Find all the roots of f(x)=4x^3-3x^2-22x-15

Question

anonymous · Answer

guess a root first
try an easy guess

anonymous · Answer

some math teacher or graduate student had to make up this problem
the easiest root to make is 1, but in this case 1 does not work because$$ 4-3-22-15\neq 0$$
second easiest one to make is $-1$ so always check that second

primeralph · Answer

A trick: if all the coefficients somehow add up to 0, then 1 or -1 may be a root.

primeralph · Answer

-4-3+22-15 = 0, so -1 is a root.

anonymous · Answer

and then 3 seemed to work as well

anonymous · Answer

is there any way to tell how many roots there are?

primeralph · Answer

Yes. The highest power indicates the number of roots, which may be complex or real. 
In this case, the highest power is 3, so there are 3 roots.

anonymous · Answer

So, I have found 2/3 of the roots how do I find the 3rd?

primeralph · Answer

You can use long division.

anonymous · Answer

factor like before

anonymous · Answer

using synthetic division?

primeralph · Answer

Guess that's what they call it.
Or if you're really into it, you can set the third root to be say d, and then expand. Then you'll get a set of equations by comparing coefficients.

anonymous · Answer

im trying to factor $$4x^2+9x+5$$

primeralph · Answer

Yeah, 4 and 5.

primeralph · Answer

As in, 4x^2 + 5x+4x+5.

anonymous · Answer

(im not the best at factoring)..

primeralph · Answer

I just did it.

primeralph · Answer

And you should learn it.

anonymous · Answer

I know, I have tried to. I just cannot seem to be very good at it..

primeralph · Answer

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