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B.Operasi pada polinomial

Operasi yang akan dibahas yaitu penjumlahan, pengurangan dan perkalian pada
polinomial.
Perhatikan Contoh Soal di bawah ini!
3
2
4
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1. Diketahui f (x) = 3x – 2x + 5x – 4x + 3 , g(x) = 4x – 6x + 7x – 1. Tentukanlah
3

a. f (x) + g(x)
b. f (x) - g(x)
2
2
2. Diketahui f (x) = x – 4x + 3 , g(x) = 6x – 1. Tentukanlah :
a. 2f(x) + 3g(x)
b. [f(x) – g(x)] x g(x)
c. [f(x) x g(x)] – 2f(x)

Jawaban :
3
2
4
2
1. Diketahui f (x) = 3x – 2x + 5x – 4x + 3 , g(x) = 4x – 6x + 7x – 1
3
a. f(x) + g(x)
3
3
f (x) + g(x) = (3x – 2x + 5x – 4x + 3) + (4x – 6x + 7x – 1)
2
4
2
2
3
= 3x + (-2 +4)x + (5-6)x + (-4+7)x + (3-1)
4
3
2
4
= 3x + 2 x – 1x + 3x + 2
b. f(x) - g(x)
3
f (x) - g(x) = (3x – 2x + 5x – 4x + 3) - (4x – 6x + 7x – 1)
2
4
2
3
= 3x + (-2 -4)x + (5+6)x + (-4-7)x + (3+1)
2
3
4
4
2
= 3x - 6x +11x - 11x + 4
3

2. Diketahui f (x) = x – 4x + 3 , g(x) = 6x – 1
2
2
a. 2f(x) + 3g(x)
2
2
2f(x) + 3g(x) = 2(x – 4x + 3) + 3(6x – 1)
2
2
= (2x – 8x + 6) + (18x – 3)
2
= 20x – 8x + 3

b. [f(x) – g(x)] x g(x)
2
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[f(x) – g(x)] x g(x) = [(x – 4x + 3) - (6x – 1)] x (6x – 1)
2
= (-5x – 4x + 4) x (6x – 1)
2
2
2
= (-30x + 5x ) + (-24x + 4x) + (24x – 4)
4
3
2
3
= -30x - 24x + 29x + 4x – 4
4
2

c. [f(x) x g(x)] – 2f(x)
2
2
[f(x) x g(x)] – 2f(x) = [(x – 4x + 3) x (6x – 1)] - 2(x – 4x + 3)
2
2
3
2
2
= [(6x - x ) + (-24x +4x) + (18x – 3)] – (2x – 8x + 6)
4
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3
4
2
= (6x -24x + 17x + 4x – 3) - (2x – 8x + 6)
3
= 6x - 24x + 15x + 12x – 9
4
2

Hal 2