Diketahui f(x) = x^4 - 4x³ + 7x² + ax + b. Jika f(x) dibagi x²-2x-3 bersisa 8x +10, maka nilai a+ b adalah........ Jika f(x) dibagi x²-3x+2 sisanya (5x-3) . Jik

jawab
1)
f(x)  = x⁴ - 4x₃  + 7x₂ + ax + b
s(x) = 8x +10

p(x) = x² -2x - 3
p(x)= 0
x² -2x - 3 =0
(x - 3)(x  +1)=0
x= 3 atau x = -1

f(x) = s(x)
f(3) = s(3)
3⁴ -4.3³ + 7.3² + a(3) + b = 8(3) + 10
81 - 108 + 63 + 3a + b = 34
36 + 3a + b = 34
3a + b = -2 .....(i)

f(-1) = s(-1)
(-1)⁴ - 4.(-1)³ + 7. (-1)² + a(-1) + b = 8(-1) +10
1 +4 + 7 -a + b = -8 +10
12 - a + b = 2
-a + b = - 10 ....(ii)

(i dan ii)
3a + b = -2
-a + b = -10.....(-)
4a = 8
a = 2

-a + b= 10
-2 + b  = 10
b = 12

a + b = 2 + 12 = 14

2)  s(x)= 5x - 3
x-2 = 0
x= 2
s(2) = 5(2) - 3 = 7
sisa dibagi ( x-2) =7