Final answer:
The factors of the function g(x) = 2x³+x²-22x+24 are (x+2), (x-1), and (x-6). The graph of function f crosses the x-axis at the points -2, 1, and 6.
Step-by-step explanation:
The factors of the function g(x) = 2x³+x²-22x+24 can be found by factoring the expression. To factor the expression, we can look for common factors and then use the quadratic formula to factor the remaining quadratic equation:
g(x) = 2x³+x²-22x+24
First, we can factor out the greatest common factor, which is 2:
g(x) = 2 (x³+ ½ x²-11x+12)
Next, we can factor the remaining quadratic expression:
g(x) = 2 (x+2)(x-1)(x-6)
The factors of the function g(x) are (x+2), (x-1), and (x-6).
To determine which statement is true about the graph of function f, we need to find the x-intercepts of the graph. The x-intercepts occur when g(x) equals zero, which happens when x=-2, x=1, and x=6. Therefore, the graph of function f crosses the x-axis at the points x=-2, x=1, and x=6. So, the correct statement is Option C: The graph crosses the x-axis at the points -2, 1, and 6.