Question

evaluate the polynomial when (a) x = 0 and (b) x = 2.
-x³ + 4x² - 14
(a) when x = 0, the polynomial equals . (type an integer or a fraction.)
(b) when x = 2, the polynomial equals . (type an integer or a fraction.)

Explanation:

Step1: Evaluate at \( x = 0 \)

Substitute \( x = 0 \) into the polynomial \( -x^3 + 4x^2 - 14 \).

$$ -(0)^3 + 4(0)^2 - 14 = 0 + 0 - 14 = -14 $$

Step2: Evaluate at \( x = 2 \)

Substitute \( x = 2 \) into the polynomial \( -x^3 + 4x^2 - 14 \).

$$ -(2)^3 + 4(2)^2 - 14 = -8 + 4(4) - 14 = -8 + 16 - 14 = -6 $$

Answer:

(a) \(-14\)
(b) \(-6\)