How do I use zero factor property in reverse?

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How do I use zero factor property in reverse?

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Answer 1 · 2014-08-22T05:25:29

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:

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

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

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

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

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

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

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How do I use zero factor property in reverse?

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