# How do I use zero factor property in reverse?

Aug 22, 2014

You use it to determine the polynomial function.

We can use it for higher degree polynomials, but let's use a cubic as an example. Suppose we have the zeros: -3, 2.5, and 4. So:

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

$x = 2.5$
$x = \frac{5}{2}$
$2 x = 5$ multiply both sides by denominator
$2 x - 5 = 0$

$x = 4$
$x - 4 = 0$

So, the polynomial function is $P \left(x\right) = \left(x + 3\right) \left(2 x - 5\right) \left(x - 4\right)$. Note that we can leave the second root as $\left(x - 2.5\right)$, because a proper polynomial function has integer coefficients. It's also a good idea to put this polynomial into standard form:

$P \left(x\right) = 2 {x}^{3} - 7 {x}^{2} - 19 x + 60$

The common mistake in this problem is the sign of the roots. So make sure you do the individuals steps to avoid this mistake.