Question

HELP ASAP!!!!!! When you factor a quadratic, what should your answer be?

Answer 1

When you factor a quadratic (polynomial) you express it as the product of two linear polynomials.

For example:

Factor the quadratic: $x^2 -5x +6$
Answer: $(x-2)(x-3)$

This is the answer because if you expand the product (x-2)(x-3) you get the given quadratic.

To find the factors you must find the roots using the quadratic formula:

$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} = \dfrac{5\pm\sqrt{(-5)^2-4\cdot6}}{2} = \dfrac{5\pm1}{2} = \left \{ {{2} \atop {3}} \right.$

Some quadratics are irreducible, meaning that you cannot find a product like that. For example: $x^2+1$ is irreducible. You cannot factor it.