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# How do I use zero factor property in reverse?

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 : -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.