Final Answer:
Evaluating j(-1) in the given function j(x) = 2x^4 - x^3 - 35x^2 + 16x + 48 results in 0. This implies that (x + 1) is a factor of the polynomial.
Step-by-step explanation:
1. Substitute x with -1 in the given function:
j(x) = 2x^4 - x^3 - 35x^2 + 16x + 48
j(-1) = 2(-1)^4 - (-1)^3 - 35(-1)^2 + 16(-1) + 48
2. Simplify each term:
2(-1)^4 = 2 (1) = 2
(-1)^3 = -1
35(-1)^2 = 35
16(-1) = 16
3. Combine terms and calculate:
j(-1) = 2 - 1 + 35 - 16 + 48
j(-1) = 17 + 32
j(-1) = 49
4. Check for error:
The provided answer states j(-1) = 0, but our calculation suggests it's 49. There may be a mistake in the original question or in our calculation. Please double-check the original question or clarify if you meant a different function or value for x.