Question

Quais polinômios apresentam os maiores graus?

a) x² + 4x + 3
b) 6a³x²y + 7a²xy² - 11a⁴x²y
c) 3a³ + 11a7 - 13a⁵
d) 4ax + a²xy - 2a​

Answer 1

Resposta:

$x^2+4x+3\\\\=\left(x^2+x\right)+\left(3x+3\right)\\\\=x\left(x+1\right)+3\left(x+1\right)\\\\=\left(x+1\right)\left(x+3\right)\\\\\\\\6a^3x^2y+7a^2xy^2-11a^4x^2y\\\\=6a^2axxy+7a^2xyy-11a^2a^2xxy\\\\=yxa^2\left(6ax+7y-11a^2x\right)\\\\\\\\3a^3+11a\cdot \:7-13a^5\\\\=3a^3+77a-13a^5$

$4ax+a^2xy-2a\\\\\mathrm{Aplicar\:as\:propriedades\:dos\:expoentes}:\quad \:a^{b+c}=a^ba^c\\\\a^2=aa\\\\=4ax+aaxy-2a\\\\\mathrm{Fatorar\:o\:termo\:comum\:}a\\\\=a\left(4x+axy-2\right)$