How To Solve Factoring Problems

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.

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Problem: \(4x^2-9\) Solution: \((2x 3)(2x-3)\) Problem: \(x^4-81\) Solution: \((x^2 9)(x 3)(x-3)\) Problem: \(x^2-7x-18\) Solution: \((x-9)(x 2)\) Here are some questions other visitors have asked on our free math help message board.

Perhaps you can learn from the questions someone else has already asked.

This lesson covers many ways to solve quadratics, such as taking square roots, completing the square, and using the Quadratic Formula. (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.) You've already factored quadratic expressions.

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.

Returning to the exercise: This equation is in "(quadratic) equals (zero)" form, so it's ready for me to solve by factoring. Try the entered exercise, or type in your own exercise.You may want to read up on the quadratic formula to help your algebra knowledge rather than relying on this solver.Afterall, the point is to learn the concept, not just get the answer... Also, while this calculator page is tailored for algebraic expressions, you might be looking to solve for the prime factorization of a number.I can't conclude anything about the individual terms of the unfactored quadratic (like the I'm not done, though, because the original exercise told me to "check", which means that I need to plug my answers back into the original equation, and make sure it comes out right.In this case, I'll be plugging into the expression on the left-hand side of the original equation, and verifying that I end up with the right-hand side; namely, with When an exercise specifies that you should solve "and check", the above plug-n-chug, they're looking for you to show that you plugged your answer into the original exercise and got something that worked out right.For example, finding all the prime numbers that divide into 56 (7 and 2).We also have a page on the greatest common factor and a link for least common multiple available.Only then can I factor and solve: Tempting though it may be, I cannot set each of the factors on the left-hand side of the equation equal to the other side of the equation and solve. Instead, I first have to multiply out and simplify the left-hand side, then subtract the was not equal to zero.There is absolutely no justification for making that assumption!Try typing these expressions into the calculator, click the blue arrow, and select "Factor" to see a demonstration.Or, use these as a template to create and solve your own problems.


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