Lista 2. Polinômios, frações parciais

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Lista 2. Polinoˆmios, frac¸o˜es parciais
1. Fatore completamente:
1.1 x3 + x 1.9 2(5x + 1)2 − 18
1.2 4y3 − 20y2 + 25y 1.10 5(2x− 3)2 − 20
1.3 18y3 + 48y2 + 32y 1.11 12x2 + 22x− 20
1.4 2x3 − 16x2 + 14x 1.12 3x2 + 13xy − 10y2
1.5 16y − y3 1.13 2ac− 2bd + 4ad− bc
1.6 3x4 + 24x 1.14 6ac− 2bd + 4bc− 3ad
1.7 5y + 3y2 − 2y3 1.15 x3 − 3x2 − 4x + 12
1.8 z − 8z4 1.16 x4 − 4x3 − x2 + 4x
2. Fac¸a a decomposic¸a˜o em frac¸o˜es parciais:
2.1 4t3−2t2+t
2.2 3+(t−2)
3
t4−6t3+9t2+4t−12
2.3 2t5+4t3
Respostas:
1.1 x(x2 + 1) 1.9 2(5x + 4)(5x− 2)
1.2 y(2y − 5)2 1.10 5(2x− 1)(2x− 5)
1.3 2y(3y + 4)2 1.11 2(2x + 5)(3x− 2)
1.4 2x(x− 1)(x− 7) 1.12 (x + 5y)(3x− 2y)
1.5 y(4− y)(4 + y) 1.13 (2a− b)(c + 2d)
1.6 3x(x + 2)(x2 − 2x + 4) 1.14 (3a + 2b)(2c− d)
1.7 y(1 + y)(5− 2y) 1.15 (x− 3)(x + 2)(x− 2)
1.8 z(1− 2z)(1 + 2z + 4z2) 1.16 x(x− 1)(x + 1)(x− 4)
2.1 4t − 4t−1 + 4(t−1)2
2.2 1t−3 +
2
3(t+1) − 23(t−2) − 1(t−2)2
2.3 − 18t + 12t3 + t8(t2+4)
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