Using Division of Polynomials, State Whether 2y − 5 is a Factor of 4y4 − 10y3 − 10y2 + 30y − 15

Using division of polynomials, state whether

2y − 5 is a factor of 4y⁴ − 10y³ − 10y² + 30y − 15

Sum

\[\because\] The remainder is non zero,

2y - 5 is not a factor of \[4 y^4 - 10 y^3 - 10 y^2 + 30y - 15\]

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

x² + 3 + 6x + 5x⁴

Divide 72xyz² by −9xz.

Divide 4z³ + 6z² − z by −\[\frac{1}{2}\]

Divide 9x²y − 6xy + 12xy² by −\[\frac{3}{2}\]

Divide x² + 7x + 12 by x + 4.

What must be added to x⁴ + 2x³ − 2x² + x − 1 , so that the resulting polynomial is exactly divisible by x²+ 2x − 3?

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

5y³ − 6y² + 6y − 1, 5y − 1

Divide:
ax² − ay² by ax + ay

Divide: (32y² – 8yz) by 2y

Statement A: If 24p²q is divided by 3pq, then the quotient is 8p.

Statement B: Simplification of `((5x + 5))/5` is 5x