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Unit 3 Factoring: Common and Simple Trinomial

Unit 3 Factoring: Common and Simple Trinomial. LG : I can write quadratic equations in factored form using common factoring and simple trinomial factoring. Recall: Distributive Property Term outside of brackets is multiplied by all terms inside brackets

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Unit 3 Factoring: Common and Simple Trinomial

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  1. Unit 3Factoring: Common and Simple Trinomial LG: I can write quadratic equations in factored form using common factoring and simple trinomial factoring

  2. Recall: Distributive Property • Term outside of brackets is multiplied by all terms inside brackets General Form: a(b + c) = ab + ac Now: Common Factoring (reverse of distributive property) • Determine the largest factor (number and/or variable) that divides into each term. General Form: ab + ac = a(b + c)

  3. Common Factoring: Examples • Ex. 1: 5x - 15 • Ex. 2: 21y – 28x • Ex. 3: 10x – 15y – 30 • Ex. 4: 18x3 – 24x2 + 12x Always Look for Common Factors First!

  4. Simple Trinomial Factoring • Recall: general form of quadratic y = ax2 + bx + c • Simple Trinomial Factoring– can be used when a = 1 or ‘a’ can be removed by common factoring. • STF is like FOIL in reverse • Example: y = (x + 3) (x + 2) y = x2 + 3x + 2x + 6y = x2 + 5x + 6

  5. Factor: x2 + 7x + 6 = (x + ____ ) (x + ____ ) • To factor a simple trinomial, we need to find two numbers that add to give ‘b’ and multiply to give ‘c’ • Because the coefficient of x2 is 1, we know that the coefficient of x in each binomial is 1. • The same equation could be disguised by including a common factor: 2x2 + 14x + 12 Always Look for Common Factors First!

  6. Always Look for Common Factors First! Practice Factor y = x2+ 4x + 3 y = x2 – 10x + 9 y = x2 –x – 20 y = 2x2 – 4x + 2 y = 5x2 – 40x + 80 y = 4x2 – 24x + 36

  7. Consolidation Why bother factoring???

  8. Remember… • There are THREE different forms of the QUADRATIC EQUATION • Each is uniquely useful! • What info does factored form tell us?

  9. Always Look for Common Factors First! Homework • Pg. 230 # 6a-f • Pg. 298 # 5a-e • Pg. 307# 2, 3 • Quiz Tomorrow! • Identifying Quadratic Relations (equation, graph, table of values) • Special Features of Parabolas • Distributive property and exponent laws • FOIL

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