Warmup Factor. 1. GCF 2. GCF 3. Grouping/GCF 4. Grouping.

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Factoring trinomials ax² + bx +c a = any number besides 1 and 0

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Presentation transcript:

Warmup Factor. 1. GCF 2. GCF 3. Grouping/GCF 4. Grouping

4.4 Factoring Trinomials Day 3 a=1 and a>1 Objective: To factor quadratic trinomials.

Remember… (x+2)(x+5) We used double distribution to multiply this. Today, we are going to work BACKWARDS!  New method…. The X!!

Example 1 1st•3rd 2nd 45 9 5 14 (x + 9)(x + 5) x2 + 14x + 45 Pick 2 #s that multiply to get the top and add to get the bottom. Those go on the sides of the X. (x + 9)(x + 5)

When a=1 you don’t have to use the box No box is necessary When a>1 you have to use the x and the box

When a>1 you must use the x and the box. This song will “teach you how to factor” https://youtu.be/OFSrINhfNsQ

First and Last Coefficients Factor the x-box way y = ax2 + bx + c Base 1 Base 2 Product ac=mn First and Last Coefficients 1st Term Factor n GCF n m Middle Last term Factor m b=m+n Sum Height

Factor the x-box way Example: Factor 3x2 -13x -10 (3)(-10)= -30 x -5 -15 2 -13 2x -10 +2 3x2 -13x -10 = (x-5)(3x+2)

Examples Factor using the x-box method. 1. x2 + 4x – 12 x +6 x2 6x x a) b) x +6 -12 4 x2 6x -2x -12 x 6 -2 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

Examples continued x -4 x x2 -4x -5x 20 a) b) x -4 -4 -5 20 -9 x x2 -4x -5x 20 -5 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

Think-Pair-Share Based on the problems we’ve done, list the steps in the diamond/box factoring method so that someone else can do a problem using only your steps. 2. Trade papers with your partner and use their steps to factor the following problem: x2 +4x -32.

Try w/ a partner 

You are up 6y2 – 13y – 5 1st•3rd 2nd -30 -15 2 -13 (2y – 5)(3y + 1)

You can do it continued 2x -7 x 2x2 -7x 2x -7 a) b) 2x -7 -7 2 -14 -5 x 2x2 -7x 2x -7 +1 Solution: 2x2 - 5x – 7 = (2x - 7)(x + 1)

Keep up the good work 3x +2 5x 15x2 10x -3x -2 a) b) 3x +2 -30 7 5x 15x2 10x -3x -2 10 -3 -1 Solution: 15x2 + 7x – 2 = (3x + 2)(5x - 1)

TOO

Example 3 So what is another way we can solve this if we can’t factor? How many solutions does this have? How can you tell?

Helpful X hints. + + + + - - + - - - + big - small - big + small + -

Mixed Review PRACTICE! GCF Difference of Squares Perfect Squares Difference of Cubes Grouping Trinomials x2 + 8x + 16

Homework Factoring WS #3