Tic-Tac-Toe FactoringA fun way to factor quadratics!

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.

Where do you begin?

Draw a tic-tac-toe board.

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

Now, for placement

Placement of your values

a b a·c

672 xxExample:

1 7 6

a=1b=7c = 6a⋅c = 6

Fill in the boxes like this

a b a⋅c

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⋅3where 1+6=7 and 2+3=5

Since b = 7, you would choose 1and 6 as your factors.

Now, you have to do some thinking!

Place the factors beneath the a⋅c value on the Tic-Tac-Toe board (order doesn’t matter).

Placement of Factors

1 7 6

1

6

Factors of a⋅c with a sum of b

a⋅c a b

You have to find the GCF (greatest common factor) of the numbers in these boxes…

…and put it here

The next part is tricky!

1 7 6

1

1 6

Complete the multiplication equations to fill the blanks.

Whew, the hard parts are done!

1 7 6

1

1 6X =X=

X =1 1

6

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.

Finishing up

1 7 6

1 1 1

1 6 6

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

You are finished…

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 -1 -1 -6 -6 0 -1 0 -6

x =-1 x =-6

The solutions are -1 and -6 These solutions indicate that the parabola

intercepts the x-axis at -1 and 6.

Finding the Zeros