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A 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 ax.

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Presentation on theme: "A 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 ax."— Presentation transcript:

1 A fun way to factor quadratics!

2  You start by identifying the a, b and c values in your quadratic expression or equation.  Remember the form is ax 2 +bx+c  You may want to write down the values next to your problem.

3  Draw a tic-tac-toe board.  You will place numbers in specific spots to properly factor your problem

4 ab a·c

5 176 a=1 b=7 c = 6 a⋅c = 6 Fill in the boxes like this aba⋅c

6  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.

7 Place the factors beneath the a⋅c value on the Tic-Tac-Toe board (order doesn’t matter). 176 1 6 Factors of a⋅c with a sum of b a⋅cab

8  You have to find the GCF (greatest common factor) of the numbers in these boxes… …and put it here 176 1 16

9  Complete the multiplication equations to fill the blanks. 176 1 16 X = X = X = 11 6

10  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. 176 111 166

11  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) = x 2 + 7x + 6

12  To find the zeros, use the zero product property to set each binomial equal to zero and solve for the variable.  x+1=0x+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.


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