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Homework, pencil, red pen, highlighter, graph paper notebook

Homework, pencil, red pen, highlighter, graph paper notebook. total:. U1D5. Have out:. Bellwork:. Solve the system of equations. 1). y = 2x – 8. 2). x = –3y – 6. y = –3x + 7. 5y + 2 = x. +1. +1. 2x – 8 = –3x + 7. 5y + 2 = –3y – 6. +3x. +3x. +3y. +3y. x = 5y + 2. y = 2x – 8.

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Homework, pencil, red pen, highlighter, graph paper notebook

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  1. Homework, pencil, red pen, highlighter, graph paper notebook total: U1D5 Have out: Bellwork: Solve the system of equations. 1) y = 2x – 8 2) x = –3y – 6 y = –3x + 7 5y + 2 = x +1 +1 2x – 8 = –3x + 7 5y + 2 = –3y – 6 +3x +3x +3y +3y x = 5y + 2 y = 2x – 8 x = 5(–1) + 2 5x – 8 = 7 8y + 2 = –6 y = 2(3) – 8 x = –5 + 2 +8 +8 –2 –2 y = 6 – 8 +1 +1 x = –3 5x = 15 8y = –8 y = –2 +1 +1 5 5 8 8 x = 3 y = –1 +1 (3, –2) (–3, –1) +1 +1 +1

  2. 2x2 + 10x Add to your notes Greatest Common Factor (GCF) Greatest common factor (GCF) – the largest (greatest) number that divides both numbers a and b evenly with no remainder. Example #1: What is the GCF of… 5 a) 20 and 15? b) 4x2 and 18x3? 2x2 The GCF is also useful for factoring. Ask yourself, “what is the GCF of the terms in 2x2 + 10x? A GENERIC RECTANGLE may help. Example #2: + 5 x 2x is the GCF of 2x2 and 10x. 2x 2x(x + 5) When you factor completely, always look for the GCF first.

  3. –10x2 –15 3x2 x2 –6x +7x Greatest Common Factor (GCF) Now, you try it. Do parts a – c now. a) x2 + 7x b) 3x2 – 6x c) –10x2 – 15 x + 7 x – 2 2x2 + 3 x 3x –5 –5(2x2 + 3) x(x + 7) 3x(x – 2)

  4. product # # sum Add to your notes... Factoring Trinomials If you are factoring a trinomial (3 terms) with an x2, use a DIAMOND PROBLEM and rewrite the expression in factored form. product sum Example: x2 – 7x – 18 Ask yourself: “What two #s multiply to –18 but add to –7?” -18 -9 2 Write the factored form. -7 (x – 9)(x + 2)

  5. Use diamond problems to factor these trinomials. If it cannot be factored, write “not factorable.” Practice: a) x2 + 9x + 8 b) x2 – 2x – 8 –8 8 –4 2 8 1 –2 9 (x – 4)(x + 2) (x + 8)(x + 1) c) x2 + x – 20 d) x2 + 7x – 9 –20 –9 –4 5 1 7 Not factorable (x + 5)(x – 4)

  6. More factoring... Add to your notes... If you are factoring a polynomial when x2 has a coefficient other than 1, you will need to use both a DIAMOND PROBLEM and a GENERIC RECTANGLE. Example #1: 2x2 – 5x – 12 ax2 + bx + c x – 4 2(–12) 2x 2x2 –8x product –24 a  c –8 3 + 3x –12 +3 b –5 sum (2x + 3)(x – 4)

  7. Product 6 7 Sum One more example: 2x2 + 7x + 3 x + 3 (2) (3) 2x 2x2 + 6x + 1 + x + 3 6 1 (2x + 1)(x + 3) Practice: Try these on your own. a) 2x2 – 3x – 5 b) 6x2 + x – 2

  8. –12 –10 +1 –3 Practice: 2x – 5 (2) (-5) a) 2x2 – 3x – 5 x 2x2 – 5x –5 2 (x + 1)(2x – 5) + 1 + 2x – 5 2x – 1 (6) (-2) b) 6x2 + x – 2 3x 6x2 – 3x –3 4 (3x + 2)(2x – 1) + 2 + 4x – 2

  9. Add to your notes... Difference of Squares A quadratic binomial (TWO TERMS) that has a perfect squarefor both terms with a subtraction sign in between them can be factored quickly. Rule: There is a pattern for Factoring Difference of Squares. a2 – b2 = (a + b)(a – b) Examples: a) x2 – 4 b) x2 – y2 c) 9x2 – 49 (x + 2)(x – 2) (x + y)(x – y) (3x + 7)(3x – 7)

  10. Product 10 –7 Sum Zero Product Property Add to your notes: Zero Product Property: If a ● b = 0, then a = 0 or b = 0. It is used to solve quadratic equations. Example: x2 – 7x = –10 Steps: +10 +10  Set the equation equal to 0. x2 – 7x + 10 = 0  Factor completely.  Set each factor equal to 0. (x – 2)(x – 5) = 0  Solve each equation. –2 –5 x – 2 = 0 or x – 5 = 0 +2 +2 +5 +5 x = 2 x = 5

  11. Assignment:Complete the worksheet. I Love Algebra 2

  12. 8/31/11 Factoring & Zero Product Property Did you remember to set up your page for today?

  13. –10 6 –3 7 Practice: b) 2x2 – 3x – 5 a) 3x2 + 7x + 2 2x – 5 (2) (-5) (3) (2) x + 2 x 2x2 – 5x 3x 3x2 + 6x –5 2 6 1 + 1 + 2x – 5 + 1 + x + 2 (x + 1)(2x – 5) (3x + 1)(x + 2)

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