When x³ + kx² - 3x + 2 is divided by x - 2, the remainder is 24. Find k.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
When is divided by , the remainder is . Find .
Need a reminder? The key ideaShow
Remainder theorem: dividing by leaves the remainder . For , use . Factor theorem: is a factor exactly when .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The remainder. .
Step 2. Solve. , so and .
Answer: .
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