This document provides steps to factor the quadratic equation 5x^2 + 32x + 12 using the tic-tac-toe method. The steps are: 1) place the first and last terms in the top left and center squares, 2) multiply them diagonally, 3) find factors that add up to the middle term, 4) place the factors in the top center and left center boxes, 5) pull out common factors and place them on the bottom, 6) the factored form is (x+6)(5x+2). The factored form of the given equation is (x+6)(5x+2).

1. COMPLICATED
QUADRATIC
EQUATION
(Tic/Tac/Toe)

2. These are harder
to solve as you
have to consider
factors on the first
and last term.
Factor
5x2
+ 32x + 12

3. Here are some step you can follow to factor it using the
Tic /Tac/Toe method
1. Place the first and last term in the top left and center squares
5x2
+ 3x + 12
5x2
12

4. 1. Place the first and last term in the top left and center squares
5x2
12
2. Multiply them diagonally
5x2
* 12 = 60x2
60x2

5. 1. Place the first and last term in the top left and center squares
5x2
12
2. Multiply them diagonally
5x2
* 12 = 60x2
60x2
3. Now find factors of 60x2
that
adds up to value of “b” (32x)
1x . 60x2x . 30x
3x . 20x 4x . 15x
That
2x + 30x = 32x
4.Place these in the top center and left center boxes.
2x, 30x
2x
30x

6. 1. Place the first and last term in the top left and center squares
5x2
12
2. Multiply them diagonally
5x2
* 12 = 60x2
60x2
3. Now find factors of 60x2
that
adds up to value of “b” (32x)
1x . 60x2x . 30x
3x . 20x 4x . 15x
That
2x + 30x = 32x
4.Place these in the top center and left center boxes.
2x, 30x
2x
30x
5. Now pull out the common factors across and down and
place them at the bottom side
x
6
5x 2

7. 1. Place the first and last term in the top left and center squares
5x2
12
2. Multiply them diagonally
5x2
* 12 = 60x2
60x2
3. Now find factors of 60x2
that
adds up to value of “b” (32x)
1x . 60x2x . 30x
3x . 20x 4x . 15x
That
2x + 30x = 32x
4.Place these in the top center and left center boxes.
2x, 30x
2x
30x
5. Now pull out the common factors across and down and
place them at the bottom side
x
6
5x 2
6.Your answer will be
(x+ 6)

8. 1. Place the first and last term in the top left and center squares
5x2
12
2. Multiply them diagonally
5x2
* 12 = 60x2
60x2
3. Now find factors of 60x2
that
adds up to value of “b” (32x)
1x . 60x2x . 30x
3x . 20x 4x . 15x
That
2x + 30x = 32x
4.Place these in the top center and left center boxes.
2x, 30x
2x
30x
5. Now pull out the common factors across and down and
place them at the bottom side
x
6
5x 2
6.Your answer will be
(x+6) (5x + 2)

9. Factor of
5x2
+ 32x + 12
is
(X+6) (5x+2)

10. Factor of
5x2
+ 32x + 12
is
(X+6) (5x+2)