Answer :
To find the value of [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = 6x^4 - 26x^3 - 23x^2 + 17x - 4 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\( f(5) = 6(5)^4 - 26(5)^3 - 23(5)^2 + 17(5) - 4 \)[/tex].
2. Calculate each term step-by-step:
- Compute [tex]\( 5^4 \)[/tex]: [tex]\( 5^4 = 625 \)[/tex].
- Compute [tex]\( 6 \times 625 \)[/tex]: [tex]\( 6 \times 625 = 3750 \)[/tex].
- Compute [tex]\( 5^3 \)[/tex]: [tex]\( 5^3 = 125 \)[/tex].
- Compute [tex]\( 26 \times 125 \)[/tex]: [tex]\( 26 \times 125 = 3250 \)[/tex].
- Compute [tex]\( 5^2 \)[/tex]: [tex]\( 5^2 = 25 \)[/tex].
- Compute [tex]\( 23 \times 25 \)[/tex]: [tex]\( 23 \times 25 = 575 \)[/tex].
- Compute [tex]\( 17 \times 5 \)[/tex]: [tex]\( 17 \times 5 = 85 \)[/tex].
3. Substitute the calculated values back into the expression:
- [tex]\( f(5) = 3750 - 3250 - 575 + 85 - 4 \)[/tex].
4. Perform the arithmetic operations:
- First, subtract: [tex]\( 3750 - 3250 = 500 \)[/tex].
- Next, subtract further: [tex]\( 500 - 575 = -75 \)[/tex].
- Add next: [tex]\( -75 + 85 = 10 \)[/tex].
- Finally, subtract the last term: [tex]\( 10 - 4 = 6 \)[/tex].
The value of [tex]\( f(5) \)[/tex] is [tex]\( 6 \)[/tex].
1. Substitute [tex]\( x = 5 \)[/tex] into the function:
[tex]\( f(5) = 6(5)^4 - 26(5)^3 - 23(5)^2 + 17(5) - 4 \)[/tex].
2. Calculate each term step-by-step:
- Compute [tex]\( 5^4 \)[/tex]: [tex]\( 5^4 = 625 \)[/tex].
- Compute [tex]\( 6 \times 625 \)[/tex]: [tex]\( 6 \times 625 = 3750 \)[/tex].
- Compute [tex]\( 5^3 \)[/tex]: [tex]\( 5^3 = 125 \)[/tex].
- Compute [tex]\( 26 \times 125 \)[/tex]: [tex]\( 26 \times 125 = 3250 \)[/tex].
- Compute [tex]\( 5^2 \)[/tex]: [tex]\( 5^2 = 25 \)[/tex].
- Compute [tex]\( 23 \times 25 \)[/tex]: [tex]\( 23 \times 25 = 575 \)[/tex].
- Compute [tex]\( 17 \times 5 \)[/tex]: [tex]\( 17 \times 5 = 85 \)[/tex].
3. Substitute the calculated values back into the expression:
- [tex]\( f(5) = 3750 - 3250 - 575 + 85 - 4 \)[/tex].
4. Perform the arithmetic operations:
- First, subtract: [tex]\( 3750 - 3250 = 500 \)[/tex].
- Next, subtract further: [tex]\( 500 - 575 = -75 \)[/tex].
- Add next: [tex]\( -75 + 85 = 10 \)[/tex].
- Finally, subtract the last term: [tex]\( 10 - 4 = 6 \)[/tex].
The value of [tex]\( f(5) \)[/tex] is [tex]\( 6 \)[/tex].
