Question

1 – Efetue as seguintes divisões dos polinômios pelos monômios:

a) 18x5 +12x4 -10x3 : 2x2

b) (9x2 y 3 – 6x3 y 2 – xy) : 3x2 y

c) (a2 b 3 c 4+a3 b 4 c 2 -ab5 c 2 ) : abc​

Answer 1

a) = x⁴×(13x+12)

b) = xy×(9xy²-6xy²y-1+3x)

c) = ab⁴c⁵+a²b⁵c³-b⁶c³

Answer 2

Explicação passo-a-passo:

$a)(18x {}^{5} + 12x {}^{4} - 10x {}^{3} )\div (2x {}^{2} ) =$

$\frac{18x {}^{5} }{2x {}^{2} } + \frac{12x {}^{4} }{2x {}^{2} } - \frac{10x {}^{3} }{2x {}^{2} } = 9x {}^{5 - 2} + 6x {}^{4 - 2} - 5x {}^{3 - 2} = 9x {}^{3} + 6x {}^{2} - 5x$

$b)(9x {}^{2} y {}^{3} - 6x {}^{3} y {}^{2} - xy) \div (3x {}^{2} y) =$

$\frac{9x {}^{2} y {}^{3} }{3x {}^{2}y } - \frac{6x {}^{3} y {}^{2} }{3x {}^{2} y} - \frac{xy}{3x {}^{2} y} = 3x {}^{2 - 2} y {}^{3 - 1} - 2x {}^{3 - 2} y {}^{2 - 1} - \frac{x {}^{1 - 2}y {}^{1 - 1} }{3} = 3y {}^{2} - 2xy - \frac{x {}^{ - 1} }{ 3}$

$c)(a {}^{2} b {}^{3} c {}^{4} + a {}^{3} b {}^{4} c {}^{2} - ab {}^{5} c {}^{2} ) \div abc =$

$\frac{a {}^{2}b {}^{3} c {}^{4} }{abc} + \frac{a {}^{3} b {}^{4} c {}^{2} }{abc} - \frac{ab {}^{5} c {}^{2} }{abc} = a {}^{2 - 1} b {}^{3 - 1} c {}^{4 - 1} + a {}^{3 - 1} b {}^{4 - 1} c {}^{2 - 1} = a {}^{1 - 1} b {}^{5 - 1} c {}^{2 - 1} = a {}b {}^{2} c {}^{3} + a {}^{2} b {}^{3} c - b {}^{4} c$