Advanced math
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What this topic is really about
Because 2 raised to the fifth power equals 32 (2×2×2×2×2=32), x must be 5. The choice 4 is tempting but 2^4=16, which is half the required value, so it cannot satisfy the equation. Options C and D give 64 and 8 respectively, far from 32.
The correct expansion of the given expression is 2x^2 - 5x - 12.. Expanding the expression using the FOIL method yields 2x^2 - 8x + 3x - 12, which simplifies to 2x^2 - 5x - 12.
See the mechanism
The FOIL method is used to expand the expression, which stands for First, Outer, Inner, Last. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
(2x + 3)(x − 4) =
- Identify what the question tests: (2x + 3)(x − 4) =.
- Expanding the expression using the FOIL method yields 2x^2 - 8x + 3x - 12, which simplifies to 2x^2 - 5x - 12.
- Option B is incorrect because it incorrectly adds 8x and -3x to get a positive middle term instead of subtracting 8x from 3x.
- Why it matters: The FOIL method is used to expand the expression, which stands for First, Outer, Inner, Last. This method helps to ensure that all terms are included and that the signs are correct. By applying the FOIL method, we get 2x^2 - 8x + 3x - 12, which simplifies to 2x^2 - 5x - 12.
Traps the examiner sets
- Many students incorrectly apply the FOIL method, often adding or subtracting the wrong terms, which can lead to incorrect answers like 2x^2 + 5x - 12 or 2x^2 - 11x - 12.
- Some people may get confused and try to use the quadratic formula or other methods, but factoring is the most efficient way to solve this equation. Others may make errors in factoring, such as incorrect signs or factors.
- Option B is incorrect because it incorrectly adds 8x and -3x to get a positive middle term instead of subtracting 8x from 3x.
- Option C is incorrect because using negative values would result in a positive middle term of 6x rather than -6x when expanded.
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