Question

fatore os polinômios 2x*3+12x*2+18x​

Answer 1

Resposta:

2x³+12x²+18x=2x(x+3)²

Explicação passo-a-passo:

2x³+12x²+18x=2x(x²+6x+9)

$\displaystyle~Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+6x+9=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=6~e~c=9\\\\\Delta=(b)^{2}-4(a)(c)=(6)^{2}-4(1)(9)=36-(36)=0\\\\x^{'}=x^{''}=\frac{-(b)\pm\sqrt{\Delta}}{2(a)}=\frac{-(6)\pm\sqrt{0}}{2(1)}=\frac{-6\pm0}{2}=\frac{-6}{2}=-3$

x²+6x+9=(x-x')(x-x")=(x-x')²=(x-(-3))²=(x+3)²

2x³+12x²+18x=2x(x²+6x+9)=2x(x+3)²