Divide X4 − 2x3 + 2x2 + X + 4 by X2 + X + 1.

Divide x⁴ − 2x³ + 2x² + x + 4 by x² + x + 1.

Sum

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Write the degree of each of the following polynomials.

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

x² + 3 + 6x + 5x⁴

Divide \[y^4 - 3 y^3 + \frac{1}{2} y^2 by 3y\]

Divide 3x³y² + 2x²y + 15xy by 3xy.

Divide 4y² + 3y +\[\frac{1}{2}\] by 2y + 1.

Using division of polynomials, state whether

4x − 1 is a factor of 4x² − 13x − 12

Using division of polynomials, state whether

z²+ 3 is a factor of z⁵ − 9z

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

3x² + 4x + 5, x − 2

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

4 − z, 3z² − 13z + 4

Divide:
acx² + (bc + ad)x + bd by (ax + b)