Question

Please help I don't understand this. I will give brainy and 10pts

Answer 1

Polynomial

`x^(2)+3x^(5)-6x+12x^(3)`

`x^(4)+3x^(3)-5x^(2)-7x+20`

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

Not a polynomial

`(5)/(x^(3))-(1)/(x^(2))+(8)/(x)}-40`

`x^(-3)-x^(-2)-6x^(-1)+8`

`4\sqrt[3]{x}-√(x)-20`

Explanation:

A polynomial is an algebraic expression that has multiple terms made up of numbers and variables

A Polynomial has positive integer exponents and the operations in it are addition, subtraction, and multiplication only

∵ The expression
`(5)/(x^(3))-(1)/(x^(2))+(8)/(x)}-40` has division operation

∴
`(5)/(x^(3))-(1)/(x^(2))+(8)/(x)}-40` ⇒ Not a polynomial

∵ The expression
`x^(2)+3x^(5)-6x+12x^(3)` has positive integer

exponents and the operations in it are addition, subtraction

∴
`x^(2)+3x^(5)-6x+12x^(3)` ⇒ Polynomial

∵ The expression
`x^(4)+3x^(3)-5x^(2)-7x+20` has positive integer

exponents and the operations in it are addition, subtraction

∴
`x^(4)+3x^(3)-5x^(2)-7x+20` ⇒ Polynomial

∵ The expression
`x^(-3)-x^(-2)-6x^(-1)+8` has negative integer

exponents

∴
`x^(-3)-x^(-2)-6x^(-1)+8` ⇒ Not a polynomial

∵ The expression
`4\sqrt[3]{x}-√(x)-20` has non integer exponents

(
`\sqrt[3]{x}=x^{(1)/(3)}` and
`√(x)=x^{(1)/(2)}`)

∴
`4\sqrt[3]{x}-√(x)-20` ⇒ Not a polynomial

∵ The expression
`x^(3)-2x^(2)+x-12` has positive integer

exponents and the operations in it are addition, subtraction

∴
`x^(3)-2x^(2)+x-12` ⇒ Polynomial