# How do you evaluate #f(x)=-x^5-4x^3+6x^2-x# at x=-2 using direct substitution and synthetic division?

Three Drop the first coefficient of the dividend below the division symbol.

Four Multiply the result by the constant, and put the product in the next column.

Five Add down the column.

Six Repeat Steps Four and Five until you can go no farther.

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

To evaluate the function ( f(x) = -x^5 - 4x^3 + 6x^2 - x ) at ( x = -2 ) using direct substitution, follow these steps:

- Substitute ( x = -2 ) into the function.
- Evaluate the expression.

Direct Substitution:

[ f(-2) = -(-2)^5 - 4(-2)^3 + 6(-2)^2 - (-2) ] [ f(-2) = -(-32) - 4(-8) + 6(4) + 2 ] [ f(-2) = 32 + 32 + 24 + 2 ] [ f(-2) = 90 ]

To evaluate the function using synthetic division, follow these steps:

- Set up the coefficients of the polynomial in descending order of powers of ( x ).
- Perform synthetic division with ( x = -2 ).
- Evaluate the result.

Coefficients of ( f(x) = -x^5 - 4x^3 + 6x^2 - x ): [ -1, 0, -4, 6, 0, -1 ]

Synthetic Division:

[ \begin{array}{c|rrrrr} -2 & -1 & 0 & -4 & 6 & 0 & -1 \ \hline & & 2 & -4 & 16 & -44 & 88 \ \end{array} ]

The result of the synthetic division is 88.

Therefore, ( f(-2) = 88 ).

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 determine the binomial factors of #x^3+4x^2-x-4#?
- How do you use synthetic division to divide #3x^3 - x^2 + 8x-10# by #x-1#?
- How do you divide #(r^3+6r^2-21r-18) div (r-3)# using synthetic division?
- One factor of #f(x)=4x^3-4x^2-16x+16# is #(x-2)#. What are all the roots of the function?
- How do you divide #(r^2+6r+15)div(r+5)# using synthetic division?

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