Final answer:
To determine Q(x), the formula P(x) * Q(x) = HCF * LCM is used. Upon dividing the LCM by P(x), considering the HCF, the correct polynomial Q(x) is found to be 6x² - 5x - 1, which is option (c).
Step-by-step explanation:
The question is asking to determine the polynomial Q(x) given that the Highest Common Factor (HCF) of P(x) and Q(x) is (2x-1) and their Least Common Multiple (LCM) is (6x³ + 25x² - 24x + 5), while P(x) is given as (2x²+9x – 5). The relationship between two polynomials P(x) and Q(x), their HCF, and LCM can be represented by the formula: P(x) * Q(x) = HCF * LCM.
To find Q(x), we can rearrange the formula to Q(x) = (HCF * LCM) / P(x). Plugging in the provided values gives us:
Q(x) = ((2x - 1) * (6x³ + 25x² - 24x + 5)) / (2x²+9x – 5)
After dividing the LCM by P(x), we find that the polynomial that matches this operation is 6x² - 5x - 1, which is option (c).