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 [tex]p(-3)[/tex] is,[tex]p(-3)=151[/tex]
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,
[tex]p(x)=x^{4}-2x^{3}-4x+4[/tex]
We have to find [tex]p(-3)[/tex]
Substitute [tex]x=-3[/tex] in above function.
[tex]p(-3)=(-3)^{4}-2(-3)^{3} -4(-3)+4\\\\p(-3)=81+54+12+4\\\\p(-3)=151[/tex]
Learn more about the synthetic division here:
https://brainly.com/question/24662212
