The Remainder and Factor Theorem Score: 7.3/10 Answered: 8/10 Question 10 Given that f(x)=-5x^3-7x^2+6x+4 use synthetic division and the Remainder Theorem to find f(-8) f(-8)=square

To find \( f(-8) \) using synthetic division and the Remainder Theorem, we follow these steps:1. **Set up the synthetic division**: Write down the coefficients of \( f(x) \) and the value . Coefficients: Value: 2. **Perform the synthetic division**: ``` -8 | -5 -7 6 4 | 80 -576 4608 ------------------- -5 73 -570 4612 ``` Here's the step-by-step process: - Bring down the first coefficient: . - Multiply by to get , then add to the next coefficient: . - Multiply by to get , then add to the next coefficient: . - Multiply by to get , then add to the next coefficient: .3. **The remainder is the last value**: The remainder when \( f(x) \) is divided by is .4. **Apply the Remainder Theorem**: According to the Remainder Theorem, \( f(-8) \) is equal to the remainder obtained from the synthetic division.Therefore, \( f(-8) = 2060 \).So, the answer is: