# What are all the possible rational zeros for #f(x)=x^3+3x^2+x-2# and how do you find all zeros?

##### 2 Answers

All the zeroes of

only rational zero is

#### Explanation:

We observe that the sum of the co-effs. of

**not** a factor.

Also, the sum of the co-effs. of odd-powered terms is 2, and that

of even-powered 1, Since, these are not equal, so,

**not** a factor.

Now,

Hence, the possible linear factors

We have already verified that **not** factors.

For

Now,

For the Quadratic

Thus, all the zeroes of

only rational zero is

Enjoy Maths.!

All the possible rational zeros for f(x) are

all zeros are -2 (rational) and

#### Explanation:

All the possible rational zeros for f(x) are the factors of the known term 2:

You would apply the remainder rule to find the first zero:

and you conclude that **1 isn't a zero** for f(x);

and you conclude that **-1 isn't a zero** for f(x);

and you conclude that **2 isn't a zero** for f(x);

then **-2 is a zero** for f(x)

Then you would divide f(x) by (x+2) and get the polynomial:

that, solved by the quadratic formula, will give the not rational zeros: