# What are all the possible rational zeros for #y=x^4-2x^3-21x^2+22x+40# and how do you find all zeros?

All the zeros are for

By signing up, you agree to our Terms of Service and Privacy Policy

The "possible" rational zeros are:

#+-1, +-2, +-4, +-5, +-8, +-10, +-20, +-40#

The actual zeros are:

That means that the only possible rational zeros are:

Start by trying each in turn:

By signing up, you agree to our Terms of Service and Privacy Policy

To find all possible rational zeros for the polynomial (y = x^4 - 2x^3 - 21x^2 + 22x + 40), you can use the Rational Root Theorem. The Rational Root Theorem states that any rational zero of a polynomial must be of the form (\frac{p}{q}), where (p) is a factor of the constant term (40 in this case) and (q) is a factor of the leading coefficient (1 in this case).

So, the possible rational zeros are all the combinations of factors of 40 divided by factors of 1. Factors of 40 are ±1, ±2, ±4, ±5, ±8, ±10, ±20, ±40, and factors of 1 are ±1.

Combining them, we get the list of possible rational zeros:

(\pm 1, \pm 2, \pm 4, \pm 5, \pm 8, \pm 10, \pm 20, \pm 40)

To find all zeros, you can use methods like synthetic division or polynomial long division along with factoring or numerical methods like Newton's method or the quadratic formula to find any remaining zeros.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you long divide #(2x^4+7) ÷ ( x^2-1)#?
- How do you divide #5x^2 - 6x^3 + 1 + 7x# by #3x - 4#?
- For what values of #k# does the quadratic #x^2+3x+k# have less than two distinct real zeros?
- What is the quotient when #2x^3 + x + 3# is divided by x + 1?
- How do you use synthetic division to divide #(4x^3+16x^2-23x-15)/(x+1/2)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7