There are different ways that you can use to solve quadratic equations; it can be through using square roots, completing the square or to use the quadratic formula. You may have learnt how to factor but what it is new with this expression is that quadratic expression may be a part of the equation so you should solve values of a variable which make an equation to be true.
For solving quadratic through factoring, there is a need to use the Zero product property. It is the property which says that when something is not obvious but when it may have been pointed out.
Zero Product Property: when two or even more things are put together and results become zero, it means that a number of these that have been multiplied may have been equal to a zero. This means that the easy way to get zero while multiplying the factors is when among the factors there is a zero.
This means when two or even more factors are being multiplied and the answer is zero, then one of such factors already equal zero. It is easy to set every factor to equal to zero and to solve resulting equation for a solution on original equation.
It is easy to draw a helpful conclusion on the factors that any of the factors may be equal at zero to make sure that the factors do equal at zero, this is the product on its own is zero. When the product of a factor is something else but not zero, then there is no way of making such claim on the values of such factors.
This is why, if it comes to solve quadratic equations through factoring, there is a need to have an equation that the quadratic expression is zero so that the attempt of solving such quadratic equation can be done by factoring.
If the exercise asks to solve and to check, they want someone to plug the answer he gets in original exercise and to get something which may work out. The same checking technique should be used in verifying the answer and in solving the exercise. The example is when someone is not sure of a factor and then solve the question at the next test, it is about plugging the answer in an original equation and to confirm that the solution may lead to the true statements.
When the equation is not the quadratic or equals to zero, it should not be solved yet. The right thing that someone should do is getting the terms on a side while the zero is found on the other side.
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