What is the value of f(4) for the function f(x) = x^5 - x^4 - 10x^3 - 5x^2 + 1?

To find the value of f(4) for the function f(x) = x^5 - x^4 - 10x^3 - 5x^2 + 1, you need to substitute 4 into the function.

First, calculate each term individually:

1. ( 4^5 = 1024 )

2. ( 4^4 = 256 )

3. ( -10 \times 4^3 = -10 \times 64 = -640 )

4. ( -5 \times 4^2 = -5 \times 16 = -80 )

5. The constant term is ( 1 ).

Now, combine these results:

• Start with ( 1024 ) from the ( 4^5 ) term.

• Subtract ( 256 ):

( 1024 - 256 = 768 ).

• Then subtract ( 640 ):

( 768 - 640 = 128 ).

• Next, subtract ( 80 ):

( 128 - 80 = 48 ).

• Finally, add the constant term ( 1 ):

( 48 + 1 =