Question

Use synthetic substitution for x = -3 to evaluate the polynomials

P(x) = 2x3 - 3x2 + 5x -7.

A) -92
B) -46
C) -16
D) -22

Answer 1

Evaluating the polynomial P(x) = 2x^3 - 3x^2 + 5x - 7 for x = -3 using synthetic substitution results in P(-3) = -130, which does not match any of the provided answer options, indicating a potential error.

Step-by-step explanation:

To evaluate the polynomial P(x) = 2x^3 - 3x^2 + 5x - 7 for x = -3 using synthetic substitution, we follow these steps:

1. Write down the coefficients of the polynomial: 2, -3, 5, -7.
2. Write the value to be substituted to the left of the coefficients and draw a line: -3 | 2 -3 5 -7.
3. Bring down the leading coefficient: 2.
4. Multiply the value just written (2) by -3 (the value for substitution) and write the result below the second coefficient: 2 | -3 | 5 -9 -7.
5. Add the numbers in the second column: -3 + (-9) = -12.
6. Continue this process until all coefficients have been used: -12 * -3 = 36 and 5 + 36 = 41, then 41 * -3 = -123 and -7 + (-123) = -130.
7. The last number obtained (-130) is the result of the substitution.

Therefore, P(-3) = -130. However, this result does not match any of the answer choices provided (A) -92, (B) -46, (C) -16, or (D) -22, which suggests there may have been an error in the original question or answer choices.