Quiz 10: Training For Problem Solving Skills

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Created by Isabelle Yeong on June 29th 2015

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Question 1: What is the next square number after (x-6)⁴?

((x-6)²)²+1

((x-6+1)²)²

((x-6)²+1)²

Clear selection

Question 2: What is/are the first thing that comes to your mind when you see x⁴-24 x³+216 x²-804 x+936?

It has a repeated factor, perhaps?

We can factor it using the rational root test.

Binomial expansion.

Question 3: What is the best equivalent representation of x⁴-24 x³+216 x²-804 x+936 written as a square number?

(x-6)√((x-6)³+60)²

(x³-18 x²+108 x-156)√(x-6)

((x-6)²)²+60(x-6)

Clear selection

Question 4: If x≥6, what are the two squares of consecutive numbers that the number represented by x⁴-24 x³+216 x²-804 x+936 lie between?

(x-6)⁴<x⁴-24 x³+216 x²-804 x+936<((x-6)²)²+1

(x-6)⁴<x⁴-24 x³+216 x²-804 x+936<((x-6+1)²)²

(x-6)⁴<x⁴-24 x³+216 x²-804 x+936<((x-6)²+1)²

Clear selection

Question 5: Given that x is an integer, and based on your answer in question 4, find the range of values of x that satisfies the RHS of the inequality?

x>35

x>36

x>6

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Question 6: Based on your answer in question 4 and 5, what can you say about the expression x⁴-24 x³+216 x²-804 x+936, if it is meant to be a square?

x⁴-24 x³+216 x²-804 x+936 can't be a square in a certain domain.

x⁴-24 x³+216 x²-804 x+936 can't be a square for all real x..

x⁴-24 x³+216 x²-804 x+936 is always a square.

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