Presentation on theme: "Tic-Tac-Toe Factoring"— Presentation transcript:
1Tic-Tac-Toe Factoring A fun way to factor quadratics!
2ax2+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 isax2+bx+cYou may want to write down the values next to your problem.
3Now, for placement Draw a tic-tac-toe board. You will place numbers in specific spots to properly factor your problem
5Example: 1 7 6 a b a⋅c a=1 b=7 c = 6 a⋅c = 6 Fill in the boxes like thisaba⋅c176
6Now, 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=7So, the factor pairs of 6 are 1⋅6 and 2⋅3where 1+6=7 and 2+3=5Since b = 7, you would choose 1and 6 as your factors.
7Placement of FactorsPlace the factors beneath the a⋅c value on the Tic-Tac-Toe board (order doesn’t matter).aba⋅c176Factors of a⋅c with a sum of b
8The next part is tricky!You have to find the GCF (greatest common factor) of the numbers in these boxes……and put it here176
9Whew, the hard parts are done! Complete the multiplication equations to fill the blanks.176=11=XX6=X
10Finishing upNow, 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.176
11You 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
12Finding the ZerosTo 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=0x = x =-6The solutions are -1 and -6These solutions indicate that the parabola intercepts the x-axis at -1 and 6.