.... 6. Jika suatu polinomial P(x) disusun oleh g(x) = 5x - 1, h(x) = x³ + 3x - 2 dan s(x) = 15 sedemikian sehingga P(x) = g(x).h(x) + s(x), maka P(x) adalah .... 7. Diketahui f(x) = 6x6 - 7x5 - 10x4 + 7x³7x² + 2x - 20 dan g(x) = (3x4 - 5x³ + 2x² + ax + 2)(2x² + bx − 3) + cx − 14. Jika f(x) = g(x) dan
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Materi : Polinomial
Soal Nomor 5
g(x) = 5x - 1
h(x) = x³ + 3x - 2
s(x) = 15
____________
P(x) = g(x) . h(x) + s(x)
P(x) = ( 5x - 1 )( x³ + 3x - 2 ) + 15
P(x) = 5x⁴ - x³ + 15x² - 13x + 2 + 15
P(x) = 5x⁴ - x³ + 15x² - 13x + 17
Soal Nomor 6
f(x) = 6x⁶ - 7x⁵ - 10x⁴ + 7x³ - 7x² + 2x - 20
g(x) = ( 3x⁴ - 5x³ + 2x² + ax + 2 )( 2x² + bx - 3 ) + cx - 14
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(2x²) => 6x⁶ - 10x⁵ + 4x⁴ + (2a)x³ + 4x²
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(bx) => (3b)x⁵ - (5b)x⁴ + (2b)x³ + (ab)x² + (2b)x
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(-3) => - 9x⁴ + 15x³ - 6x² - (3a)x - 6 + cx - 14
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g(x) = 6x⁶ + (3b - 10)x⁵ + (-5b - 5)x⁴ + (2a + 2b + 15)x³ + (ab - 2)x² + (2b + c)x - 20
____________________________/
f(x) = g(x)
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6x⁶ = 6x⁶
---
( 3b - 10 )x⁵ = - 7x⁵
3b - 10 = - 7
3b = 10 - 7
3b = 3
b = 1
---
( - 5b - 5 )x⁴ = - 10x⁴
- 5b - 5 = - 10
5b = 10 - 5
5b = 5
b = 1
---
( 2a + 2b + 15 )x³ = 7x³
2a + 2(1) + 15 = 7
2a + 17 = 7
2a = 7 - 17
2a = -10
a = -5
---
( ab - 2 )x² = - 7x²
ab - 2 = -7
ab = 2 - 7
ab = - 5
---
( 2b + c )x = 2x
2(1) + c = 2
c + 2 = 2
c = 2 - 2
c = 0
Kesimpulan
a = -5 , b = 1 , c = 0
______________/
Nilai a - bc = - 5 - ( 1 . 0 ) = - 5 - 0 = -5
Semoga bisa membantu
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