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Based on the polynomial remainder theorem, what is the value of the function when x = 4? f(x)=x4−2x3+5x2−20x−4

Respuesta :

emarina
The answer is f(x) = 124
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ANSWER

The remainder is

[tex]124[/tex]

EXPLANATION

According to the remainder theorem, if

[tex]f(x) = {x}^{4} - 2 {x}^{3} + 5 {x}^{2} - 20x - 4[/tex]

is divided by

[tex](x - 4)[/tex]

then the remainder is given by

[tex]f(4)[/tex]

So we substitute
[tex]x = 4[/tex]
into the given function to get,

[tex]f(4) = {4}^{4} - 2 {(4)}^{3} + 5 {(4)}^{2} - 20(4) - 4[/tex]

We evaluate to get,

[tex]f(4) = 256- 2 {(64)} + 5 {(16)} - 20(4) - 4[/tex]

This will simplify to,

[tex]f(4) = 256- 128 + 80- 80 - 4[/tex]

[tex]f(4) = 124[/tex]