Questions: Given R(x)=-x^3+2x^2-3x+4, evaluate R(-1)

Solution Steps

To evaluate \( R(-1) \), substitute \(-1\) for \( x \) in the polynomial \( R(x) = -x^3 + 2x^2 - 3x + 4 \). Then, compute the result by performing the arithmetic operations.

To evaluate \( R(-1) \), we substitute \(-1\) into the polynomial \( R(x) = -x^3 + 2x^2 - 3x + 4 \): \[ R(-1) = -(-1)^3 + 2(-1)^2 - 3(-1) + 4 \]

Now, we calculate each term:

• The first term: \(-(-1)^3 = -(-1) = 1\)
• The second term: \(2(-1)^2 = 2(1) = 2\)
• The third term: \(-3(-1) = 3\)
• The fourth term: \(4\)

Now, we sum all the calculated terms: \[ R(-1) = 1 + 2 + 3 + 4 = 10 \]

Final Answer