Question

Diberikan fungsi [tex]\displaystyle f(x)=x^6-10x^5-10x^4-10x^3-10x^2-10x-10[/tex]. Tentukan nilai dari [tex]\displaystyle f(11)[/tex]

Answer 1

[tex]f(11) = \boxed{\,\bf1\,}[/tex]
 

Penjelasan dengan langkah-langkah:

[tex]\begin{aligned}f(x)&=x^6-10x^5-10x^4-10x^3-10x^2-10x-10\\&=x\left(x^5-10x^4-10x^3-10x^2-10x-10\right)-10\\&=x\left(x\left(x^4-10x^3-10x^2-10x-10\right)-10\right)-10\\&=x\left(x\left(x\left(x^3-10x^2-10x-10\right)-10\right)-10\right)-10\\&=x\left(x\left(x\left(x\left(x^2-10x-10\right)-10\right)-10\right)-10\right)-10\\&=x\left(x\left(x\left(x\left(x(x-10)-10\right)-10\right)-10\right)-10\right)-10\\\end{aligned}[/tex]

Jika [tex]x=11[/tex], maka [tex]x-10 = 1[/tex], yang menyebabkan:
[tex]x\left(x\left(x\left(x\left(x(x-10)-10\right)-10\right)-10\right)-10\right) = 11[/tex]

Oleh karena itu:
[tex]f(11) = 11-10=\boxed{\,\bf1\,}[/tex]

Answer 2

Verified answer

Polinomial

f(x) = x⁶ - 10x⁵ - 10x⁴ - 10x³ - 10x² - 10x - 10

f(x) = (x - 11) H(x) + sisa

f(11) = sisa

skema horner

f(11) = 1