*Therefore, we were able to create two equations and determine two solutions from this observation.We are left with three factors: 5x, (x 3), and (x - 3). " section, at least one of the three factors must be equal to zero.And making that assumption would cause us to lose half of our solution to this equation. I'll apply the difference-of-squares formula that I've memorized: You can use the Mathway widget below to practice solving quadratic equations by factoring.*

The above, where I showed my checks, is all they're wanting. By the way, you can use this "checking" technique to verify your answers to any "solving" exercise.

So, for instance, if you're not sure of your answer to a "factor and solve" question on the next test, try plugging your answers into the original equation, and confirming that your solutions lead to true statements.

This equation is not in "(quadratic) equals (zero)" form, so I can't try to solve it yet.

The first thing I need to do is get all the terms over on one side, with zero on the other side.

These methods work well for equations like x 2 = 10 - 2x and 2(x - 4) = 0.

But what about equations where the variable carries an exponent, like x Solving the first subproblem, x - 2 = 0, gives x = 2. You should observe that as long as a does not equal 0, b must be equal to zero.

Put another way, the only way for us to get zero when we multiply two (or more) factors together is for one of the factors to have been zero.

So, if we multiply two (or more) factors and get a zero result, then we know that at least one of the factors was itself equal to zero.

In particular, we can set each of the factors equal to zero, and solve the resulting equation for one solution of the original equation.

We can only draw the helpful conclusion about the factors (namely, that one of those factors must have been equal to zero, so we can set the factors equal to zero) if the product itself equals zero.

## Comments Solve Factoring Problems

## Solve a Quadratic Equation by Factoring - WebMath

Solve a Quadratic Equation by Factoring. Well, suppose you have a quadratic equation that can be factored, like. So the solutions must be x=-2 and x=-3. Note that if your quadratic equation cannot be factored, then this method will not work. Type the quadratic equation here in general form. =0.…

## Solving Quadratics by Factoring - mesacc.edu

Use a factoring strategies to factor the problem. Step 3 Use the Zero Product Property and set each factor containing a variable equal to zero. Step 4 Solve each factor that was set equal to zero by getting the x on one side and the answer on the other side.…

## Cymath Math Problem Solver with Steps Math Solving App

Solve calculus and algebra problems online with Cymath math problem solver with steps to show your work. Get the Cymath math solving app on your smartphone!…

## Solving Quadratic Equations by Factoring Purplemath

This lesson covers many ways to solve quadratics, such as taking square roots, completing the square, and using the Quadratic Formula. But we'll start with solving by factoring. Before reaching the topic of solving quadratic equations, you should already know how to factor quadratic expressions. If not, first review how to factor quadratics.…

## Factoring Calculator - Free Math Help

Enter your problem in the box above and click the blue arrow to submit your question you may see a range of appropriate solvers such as "Factor" appear if there are multiple options. If you're not sure what to enter, look over the sample problems below to see the types of expressions this tool can factorise.…

## Step-by-Step Math Problem Solver

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose.…

## Mathway Algebra Problem Solver

Free math problem solver answers your algebra homework questions with step-by-step explanations. Mathway. While we cover a very wide range of problems, we are.…

## Factoring Calculator - MathPapa

Shows you step-by-step how to factor expressions! This calculator will solve your problems.…

## Solve by Factoring Lessons Wyzant Resources

The Solve by Factoring process will require four major steps Move all terms to one side of the equation, usually the left, using addition or subtraction. Factor the equation completely. Set each factor equal to zero, and solve. List each solution from Step 3 as a solution to the original.…

## Factoring - Step-by-Step Math Problem Solver

Step 5 Step 1 Find the key number 4 -10 = -40. Step 2 Find factors of - 40 that will add to give the coefficient of the middle term +3. Step 3 Rewrite the original problem by breaking the middle term into the two parts found in step 2. 8x - 5x = 3x, so we may write. Step 4 Factor this.…