How do you solve : 3x^4 - 11x^3 -x^2 + 19x + 6

You can't use long division in this equation.

Step-by-step explanation:

This is a polynomial so we can use rational roots Theorem to solve the equation.

The rational roots simply states that the roots of a polynomial, in the form of

The possible roots of the polynomial are the factors of

p/r.

We say r^0 to represent the constant and p to represent the leading coeffceint.

So the rational roots states the possible roots of a polynomial is

the factors of leading coeffceint/ the factors of the constant.

In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.

The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are

positive or negative (1,1/2, 1/3,1/6, 3, 3/2).

Now, we see which of the following roots will that the polynomial, P will equal zero.

It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.

So our factored version of the polynomial is

Now can we continue and factor the right side of the factors.

3 also works so x-3 is a factor as well so

Now factor the quadratic using factoring by grouping

So our factor are

So in conclusion our factors are

And our x values are -1/3, 2, -1, and 3.

answer: the equation matches the regression

step-by-step explanation:

true? is that what you're asking or do you mean something else?