PEMBAHASAN

Polinomial

f(x) = (x - 3)(2x + 1) H(x) + S(x)

f(x) = (2x² - 5x - 3) H(x) + (ax + b)

H(x) = hasil bagi

S(x) = sisa bagi

dibagi (x - 3), sisa (-24)

x - 3 = 0

x = 3

f(3) = -24

3a + b = -24 ... (1)

dibagi (2x + 1), sisa 11

2x + 1 = 0

x = -1/2

f(-1/2) = 11

-1/2 a + b = 11 ... (2)

Dari persamaan (1) dan (2)

3a + b = -24

-1/2 + b = 11__(-)

3 1/2 a = -35

7/2 a = -35

a = -35 × 2/7

a = -10

3a + b = -24

3(-10) + b = -24

-30 + b = -24

b = 6

Sisa pembagian f(x) oleh (2x² - 5x - 3)

= ax + b

= -10x + 6