Diketahui suku banyak p(x)=ax³+5x²+bx-3 mempunyai sisa 25 jika bagi oleh(x-2) dan sisa -35 jika dibagi(x+4).Nilai dari 2a+b adalah

diketahui suku banyak p(x)=ax³+5x²+bx-3 mempunyai sisa 25 jika bagi oleh(x-2) dan sisa -35 jika dibagi(x+4).Nilai dari 2a+b adalah

Suku Banyak

P(x) = ax³ + 5x² + bx – 3
P(x) = (x – 2) H(x) + S(x)
P(x) = (x + 4) H(x) + S(x)

H(x) = hasil bagi
S(x) = sisa bagi
S(x) = ax + b

• dibagi (x – 2), sisa 25
P(x) = (x – 2) H(x) + S(x)
P(2) = sisa
P(2) = 25
2a + b = 25 … (1)

• dibagi (x + 4), sisa (-35)
P(x) = (x + 4) H(x) + S(x)
P(-4) = -35
-4a + b = -35 … (2)

persamaan (1) dan (2) :
2a + b = 25
-4a + b = -35
kurangkan
6a = 60
a = 10

2a + b = 25
2.10 + b = 25
20 + b = 25
b = 5

2a + b
= 2.10 + 5
= 20 + 5
= 25

∴ Nilai 2a + b adalah 25.

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