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Tic-Tac-Toe Factoring

Tic-Tac-Toe Factoring. A fun way to factor quadratics!. Where do you begin?. You start by identifying the a , b and c values in your quadratic expression or equation. Remember the form is a x 2 + b x+ c You may want to write down the values next to your problem. Now, for placement.

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Tic-Tac-Toe Factoring

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  1. Tic-Tac-Toe Factoring A fun way to factor quadratics!

  2. 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.

  3. Now, for placement • Draw a tic-tac-toe board. • You will place numbers in specific spots to properly factor your problem

  4. Placement of your values

  5. Example: a=1 b=7 c = 6 a⋅c = 6 Fill in the boxes like this a b a⋅c

  6. Now, you have to do some thinking! • Find the factorspairs of a⋅cthat have a sum equal to the value of b. • In our example, a⋅c=6and 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 6as your factors.

  7. Placement of Factors • Place the factors beneath the a⋅cvalue on the Tic-Tac-Toe board (order doesn’t matter). a b a⋅c Factors of a⋅cwith a sum of b

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

  9. Whew, the hard parts are done! • Complete the multiplication equations to fill the blanks. = = 1 1 X X 6 = X

  10. 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.

  11. 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

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

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