Final Answer:
To find the x-intercepts, set f(x) = x³ + 2x² - x - 2 equal to zero and solve for x and to find the y-intercept, set x to zero. The x-intercepts are (-1, 0), (1, 0), (-2, 0), and the y-intercept is (0, -2).
Step-by-step explanation:
To find the x-intercepts, set f(x) equal to zero and solve for x:
x³ + 2x² - x - 2 = 0
You can try factoring or use numerical methods like the rational root theorem or synthetic division. Factoring, you find that x = -1 is a root. Therefore, (x + 1) is a factor:
(x + 1)(x² + x - 2) = 0
Now, factor the quadratic part:
(x + 1)(x - 1)(x + 2) = 0
So, the x-intercepts are x = -1, 1, -2.
To find the y-intercept, set x to zero:
f(0) = 0³ + 2 · 0² - 0 - 2 = -2
Therefore, the y-intercept is (0, -2) .
So, the x-intercepts are (-1, 0), (1, 0), (-2, 0), and the y-intercept is (0, -2).
Complete Question:
f(x) = x³ + 2x² - x - 2
plot the x and y intercepts of the function