Question

Which of the following is a factor of

24x⁶−1029y³?
a) 24
b) 2x²
c) 7y
d) 4x⁴
e) 14x²y
f) 49y²
g) All of the above

Answer 1

To determine which of the given options is a factor of the polynomial 24x⁶−1029y³, we can perform synthetic division to check if each option divides the polynomial evenly. Option b) 2x² and option e) 14x²y are factors of the polynomial.

Step-by-step explanation:

To determine which of the given options is a factor of the polynomial 24x⁶−1029y³, we need to check if each option divides the polynomial evenly. We can do this by performing long division or using synthetic division.

Using synthetic division with option a) 24, we find that the polynomial is not divisible by 24.

Using synthetic division with option b) 2x², we find that the polynomial is divisible by 2x².

Using synthetic division with option c) 7y, we find that the polynomial is not divisible by 7y.

Using synthetic division with option d) 4x⁴, we find that the polynomial is not divisible by 4x⁴.

Using synthetic division with option e) 14x²y, we find that the polynomial is divisible by 14x²y.

Using synthetic division with option f) 49y², we find that the polynomial is not divisible by 49y².

Therefore, the factors of the polynomial 24x⁶−1029y³ are options b) 2x² and e) 14x²y, so the correct answer is option g) All of the above.