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.
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.
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.
The new thing here is that the quadratic expression is part of an equation, and you're told to solve for the values of the variable that make the equation true.
Here's how it works: of those things that we multiplied must also have been equal to zero.
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.
If the product of factors is equal to This equation is already in the form "(quadratic) equals (zero)" but, unlike the previous example, this isn't yet factored.
I MUST factor the quadratic first, because it is only when I MULTIPLY and get zero that I can say anything about the factors and solutions.