Respuesta :

PHDFlopper
Use the rational root theorem:
(x+2)(2[tex] x^{3} [/tex]+[tex] x^{2} [/tex]+x+6)
Use the rational root theorem AGAIN:
(x+2)(2x+3)([tex] x^{2} [/tex]-x+2)
The answer is the first choice

Answer:2x+3

Step-by-step explanation:

GIven

[tex]2x^4+5x^3+3x^2+8x+12 [/tex]

[tex]2x^4+3x^3+2x^3+3x^2+8x+12[/tex]

[tex]x^3\left ( 2x+3\right )+x^2\left ( 2x+3\right )+4\left ( 2x+3\right )[/tex]

[tex]\left ( 2x+3\right )\left ( x^3+x^2+4\right ) [/tex]

Thus 2x+3 is a factor of given Function