Suku BanYAk
sisa =  nilai FunGsi

Penjelasan dengan langkah-langkah:

Diketahui suku banyak f(x) = x⁵ + x⁴ - (2m-1)x³ + x² + mx + 4. Jika dibagi (x-3) sisanya 7. tentukan: a. suku banyak f(x) b. sisanya jika dibagi x + 2 c. sisanya jika dibagi x²-x-2 ​

a) suku banyak f(x) = ...

f(x) = x⁵ + x⁴ - (2m-1)x³ + x² + mx + 4
Jika dibagi (x-3) sisanya 7
x- 3= 0
x= 3
f(3) = 7
3⁵ + 3⁴ - (2m-1)3³ + 3² + m(3) + 4 =  7
243 + 81 -54m + 27  + 9 +  3m + 4= 7
-51 m = - 357
m = 7
f(x) = f(x) = x⁵ + x⁴ - {2(7) -1 }x³ + x² + 7x + 4
f(x) = x⁵ + x⁴ - 13x³ + x² + 7x + 4

b.sisa jika dibagi x + 2
x + 2= 0
x = -2
sisa  =  f(-2)
f(x) = x⁵ + x⁴ - 13x³ + x² + 7x + 4

f(-2) = (-2)⁵ + (-2)⁴ - 13(-2)³ + (-2)² + 7(-2) + 4
f(-2) = -32 +  16  + 104 + 4    - 14 + 4
f(-2) = 82
f(x) dibagi (x +2)  , sisa = 82

c. f(x) dibagi (x² -x - 2) , sisa misal s(x) = ax + b
x² - x - 2 = 0
(x + 1)(x -2) =0
x= - 1  atau x = 2

f(x) = x⁵ + x⁴ - 13x³ + x² + 7x + 4

s(-1) = f(-1)
s(-1) = 11

s(2) = f(2)
s(2) = -34

eliminasi
s(-1) = 11
s(2) = - 34    -
-3a = 45
a = - 15

s(2) = 11
b= 11 - 2a
b = 11 - 30
b = - 19

f(x) dibagi (x² -x - 2) , sisa misal s(x) = ax + b
s(x) = -15 x  -  19