Question

If 2x+1 is a factor of 2x^3+ax^2+X+2, find a

Answer 1

Answer:

hhhhhhhvvvvvbnnbvbmkcgvhhnn

Answer 2

Step-by-step explanation:

$\mathrm{Domain\:of\:}\:2x^3+ax^2+x+2\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

The function has no undefined points  no  domain constraints.

Therefore, the domain is,

$-\infty \:<x<\infty \:$

$\mathrm{Range\:of\:}2x^3+ax^2+x+2:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}$

$\mathrm{The\:range\:of\:polynomials\:with\:odd\:degree\:is\:all\:the\:real\:numbers}$

$-\infty \:<f\left(x\right)<\infty \:$

$\mathrm{Axis\:interception\:points\:of}\:2x^3+ax^2+x+2:\quad \mathrm{Y\:Intercepts}:\:\left(0,\:2\right)$

$\mathrm{Y\:Intercepts}:\:\left(0,\:2\right)$

$\mathrm{Asymptotes\:of}\:2x^3+ax^2+x+2:\quad \mathrm{None}$

$\mathrm{Extreme\:Points\:of}\:2x^3+ax^2+x+2:\quad \mathrm{None}$

$\mathrm{Suppose\:that\:}x=c\mathrm{\:is\:a\:critical\:point\:of\:}f\:'\left(c\right)\mathrm{\:such\:that\:}f\:'\left(c\right)=0$

$\mathrm{and\:that\:}f\:''\left(x\right)\mathrm{\:is\:continuous\:in\:a\:region\:around\:}x=c\mathrm{.\:Then,\:}$

$\mathrm{If\:}f\:''\left(c\right)<0\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:maximum.}$

$\mathrm{If\:}f\:''\left(c\right)>0\mathrm{\:then\:}x=c\mathrm{\:is\:a\:local\:minimum.}$

$\mathrm{If\:}f\:''\left(c\right)=0\mathrm{\:then\:test\:failed\:and\:}x=c\mathrm{\:can\:be\:a\:local\:maximum,}$

$\mathrm{\:local\:minimum\:or\:neither.}$

$f''(x)= 12x+ 2a$

None