(24)Calcule os quocientes a seguir. a) (8x^5+6x^3):(+2x^2) b) (12ab+15a^2b+9ab^2):(3ab) c) (20x-10x^2):(-5x) d) (a^3+a^2+a):(a) e) (x^5+x^2):(-x^2) f) (7x^2-8x+5):(-1)

Vamos calcular os quocientes fornecidos:<br /><br />a) \((8x^{5}+6x^{3}):(+2x^{2})\)<br /><br />Dividimos cada termo pelo divisor \(+2x^{2}\):<br /><br />\[<br />\frac{8x^{5}}{2x^{2}} = 4x^{3}<br />\]<br />\[<br />\frac{6x^{3}}{2x^{2}} = 3x<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />4x^{3} + 3x<br />\]<br /><br />b) \((12ab+15a^{2}b+9ab^{2}):3ab\)<br /><br />Dividimos cada termo pelo divisor \(3ab\):<br /><br />\[<br />\frac{12ab}{3ab} = 4<br />\]<br />\[<br />\frac{15a^{2}b}{3ab} = 5a<br />\]<br />\[<br />\frac{9ab^{2}}{3ab} = 3b<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />4 + 5a + 3b<br />\]<br /><br />c) \((20x-10x^{2}):(-5x)\)<br /><br />Dividimos cada termo pelo divisor \(-5x\):<br /><br />\[<br />\frac{20x}{-5x} = -4<br />\]<br />\[<br />\frac{-10x^{2}}{-5x} = 2x<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />-4 + 2x<br />\]<br /><br />d) \((a^{3}+a^{2}+a):(a)\)<br /><br />Dividimos cada termo pelo divisor \(a\):<br /><br />\[<br />\frac{a^{3}}{a} = a^{2}<br />\]<br />\[<br />\frac{a^{2}}{a} = a<br />\]<br />\[<br />\frac{a}{a} = 1<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />a^{2} + a + 1<br />\]<br /><br />e) \((x^{5}+x^{2}):(-x^{2})\)<br /><br />Dividimos cada termo pelo divisor \(-x^{2}\):<br /><br />\[<br />\frac{x^{5}}{-x^{2}} = -x^{3}<br />\]<br />\[<br />\frac{x^{2}}{-x^{2}} = -1<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />-x^{3} - 1<br />\]<br /><br />f) \((7x^{2}-8x+5):(-1)\)<br /><br />Dividimos cada termo pelo divisor \(-1\):<br /><br />\[<br />\frac{7x^{2}}{-1} = -7x^{2}<br />\]<br />\[<br />\frac{-8x}{-1} = 8x<br />\]<br />\[<br />\frac{5}{-1} = -5<br />\]<br /><br />Portanto, o quociente é:<br /><br />\[<br />-7x^{2} + 8x - 5<br />\]