 Outside: x • 5 = 5x Inside: 3•x = 3x Last: 3•5 = 15 O (x + 3)(x + 5) = x2 + 5x + 3x +15 = x2 + 8x + 15

  3. or BOX method Ex. (x + 3)(x + 5) x + 3 x + 5

  4. Checkpoint 1. ANSWER ( ) ( ) – x 4 x 6 + 2. ANSWER ( ) ( ) – – – 3x 1 x 1 1 3x2 2x + – 24 x2 + 2x 3. ANSWER ( ) ( ) – – – 10 2x2 9x 2x 5 x 2 + Multiply Binomials Find the product.

  5. In this section, we’re going in reverse where the problem is Factoring x2 + 8x + 15 and your answer is (x + 3) (x + 5)

  6. Vocabulary Factors: are the numbers you multiply together to get another number: 3and 4 are factors of 12, because 3x4=12. 2and 5are factors of 10, because 2x5=10 Examples:

  7. The Big “X”method Factor: x2 + bx + c Think of 2 numbers that Multiply to c and Add to b multiply c #1 #2 b add Answer: (x ± #1) (x ± #2)

  8. Factor: x2 + 8x + 15 Think of 2 numbers that Multiply to 15 and Add to 8 3 x 5 = 15 3 + 5 = 8 15 3 5 multiply 8 c #1 #2 b Answer: (x + 3) (x + 5) add

  9. Quick Review Multiplying integers Positive X Positive = Positive Positive X Negative = Negative Negative X Negative = Positive Adding Integers Positive + Positive = Positive Negative + Negative = Negative Positive + Negative = Subtract and take sign of “bigger” number

  10. Factor: x2-6x + 8 Think of 2 numbers that Multiply to 8 and Add to -6 -4 x -2 = 8 -4 + -2 = -6 8 -4 -2 multiply -6 c #1 #2 b Answer: (x - 4) (x - 2) To check: Foil (x – 4)(x – 2) and see if you get x2-6x+8 add

  11. Factor: x2+ 8x - 9 Think of 2 numbers that Multiply to -9 and Add to 8 9 x -1 = -9 9 + -1 = 8 -9 -1 9 8 multiply c #1 #2 b Answer: (x - 1) (x + 9) add

  12. Checkpoint ANSWER ( ) ( ) x + 1 x + 5 b2 x2 + + 6x 7b + + 5 12 2. ANSWER ( ) ( ) b + 3 b + 4 x2 + bx + c 3. ANSWER ( ) ( ) – – s 4 s 1 s2 – 5s + 4 ANSWER ( ) ( ) – y + 12 y 1 ANSWER ( ) ( ) – x + 3 x 2 5. 4. – x2 y2 – + x 6 11y 12 + Factor Factor the expression. 1.

  13. means finding the values of x that would make the equation equal to 0. Solving ax2+bx+c = 0 Zero Product Property When the product of two expressions equals zero , then at least one of the expressions must equal zero. If (x + 9)(x + 3) = 0, then x + 9 = 0 or x + 3 = 0 . Example:

  14. Solve the equation . x2 + 2x - 15 = 0 Factor. ( ) ( ) – x 3 x 5 0 + = – or x 3 0 x 5 0 + = = – x 3 x 5 = = (mult) -15 SOLUTION -3 5 2 (add) + 3 = + 3 - 5 = - 5

  15. Solve the equation . = - 8 x2 + 9x -8 x2 x2 + + 9x 9x = 8 0 + = Factor. ( ) ( ) + x 8 x 1 0 + = Use the zero product property. + or x 8 0 x 1 0 + = = – Solve for x. x -8 x 1 = = (mult) 8 SOLUTION 1 8 9 (add) Rewrite in standard form - 8 = - 8 - 1 = - 1 Check:

  16. Checkpoint 9, 1 1. ANSWER 7, 2 2. – ANSWER 3. 5, 1 – ANSWER – x2 10x + 9 0 = y2 + 5y 14 = – – x2 5 4x = Solve a Quadratic Equation by Factoring Solve the equation.

  17. Summary: If the problem asks you to FACTOR Answer: ( )( ) If the problem asks you to SOLVE:Answer: x = ____, ____

  18. Homework 5.1 p.226 #45, 48, 51, 54 5.3 p.237 #15-21, 37-42

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