Algebra

First, factorise out the common factor of 2 to get 2 times the quantity x squared minus 4, then apply the difference of two squares to get 2 times x minus 2 times x plus 2. Option B is incorrect because it is not fully factorised, as the first bracket still contains a common factor of 2. Option D is incorrect because expanding it does not yield the original expression.

The quadratic factorises to the product of x minus 2 and x minus 3 equals 0, which yields the solutions x equals 2 or 3. Option C is a common mistake where the signs from the factorised brackets are not reversed to solve for x. Option A is incorrect because those values would satisfy a quadratic that multiplies to negative 6 instead of positive 6.

Expanding the bracket gives 3x minus 6 equals 5x plus 4, which rearranges to 2x equals negative 10, solving to x equals negative 5. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option B is incorrect because it fails to track the negative sign when dividing.
• !First, factorise out the common factor of 2 to get 2 times the quantity x squared minus 4, then apply the difference of two squares to get 2 times x minus 2 times x plus 2.
• !Option C is a common mistake where the signs from the factorised brackets are not reversed to solve for x.
• !Option D is incorrect because 6 is only the change in the y-coordinates, forgetting to divide by the change in x.

Answer each from memory — you'll see instantly whether you're right and why.

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