How to Factor Equations

A quadratic equation's factors are expressions with two terms.
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One way of solving quadratic equations is by factoring the equation and then solving each part of the equation for zero.

Factoring Quadratic Equations

    Solve the equation for zero.

    Example: (x^2)-7x=18 --->(x^2)-7x-18=0 by subtracting 18 from both sides.

    Factor the left side of the equation by determining two numbers that add up to, in this case, -7, and can be multiplied together to get -18.

    Example: -9 and 2 -9*2=-18 -9+2=-7

    Put the left side of the quadratic equation into two factors that can multiplied out to get the original quadratic equation.

    Example: (x-9)(x+2)=0

    Because x_x=x^2 -9x+2x=-7x -9_2=-18

    So you can see that all the elements of the original quadratic equation are there.

    Solve each factor of the equation for zero to get your solution set for the quadratic equation.

    Example: x-9=0 so x=9 x+2=0 so x=-2

    So, your solution set for the equation is {9, -2}

    Things You'll Need

    • Equation
    • Paper
    • Pencil