Answer:
x = 3 or x = -1 or x = -2
Step-by-step explanation:
Solve for x:
(x^3 - 7 x - 6)/(x - 4) = 0
Hint: | Multiply both sides by a polynomial to clear fractions.
Multiply both sides by x - 4:
x^3 - 7 x - 6 = 0
Hint: | Factor the left hand side.
The left hand side factors into a product with three terms:
(x - 3) (x + 1) (x + 2) = 0
Hint: | Find the roots of each term in the product separately.
Split into three equations:
x - 3 = 0 or x + 1 = 0 or x + 2 = 0
Hint: | Look at the first equation: Solve for x.
Add 3 to both sides:
x = 3 or x + 1 = 0 or x + 2 = 0
Hint: | Look at the second equation: Solve for x.
Subtract 1 from both sides:
x = 3 or x = -1 or x + 2 = 0
Hint: | Look at the third equation: Solve for x.
Subtract 2 from both sides:
Answer: x = 3 or x = -1 or x = -2
