# How do you factor completely #P(k)=k^5+3k^4-5k^3-15k^2+4k+12#?

##### 2 Answers

#### Explanation:

Using the Rational Factor Theorem we know that any solutions to

will be factors of

That is rational zeros of the given function will be

Evaluating

gives us 5 distinct zeros:

Since

The factors are therefore:

#### Explanation:

We find that, the sum of the co-effs. is

Again, the sum of the co-effs. of the even-powered terms

(i.e.,

are equal.

Thus,

Now,

Now, knowing that

Enjoy Maths.!