Question

Which of the following is a factor of 2x4 + 5x3 + 3x2 + 8x + 12?

2x + 3

x – 3

3x + 1

Not factorable

Answer 1

Use the rational root theorem:
(x+2)(2
`x^(3)`+
`x^(2)`+x+6)
Use the rational root theorem AGAIN:
(x+2)(2x+3)(
`x^(2)`-x+2)
The answer is the first choice

Answer 2

Answer:2x+3

Explanation:

GIven

`2x^4+5x^3+3x^2+8x+12`

`2x^4+3x^3+2x^3+3x^2+8x+12`

`x^3\left ( 2x+3\right )+x^2\left ( 2x+3\right )+4\left ( 2x+3\right )`

`\left ( 2x+3\right )\left ( x^3+x^2+4\right )`

Thus 2x+3 is a factor of given Function