Answer :
Final Answer
The most simplified form of the function F(x) is (a) ½x⁶ + 1½x⁵
Explanation
When working with polynomials, the goal is to represent them in their most concise and accurate form. This often involves identifying and removing any common factors and ensuring the coefficients are in their simplest terms (no common divisors).
Looking at the given options:
- (b) x⁶ + 3x⁵: This option simply multiplies both terms in the original function by 2. While the function remains mathematically equivalent, it introduces an unnecessary factor and isn't the most simplified form.
- c) x⁶/2 + 3x⁴/2:** Dividing both terms by x² technically results in a mathematically equivalent expression. However, the original function doesn't have a common factor of x². Representing it in this way alters the function's appearance and isn't the most simplified form.
- (d) x(½x⁵ + 1½x⁴): This option factors out an x from the original function, which is a valid step. However, the coefficients (½ and 1½) are already in their most basic form (fractions with no common divisors). There's no further factorization possible, and multiplying by x doesn't change the expression's core form.
Therefore, the most concise and accurate representation of F(x) is the original expression: (a) ½x⁶ + 1½x⁵. It doesn't contain any common factors to cancel, and the coefficients are in their most basic form.
Question:
Consider the function F(x) = ½x⁶ + 1½x⁵.
(a) ½x⁶ + 1½x⁵
(b) x⁶ + 3x⁵ (by multiplying both terms by 2)
(c) x⁶/2 + 3x⁴/2 (by dividing both terms by x²)
(d) x(½x⁵ + 1½x⁴) (by factoring out x)
Which of the above options represents the most simplified form of the function F(x)? Explain your reasoning.
