8. Diketahui polinomial P(x) = (x² + 3x + 1)(x² − x − 1) dan Q(x) = (x − 1)(x³ + - ax² + bx+c) + d. Jika P(x) = Q(x), maka nilai a + bc + d adalah ..... -
9. Polinomial berderajat tiga jika dibagi (x² + 2x - 3) bersisa (5x – 2), jika dibagi (x² - x - 2) bersisa (x + 6). Polinomial tersebut adalah ....
9. Polinomial berderajat tiga jika dibagi (x² + 2x - 3) bersisa (5x – 2), jika dibagi (x² - x - 2) bersisa (x + 6). Polinomial tersebut adalah ....
Materi : Polinomial
Soal Nomor 8
P(x) = ( x² + 3x + 1 )( x² - x - 1 )
P(x) = x⁴ + 2x³ - 3x² - 4x - 1
Q(x) = ( x - 1 )( x³ + ax² + bx + c ) + d
Q(x) = x⁴ + ax³ + bx² + cx - x³ - ax² - bx - c + d
Q(x) = x⁴ + (a - 1)x³ + (-a + b)x² + (-b + c )x + d
____________________________/
P(x) = Q(x)
---
x⁴ = x⁴
---
( a - 1 )x³ = 2x³
a - 1 = 2
a = 3
---
( - a + b )x² = - 3x²
- (3) + b = -3
b = 3 - 3
b = 0
---
( - b + c )x = -4x
- 0 + c = -4
c = -4
---
d = -1
Kesimpulan
a = 3, b = 0, c = -4, d = -1
Nilai a + bc + d = 3 + 0(-4) + (-1) = 3 - 1 = 2
Semoga bisa membantu
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