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Question 1
A student simplifies $df r a c x^{2} + 5 x$ and gets $x + 5$ . What error have they made?
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AThey cancelled a term instead of a factor — $x$ is not a factor of $x^{2} + 5$
Step-by-step walkthrough
Choose a solution method
Method #1Direct Approach
Step 1: Identify the rule for cancelling
You can only cancel something that is a factor of the entire numerator — that is, it must be multiplied across the whole expression, not just part of it.
Step 2: Check whether $x$ is a factor of $x^2 + 5$
The numerator $x^{2} + 5$ involves addition. $x$ divides into $x^{2}$ but does not divide into 5 (since $\frac{5}{x}$ is not a whole expression). So $x$ is NOT a factor of $x^{2} + 5$ .
Step 3: Name the type of error
The student cancelled a term ( $x^{2}$ part) rather than a factor of the whole numerator. This is the classic error: cancelling across an addition sign is not valid.
Step 4: Confirm the correct option
The correct explanation is: they cancelled a term instead of a factor. The fraction $\frac{x ^{2} + 5}{x}$ cannot be simplified further because $x$ does not factor out of the entire numerator.
Method #2Process of Elimination
Step 1: Identify what is being tested
This question tests whether you know the rule: only factors can be cancelled, not terms connected by addition or subtraction.
Step 2: Eliminate 'forgot to square the $x$ in the denominator'
There is no reason to square the denominator here. The issue is not about powers of $x$ in the denominator. Eliminate this option.
Step 3: Eliminate 'should have multiplied instead of dividing'
The operation here is division (a fraction), which is correct. Multiplying instead would give a completely different and wrong expression. Eliminate this option.
Step 4: Eliminate 'did not find the HCF of $x^2$ and 5'
Finding the HCF of $x^{2}$ and 5 would only be relevant if they were factors in a product. Since they are connected by addition, HCF cancellation doesn't apply here. Eliminate this option.
Step 5: Select the correct answer
The correct answer is: they cancelled a term instead of a factor. Because $x^{2} + 5$ has a $+$ sign, $x$ is not a factor of the whole numerator and cannot be cancelled.

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Step-by-step walkthrough

Step 1: Identify the rule for cancelling

Step 2: Check whether $x$ is a factor of $x^2 + 5$

Step 3: Name the type of error

Step 4: Confirm the correct option

Step 1: Identify what is being tested

Step 2: Eliminate 'forgot to square the $x$ in the denominator'

Step 3: Eliminate 'should have multiplied instead of dividing'

Step 4: Eliminate 'did not find the HCF of $x^2$ and 5'

Step 5: Select the correct answer

5 more questions in this topic