Final answer:
To calculate f(2) for the polynomial f(x) = 2x⁴ + x³ - 4x - 3, substitute 2 for x, to find that f(2) = 29.
Step-by-step explanation:
To find f(2) for the polynomial f(x) = 2x⁴ + x³ - 4x - 3, we need to substitute x with 2 and evaluate the expression.
Following the substitution, we get:
f(2) = 2(2)⁴ + (2)³ - 4(2) - 3
Calculating each term, we have:
- (2)⁴ = 16
- 2 × 16 = 32
- (2)³ = 8
- -4 × 2 = -8
- Then we add up all the terms: 32 + 8 - 8 - 3
This simplifies to:
- 32 + 8 = 40
- 40 - 8 = 32
- Finally, 32 - 3 = 29
So, f(2) = 29