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**Tic-Tac-Toe Factoring**

A fun way to factor quadratics!

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**ax2+bx+c Where do you begin?**

You start by identifying the a, b and c values in your quadratic expression or equation. Remember the form is ax2+bx+c You may want to write down the values next to your problem.

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**Now, for placement Draw a tic-tac-toe board.**

You will place numbers in specific spots to properly factor your problem

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**Placement of your values**

b a·c

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**Example: 1 7 6 a b a⋅c a=1 b=7 c = 6 a⋅c = 6**

Fill in the boxes like this a b a⋅c 1 7 6

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**Now, you have to do some thinking!**

Find the factors pairs of a⋅c that have a sum equal to the value of b. In our example, a⋅c=6 and b=7 So, the factor pairs of 6 are 1⋅6 and 2⋅3 where 1+6=7 and 2+3=5 Since b = 7, you would choose 1and 6 as your factors.

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Placement of Factors Place the factors beneath the a⋅c value on the Tic-Tac-Toe board (order doesn’t matter). a b a⋅c 1 7 6 Factors of a⋅c with a sum of b

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The next part is tricky! You have to find the GCF (greatest common factor) of the numbers in these boxes… …and put it here 1 7 6

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**Whew, the hard parts are done!**

Complete the multiplication equations to fill the blanks. 1 7 6 = 1 1 = X X 6 = X

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Finishing up Now, all you have to do is group some numbers to form the binomials. (x+6) (x+1) The variables go with the numbers in the left column. Rewrite the circled numbers in binomial form like this… (x+6)(x+1) You don’t usually see the 1 in front of the variable so you don’t have to put it there. 1 7 6

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**You are finished… with the factoring part, anyway.**

If you want to make sure your answer is correct, multiply the two binomials. If this results in your original trinomial, you are correct! (x+ 6)(x+ 1) = x2 + 7x + 6

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Finding the Zeros To find the zeros, use the zero product property to set each binomial equal to zero and solve for the variable. x+1=0 x+6=0 x = x =-6 The solutions are -1 and -6 These solutions indicate that the parabola intercepts the x-axis at -1 and 6.

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