Answer:
f(x) = (2x+1)(3x−4)(x+5)
x = -5, x = -1/2, and x = 4/3
Step-by-step explanation:
Start by setting up the long division:
Look at the first terms. 2x goes into 6x³ a number of 3x² times.
2x+1 times 3x² is 6x³+3x².
Subtract.
Now drop down the next term (the -29x).
Repeat the process. 2x goes into 22x² a number of 11x times.
Multiply:
Subtract:
Drop down the next term (-20):
2x goes into -40x a number of -20 times.
Multiply:
Subtract:
The remainder is 0. So f(x) can be factored as:
f(x) = (2x+1)(3x²+11x−20)
Which we can further factor using AC method:
f(x) = (2x+1)(3x−4)(x+5)
So the zeros are x = -5, x = -1/2, and x = 4/3.