Solving Quadratic Equations by Factoring – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Do you need help? Watch the Video Lesson for this Practice Problem. Solving Quadratic Equations by Factoring

By this time, you may already be familiar with the zero property of multiplication. You may also recall that the FOIL method is a handy tool when multiplying two binomials. These two techniques come in handy when using the factoring method for solving quadratic equations.

The zero property of multiplication tells us that if at least one of the factors is equal to zero, then the product is equal to zero.

The FOIL method tells us that (x + m)(x + n) = x^2 + nx + mx + mn = x^2 + (n + m)x + nm.

So, if we are given the quadratic equation: x^2 + bx + c = 0, we just need to do the following:
Using the reverse FOIL method, find the factors of c (m and n) that will make both of the following statements true: m * n = c and m + n = b.
Express the equation in the form (x + m)(x + n) = 0.
Because of the zero property, we can equate x + m = 0 and x + n = 0.
Replace x with either values of the roots in the original equation to check.

When you watch this video, you will see a clearer picture of solving quadratic equations by factoring with concrete examples.

Analyze Functions Using Different Representations.

CCSS.MATH.CONTENT.HSF.IF.C.8.A

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Exercises in this Practice Problem
State the solutions of the equation $(x+6)(x-1)=0$.
Solve the quadratic equation.
Determine the solutions of the factorized equations.
Multiply the two binomials using the FOIL method.
Check the factorization.
Determine the code.