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Published byGodfrey Hudson Modified about 1 year ago

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A fun way to factor quadratics!

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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.

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

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ab a·c

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

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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.

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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

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

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

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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

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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

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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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