Verified Answer :

Answer:

D(-3) = x^3-5x^2+ 11, remainder 34

Step-by-step explanation:

Synthesize the equation:

0  = 1 - 2 -4 + 4

Use -3

-3 = 1 -2 - 4 + 4

Continue to synthesize: Drop the first number and multiply with the -3. Add to the next number. Keep doing this.

- 3 = 1   -2   -4   4

        |    -3   15   33

       1   -5     11   34

The last number is the remainder: 34

So D(-3) = x^3-5x^2+ 11, remainder 34

The value of \(p(-3)\) is,\(p(-3)=151\)

Synthetic division :

It is a shorthand method of dividing polynomials for the special case of dividing by a linear factor whose leading coefficient is 1.

The given function is,

                   \(p(x)=x^{4}-2x^{3}-4x+4\)

We have to find  \(p(-3)\)

Substitute \(x=-3\) in above function.

            \(p(-3)=(-3)^{4}-2(-3)^{3} -4(-3)+4\\\\p(-3)=81+54+12+4\\\\p(-3)=151\)

Learn more about the  synthetic division here:

https://brainly.com/question/24662212

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