Solve the following into linear binomials:
t^3 - 3t^2 - 15t + 125
I COULD just use the calculator, but I want to know how I'm supposed to solve it in the first place.
Solve for t:
t^3-3 t^2-15 t+125 = 0
The left hand side factors into a product with two terms:
(t+5) (t^2-8 t+25) = 0
Split into two equations:
t+5 = 0 or t^2-8 t+25 = 0
Subtract 5 from both sides:
t = -5 or t^2-8 t+25 = 0
Subtract 25 from both sides:
t = -5 or t^2-8 t = -25
Add 16 to both sides:
t = -5 or t^2-8 t+16 = -9
Write the left hand side as a square:
t = -5 or (t-4)^2 = -9
Take the square root of both sides:
t = -5 or t-4 = 3 i or t-4 = -3 i
Add 4 to both sides:
t = -5 or t = 4+3 i or t-4 = -3 i
Add 4 to both sides:
Answer: |t = -5 or t = 4+3 i or t = 4-3 i
