Which of the following is the factorised form of \(x^2-2x-15=0\)?
Answer and explanation
Correct answer: \((x-5)(x+3)=0\)
Expand the factors in A: \((x-5)(x+3)=x^2+3x-5x-15=x^2-2x-15\), so A matches the given quadratic. A common distractor B expands to \((x+5)(x-3)=x^2+2x-15\) which has +2x (not -2x), so it is incorrect. Exam tip: find two numbers whose product is -15 and sum is -2 (here -5 and 3) to factor quickly.
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What is the correct answer to this question?
\((x-5)(x+3)=0\)
Why is this the correct answer?
Expand the factors in A: \((x-5)(x+3)=x^2+3x-5x-15=x^2-2x-15\), so A matches the given quadratic. A common distractor B expands to \((x+5)(x-3)=x^2+2x-15\) which has +2x (not -2x), so it is incorrect. Exam tip: find two numbers whose product is -15 and sum is -2 (here -5 and 3) to factor quickly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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