# How do you find the zeroes for #3x^4 - 4x^3 + 4x^2 - 4x + 1#?

##### 2 Answers

#### Answer:

The zeros are

#### Explanation:

The Rational Roots Theorem implies that if

If you check

Doing long division (or synthetic division) leads to

#### Answer:

Use the rational zeros theorem (or the sum of the coefficients "shortcut") to find that

#### Explanation:

So,

# = (x-1)[x^2(3x-1)+1(3x-1)]#

# = (x-1)[(x^2+1)(3x-1)]#

# = (x-1)(3x-1)(x^2+1)#

The real zeros are