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what is the zeros of the polynomial function? f(x)=x^3+x^2-42x

 Jun 2, 2015

Best Answer 

 #1
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First we're going to want to factor these out.

f(x)=x^3+x^2-42x

f(x) = (x)(x^2+x-42)   ---this second part can be factored

f(x) = (x)(x+6)(x-7)    

Now that this is factored completely, we can find the zeros. The "zeros" of a polynomial funtion like we have here are the numbers you could put in for x to make f(x) = 0. 

For instance, if we put in -6 for x, we would get this:

f(x)=(-6)(-6+6)(-6-7)

f(x)=(-6)(0)(-13)       ---anything and everything multiplied by zero is zero.

f(x) = 0

 

Basically you find the opposites of the numbers next to x.

So the zeros are 0, -6, and 7.

 Jun 3, 2015
 #1
avatar+3451 
+10
Best Answer

First we're going to want to factor these out.

f(x)=x^3+x^2-42x

f(x) = (x)(x^2+x-42)   ---this second part can be factored

f(x) = (x)(x+6)(x-7)    

Now that this is factored completely, we can find the zeros. The "zeros" of a polynomial funtion like we have here are the numbers you could put in for x to make f(x) = 0. 

For instance, if we put in -6 for x, we would get this:

f(x)=(-6)(-6+6)(-6-7)

f(x)=(-6)(0)(-13)       ---anything and everything multiplied by zero is zero.

f(x) = 0

 

Basically you find the opposites of the numbers next to x.

So the zeros are 0, -6, and 7.

NinjaDevo Jun 3, 2015

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