Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point - Example 3

[sarazuu]

so its third root would be - 39/5 ?

[jeffreykral]

I would also like to know why the unknown term is solved by using (x-c). Is that always the case? Please explain why and how you know to use that and if there are any other situations that require using (x+c)

[IronChefWannabe]

@ImCausingTraumaZ

so you're saying you ALWAYS write (x-c) and never (x+c) ?

because if he had written (x+c) to begin with then he would have ended up with c = -39/5 instead of c= 39/5

[dskrilla1]

@ImCausingTraumaZ

Honestly, no. I don't see that. At all.

[bar95900]

What math level is this Patrick?

[IronChefWannabe]

why start off with x-c and not x+c

[patrickJMT]

@IronChefWannabe if c is a root, then (x - c) is a factor

[IronChefWannabe]

@patrickJMT

so you're saying you ALWAYS write (x-c) and never (x+c) because that's just the way the formula is ?

[patrickJMT]

@IronChefWannabe what formula?

[IronChefWannabe]

@patrickJMT

the formula

(x something a) (x something b) (x - c)

I understand the somethings are going to be pposite signs of the roots.

So if the roots are +1 and -2 than I understand that its (x - 1) and (x + 2)

but its the (x - c) that confuses me.

If they stated that the 3rd root was positive then I would understand that you use the opposite sign and make it (x - c).

But they never state that. How do you know the 3rd root isn't negative ?

If it was, then shouldn't yu use (x + c) ?

[patrickJMT]

@IronChefWannabe yes, that is correct. i think your confusion is that when you see the variable 'c' you take it to be positive (since you do not see a negative sign). but 'c' could easily be negative, for example, c = -2. in that case, the factor: (x - c) becomes (x - (-c)) = ( x + c )

[patrickJMT]

@IronChefWannabe so, it is perfectly correct to write: (x - c), where c is a zero/root, in all cases.