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Answer :
To find the value of [tex]\( f(5) \)[/tex] for the function [tex]\( f(x) = 5x^2 - 7x - 10 \)[/tex] using synthetic division, follow these steps:
1. Set up the synthetic division:
- We're going to evaluate the polynomial at [tex]\( x = 5 \)[/tex].
- Write down the coefficients of the polynomial: 5, -7, and -10.
2. Perform synthetic division:
- Write the value 5 on the left (the number we're substituting into the polynomial).
- Bring down the first coefficient (5) to the bottom row.
- Multiply this number (5) by 5 and write the result (25) under the next coefficient (-7).
- Add -7 and 25 to get 18, and write it in the bottom row.
- Multiply this new bottom-row number (18) by 5 and write the result (90) under the next coefficient (-10).
- Add -10 and 90 to get 80, and write it in the bottom row.
3. Result:
- The final number in the bottom row (80) is the value of [tex]\( f(5) \)[/tex].
So, the value of [tex]\( f(5) \)[/tex] is 80.
1. Set up the synthetic division:
- We're going to evaluate the polynomial at [tex]\( x = 5 \)[/tex].
- Write down the coefficients of the polynomial: 5, -7, and -10.
2. Perform synthetic division:
- Write the value 5 on the left (the number we're substituting into the polynomial).
- Bring down the first coefficient (5) to the bottom row.
- Multiply this number (5) by 5 and write the result (25) under the next coefficient (-7).
- Add -7 and 25 to get 18, and write it in the bottom row.
- Multiply this new bottom-row number (18) by 5 and write the result (90) under the next coefficient (-10).
- Add -10 and 90 to get 80, and write it in the bottom row.
3. Result:
- The final number in the bottom row (80) is the value of [tex]\( f(5) \)[/tex].
So, the value of [tex]\( f(5) \)[/tex] is 80.
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