MediumMathematicsHigh School (9–10)GeneralAlgebra › PolynomialsAlgebra › Algebraic Identities and FactorisationNumericalBoard Exam
Show that x + 3 is a factor of x³ + 4x² + 5x + 6, and find the other factor.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Show that is a factor of , and find the other factor.
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. Test. . So is a factor.
Step 2. Divide. .
Answer: the other factor is .
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