Using Division of Polynomials, State Whether Z2 + 3 is a Factor of Z5 − 9z

Using division of polynomials, state whether

z²+ 3 is a factor of z⁵ − 9z

Sum

Remainder is zero; therefore, z² + 3 is a factor of

\[z^5 - 9z\]

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Divide the given polynomial by the given monomial.

8(x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z²

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
15z³ − 20z² + 13z − 12	3z − 6

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

Find the value of a, if x + 2 is a factor of 4x⁴ + 2x³ − 3x² + 8x + 5a.

Divide:
x² − 5x + 6 by x − 3

Divide:
ax² − ay² by ax + ay

Divide:

(a² + 2ab + b²) − (a² + 2ac + c²) by 2a + b + c

Divide: 15a³b⁴ − 10a⁴b³ − 25a³b⁶ by −5a³b²

Divide: (32y² – 8yz) by 2y