A corner shop sells bags of sweets from a stand near the till. The price, in pence, of a small bag is \(3x-2\) and the price of a large bag is \(3x^2-2x\), ...
Question 1 Report
A corner shop sells bags of sweets from a stand near the till. The price, in pence, of a small bag is \(3x-2\) and the price of a large bag is \(3x^2-2x\), where \(x\) is a code the owner uses to track weekly special offers.
- Factorise \(3x^2-2x\). (2)
- Simplify \(\dfrac{3x^2-2x}{x}\). (2)
- Solve \(3x-2=10\). (1)
Answer Details
This question tests factorising an expression by taking out a common factor, simplifying an algebraic fraction using that factorisation, and solving a simple linear equation.
- Taking out the common factor \(x\): \[3x^2-2x=x(3x-2) \text{ <b>[2]</b>}\]
- Cancelling the common factor \(x\): \[\frac{3x^2-2x}{x}=\frac{x(3x-2)}{x}=3x-2 \text{ <b>[2]</b>}\]
- Solving \(3x-2=10\): \[3x=12 \implies x=4 \text{ <b>[1]</b>}\]
Part (b) can be answered directly from the factorised form found in part (a), without needing to divide term by term, which is why factorising first is worth doing even when a question only asks for a simplification.
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