How do I use the zero factor property when solving a quadratic equation?

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How do I use the zero factor property when solving a quadratic equation?

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Answer 1 · 2014-08-18T00:17:53

You use the zero factor property after you have factored the quadratic to find the solutions.

It is best to look at an example: $x^{2} + x - 6 = 0$ $x^2+x-6=0$

This factors into:

$(x + 3) (x - 2) = 0$ $(x+3)(x-2)=0$

We find our solutions by setting each factor to zero and solve:

$x + 3 = 0$ $x+3=0$
$x = - 3$ $x=-3$

or

$x - 2 = 0$ $x-2=0$
$x = 2$ $x=2$

Previous answer (I was thinking some more complicated before):

You are not using the words precisely. You use the factor theorem with the factor property. The factor theorem states that if you find a $k$ $k$ such that $P (k) = 0$ $P(k)=0$ , then $x - k$ $x-k$ is a factor of the polynomial. The factor property states that $k$ $k$ must a factor of the constant term in $P (x)$ $P(x)$ .

Having said all that, you wouldn't normally use the factor theorem or factor property to solve a quadratic; they are many used to find factors of higher order polynomials. Once you reduce the higher order polynomial to a quadratic, you use regular factoring methods such as FPS or PFS: Factors, Product, and Sum.

$P (x) = a x^{2} + b x + c$ $P(x)=ax^2+bx+c$

The problem with the factor theorem and factor property is that it's not as easy to use when $a \neq 1$ $a!=1$ .

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How do I use the zero factor property when solving a quadratic equation?

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