Solve Quadratics by Factoring

Solve a quadratic by factoring

When a quadratic equation is written in the form

[ ax^2+bx+c=0, ]

you can often solve it by rewriting the left side as a product of two factors.

1) Put the equation in standard form

Make sure everything is on one side and the other side is 0. If needed, combine like terms first.

2) Factor the quadratic

Rewrite the trinomial as a product, such as

[ (x+p)(x+q)=0. ]

If the leading coefficient is not 1, look for factors that multiply to the constant term and combine to match the middle term.

3) Use the zero-product idea

If a product equals 0, then at least one factor must be 0. Set each factor equal to 0 and solve the resulting linear equations.

4) Simplify your answers

Write each solution in simplest form. You may get one, two, or repeated solutions.

5) Check your work

Substitute each solution back into the original equation. If the left side becomes 0, the solution is correct.

Helpful tip

If the quadratic does not factor nicely with integers, recheck your factoring steps carefully. Factoring errors are the most common mistake.