Lesson 9.6 Factor

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Presentation transcript:

Lesson 9.6 Factor 𝒂𝒙 𝟐 +𝒃𝒙+𝒄 Essential Question: How do you factor trinomials of the form 𝑎𝑥 2 +𝑏𝑥+𝑐?

Before we start… Consider 2 𝑥 2 +9𝑥+9 Consider the binomials 2𝑥+9 and 𝑥+1. Multiply the first two terms. Multiply the last two terms. Find the middle terms now. Consider 2 𝑥 2 +9𝑥+9 Consider the binomials 2𝑥+3 and 𝑥+3. Multiply the first two terms. Multiply the last two terms. Find the middle terms now.

What is factoring? 𝑥+3 𝑥+4 = 𝑥 2 +7𝑥+12 Undoing the multiplication of polynomials 𝑥+3 𝑥+4 = 𝑥 2 +7𝑥+12

How do you factor a trinomial in the form 𝑎𝑥 2 +𝑏𝑥+𝑐? You are looking for factors of a and c that add/subtract to get b.

How do you know what signs to use? 𝑎𝑥 2 +𝑏𝑥+𝑐 𝑎𝑥 2 +𝑏𝑥−𝑐 Positive means the same signs Negative means the opposite signs

Factor 2𝑥 2 −7𝑥+3

Factor 3𝑛 2 +14𝑛−5

Factor 3𝑡 2 +8𝑡+4

Factor 4𝑠 2 −9s+5

Factor 2𝑥 2 −13𝑥+6

Factor 4𝑎 2 +11𝑎−3

Factor −3𝑤 2 −13𝑤−4

Factor −4𝑥 2 +12𝑥+7

Factor −2𝑦 2 −5𝑦−3

How do you solve polynomial equations? Set the equation equal to 0. Factor the polynomial. Set each factor equal to 0. Solve each factor.

Solve 2𝑐 2 −11𝑐+5=0

Solve 2𝑦 2 +𝑦−10=0

Solve 9𝑤 2 +3𝑤−2=0

Solve 2𝑥 2 −3𝑥=35

Solve 8𝑠 2 −2𝑠=3

Solve 6𝑥 2 −5𝑥=14

Solve 7𝑎 2 +2𝑎=5

How do you factor trinomials of the form 𝑎𝑥 2 +𝑏𝑥+𝑐?

Ticket Out the Door Factor 2𝑥 2 −7𝑥+3