Which of the following is a factor of 24x6-1029y3 ？ 24 2x2+7y 4x4+14x2y+49y2 All of the above

Here, we are required to find which of the following is a factor of 24x⁶ - 1029y³.The correct factors are ;2x2 + 7y 2x2 + 7y 4x4 + 14x2y + 49y2 To find the factors of 24x⁶ - 1029y³, we need to first find the prime factors of each term.Therefore, for 24x⁶, we have;2×2×2×3 × (x²)³Therefore, we have 2³ × 3 × (x²)³And for -1029y³, we have:7 ×7×7×3 × -y³There, we have 7³ × 3 × -y³.Therefore, since 24 is not a common factor for both terms, we can conclude that it is not a factor of 24x⁶ - 1029y³.Moving on, since 3 is a factor, 24x⁶ - 1029y³ then becomes;3{2³ × (x²)³ - 7³y³}And since, 2x² and -7y are the cubic roots of 8x⁶ and -343y³ respectively.Therefore, 2x² - 7y is a factor.Consequently, the division of 8x⁶ -343y³ yields;4x⁴ + 14x²y + 49 which is a factor.However, further factorisation of 4x⁴ + 14x²y + 49 yields (2x² + 7y)(2x² + 7y).From above, we can conclude that (2x² + 7y) and 4x⁴ + 14x²y + 49 are both factors of 24x⁶ - 1029y³.Read more: