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:
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 2 +bx+c You may want to write down the values next to your problem.
Draw a tic-tac-toe board. You will place numbers in specific spots to properly factor your problem
176 a=1 b=7 c = 6 a⋅c = 6 Fill in the boxes like this aba⋅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⋅3 where 1+6=7 and 2+3=5 Since b = 7, you would choose 1and 6 as your factors.
Place the factors beneath the a⋅c value on the Tic-Tac-Toe board (order doesn’t matter) Factors of a⋅c with a sum of b a⋅cab
You have to find the GCF (greatest common factor) of the numbers in these boxes… …and put it here
Complete the multiplication equations to fill the blanks X = X = X = 11 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
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
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= x =-1 x =-6 The solutions are -1 and -6 These solutions indicate that the parabola intercepts the x-axis at -1 and 6.