Question

Kuis susah
Diketahui suku banyak
4x⁶+6x⁵+6x⁴-3ax³-5ax²+8x+4
jika dibagi 2x²+2x-1 dan
hasil baginya 2x⁴+x³+3x²-4x+3
sisanya bx+c

Tentukan hasil c-b

Answer 1

Polinomial

P(x) = (2x² + 2x - 1) . H(x) + S(x)

4x⁶ + 6x⁵ + 6x⁴ - 3ax³ - 5ax² + 8x + 4 = (2x² + 2x - 1)(2x⁴ + x³ + 3x² - 4x + 3) + (bx + c)

kesamaan ruas kiri dan ruas kanan

2x² × 2x⁴ = 4x⁶ ✔

6x⁵ = (2x⁴ × 2x) + (x³ × 2x²)

6x⁵ = 6x⁵ ✔

6x⁴ = 2x⁴(-1) + x³(2x) + 3x²(2x²)

6x⁴ = 6x⁴ ✔

-3ax³ = x³(-1) + 3x²(2x) - 4x(2x²)

-3a = -1 + 6 - 8

-3a = -3

a = 1

-5ax² = 3x²(-1) - 4x(2x) + 3(2x²)

-5x² = -5x² ✔

8x + 4 = -4x(-1) + 3(2x) + 3(-1) + sisa

8x + 4 = 10x - 3 + (bx + c)

sisa = 8x + 4 - (10x - 3)

bx + c = -2x + 7

b = -2

c = 7

c - b = 7 - (-2) = 9