Question

2) Classifique as seguintes expressões algébricas em monômio, binômio, trinômio ou polinômio.
a) 10 x-4 yz
b) x²+2xy-3x² y²
c) 2 x
d) x°- 2 x+5 x + 2
e) 9a + 3b​

Answer 1

a) 10 x-4 y z

$10x-4yz:\quad 2\left(5x-2yz\right)\\10x-4yz\\2\cdot \:5x-2\cdot \:2yz\\2\left(5x-2yz\right)$

b) x²+2 x y-3 x² y²

$x^2+2xy-3x^2y^2:\quad x\left(x+2y-3xy^2\right)\\x^2+2xy-3x^2y^2\\xx+2xy-3xx\\x\left(x+2y-3xy^2\right)$

c) 2 x

$2x\::\quad \begin{bmatrix}\mathrm{Solução:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Notação\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\2x:\quad \begin{bmatrix}\mathrm{Solução:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Notação\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\2x:\quad \mathrm{Ímpar}\\2x:\quad \mathrm{X\:intersepta}:\:\left(0,\:0\right),\:\mathrm{Y\:intersepta}:\:\left(0,\:0\right)\\\mathrm{Inversa\:de}\:2x:\quad \frac{x}{2}\\m=2$

d) x°- 2 x+5 x + 2

$x^{\circ \:}-2x+5x+2\::\quad \begin{bmatrix}\mathrm{Solução:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Notação\:intervalo}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\x^{\circ \:}-2x+5x+2:\quad \mathrm{Não\:é\:par\:nem\:ímpar}\\\:x^{\circ \:}-2x+5x+2:\quad \mathrm{Y\:intersepta}:\:\left(0,\:0^{\circ \:}-2\cdot \:0+5\cdot \:0+2\right)\\x^{\circ \:}-2x+5x+2:\quad \circ \:x^{\circ \:-1}-2+5+0\\\\\frac{d}{dx}\left(x^{\circ \:}-2x+5x+2\right)=\circ \:x^{\circ \:-1}-2+5+0$

e) 9a + 3b​

$3\cdot \:3a+3b\\3\left(3a+b\right)\\b= 3 a + 3\\6a$