Final answer:
To find the x-intercepts of F(x) = 2x³ - 10x² - 28x, factor out the greatest common factor and then solve for x. This cubic function has three x-intercepts: x = 0, x = 7, and x = -2. The degree of F(x) is 3.
Step-by-step explanation:
To find the x-intercepts of the function F(x) = 2x³ - 10x² - 28x, we need to solve for x when F(x) = 0. The degree of the function is 3, which indicates it is a cubic function and may have up to 3 real x-intercepts.
First, we factor out the greatest common factor of the terms:
2x(x² - 5x - 14) = 0
Then, we set each factor equal to zero and solve for x:
2x = 0 → x = 0 (x-intercept)
x² - 5x - 14 = 0
We can factor the quadratic:
(x - 7)(x + 2) = 0
Solving each factor for x gives us:
x - 7 = 0 → x = 7 (x-intercept)
x + 2 = 0 → x = -2 (x-intercept)
The x-intercepts of the function are at x = 0, x = 7, and x = -2. The degree of F(x) is 3.