Try this long division problem!

Many students, including JC H2 math students, have difficulty doing long division when it comes to complex problems.

Try this problem to test or sharpen your long division skills.

Question

If Tex2Img_1403575339 is a factor of Tex2Img_1403575464, prove by long division that Tex2Img_1403575555

Solution

long division

Factorial

Questions on factorial can appear in H2 math binomial expansion, partial fractions, method of difference, mathematical induction and probability. Knowing how to simplify and manipulate factorials are crucial to doing well.

Two commonly used techniques

1. Replace n! with n(n-1)!

2. Multiply by k/k  or k! / k!

Example 1

factorial 1

 Example 2 

Solve the inequality

(r+1)!(17-r)!(9-r)!(r+3)! > r!(18-r)!(10-r)!(r+2)!

(A level 2011, P2 Q11)

(r+1)r!(17-r)!(9-r)!(r+3)(r+2)! > r!(18-r)(17-r)!(10-r)(9-r)!(r+2)!

(r+1)(r+3)> (18-r)(10-r)

32r > 177

r > 5.53

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