Question

Which algebraic expression is a polynomial with a degree of 2?

1). 4x3 − 2x
2). 10x2 − sq root of X
3). 8x3+5/x + 3
4). 6x2 − 6x + 5

Answer 1

Degree 2 means the highest power of x is 2 and that is:

4). 6x² − 6x + 5

Answer 2

The algebraic expression which is a polynomial with a degree of 2 is:

4)
`6x^2-6x+5`

Explanation:

Polynomial expression--

It is a algebraic expression which contains the natural powers of x.

We know that the general form of a quadratic polynomial i.e. a polynomial of degree 2 is given by:

`p(x)=ax^2+bx+c`

where a,b and c are real numbers.

1)

`4x^3-2x`

It is a cubic polynomial i.e. a polynomial of degree 2.

Since the highest power of x in the expression is: 3

2)

`10x^2-√(x)`

It is not a polynomial since there is one term which is not a natural power of x.

3)

`8x^3+(5)/(x)+3`

Again we have a term which is not a natural power of x.

Since,

`(5)/(x)=5x^(-1)`

4)

`6x^2-6x+5`

It is a polynomial with degree 2 since it matches the general form of a polynomial of degree 2.