Question

Is the expression a polynomial? If yes, write in standardform, if not state why not

1.

`(2x+3)/(x^(2) )`

2.

`2x+5x^(2) -99`

3.

`(\sqrt{8x^(3)}) +2x^(4)+2+x`

4.

`15x+4x^(-2)`

5.

`-3x^(4) +7x+12x^(2)`

Answer 1

Explanation:

1) Not a polynomial. Because x² is in the denominator.

2) Yes, it is a polynomial.

Standard form: 5x² + 2x - 99

3) Not a polynomial.

`\sqrt{8x^(3)} = (8x^(3))^{(1)/(2)} = 8^{(1)/(2)}x^{(3)/(2)}` .

Power of x is a fraction. so , it is not a polynomial.

4) Power of x is (-2). Power of x should not be a negative integer. SO, it is not a polynomial.

5) Yes:

Standard form: -3x⁴ + 12x² + 7x