Question

HELP QUICK TIMED!!!!!!

Drag the expressions into the boxes to correctly complete the table.

Answer 1

The following expressions are polynomials:

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

`x^5-5x^4+4x^3-3x^2+2x-1`

`x^3-7x^2+9x-5x^4-20`

The following expressions are not polynomials:

`(4)/(x^4)+(3)/(x^3)-(2)/(x^2)-1`

`x^(-5)-5x^(-4)+4x^(-3)-3x^(-2)+2x^(-1)-1`

`\sqrt[4]{x}-\sqrt[3]{x}+4√(x)-8x+16`

Explanation:

We are required to differentiate the expressions as polynomials and non-polynomials.

Since, we know,

A polynomial is an expression that involves variables and their coefficients separated by mathematical operations with the variables having non-negative integer values.

i.e. A polynomial is of the form,
`a_(n)x^(n)+a_(n-1)x^(n-1)+.....+a_(1)x+a_(0)`, with 'n' being non-negative integer.

Thus, according to the definition, we have that,

The following expressions are polynomials:

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

`x^5-5x^4+4x^3-3x^2+2x-1`

`x^3-7x^2+9x-5x^4-20`

The following expressions are not polynomials:

`(4)/(x^4)+(3)/(x^3)-(2)/(x^2)-1`

`x^(-5)-5x^(-4)+4x^(-3)-3x^(-2)+2x^(-1)-1`

`\sqrt[4]{x}-\sqrt[3]{x}+4√(x)-8x+16`