Which of the Following Expressions Are Not Polynomials? √ a X + X 2 − X 3

Which of the following expressions are not polynomials?

\[\sqrt{ax} + x^2 - x^3\]

Sum

\[\sqrt{ax} + x^2 - x^3 \text{is not a polynomial because} \frac{1}{2} \text{is the power of variable x is not a non negative integer .} \]

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Write each of the following polynomials in the standard form. Also, write their degree.

x² + 3 + 6x + 5x⁴

Divide 6x³y²z² by 3x²yz.

Divide x + 2x² + 3x⁴ − x⁵ by 2x.

Divide −21 + 71x − 31x² − 24x³ by 3 − 8x.

Divide 3y⁴ − 3y³ − 4y² − 4y by y² − 2y.

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

Dividend	Divisor
15y⁴ − 16y³ + 9y2 −\[\frac{10}{3}\] y+6	3y − 2

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4 − z, 3z² − 13z + 4

Find whether the first polynomial is a factor of the second.

2a − 3, 10a² − 9a − 5