Question

How do I use zero factor property in reverse?

Answer 1

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=5/2`
`2x=5` multiply both sides by denominator
`2x-5=0`

`x=4`
`x-4=0`

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

`P(x)=2x^3-7x^2-19x+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.