Which factored form represents the equation \(x^2+11x+30=0\)?
Answer and explanation
Correct answer: \((x+5)(x+6)=0\)
For the quadratic, the constant term is 30 and the coefficient of x is 11. Find two numbers whose product is 30 and whose sum is 11 — these are 5 and 6 because \(5\cdot6=30\) and \(5+6=11\). Hence the correct factorization is \((x+5)(x+6)=0\). The closest distractor \((x+3)(x+10)=0\) has the correct product but a sum of \(3+10=13\), so it does not match the middle coefficient. Exam tip: to factor quickly, match the product (constant) and the sum (middle coefficient) before expanding.
Frequently asked questions
What is the correct answer to this question?
\((x+5)(x+6)=0\)
Why is this the correct answer?
For the quadratic, the constant term is 30 and the coefficient of x is 11. Find two numbers whose product is 30 and whose sum is 11 — these are 5 and 6 because \(5\cdot6=30\) and \(5+6=11\). Hence the correct factorization is \((x+5)(x+6)=0\). The closest distractor \((x+3)(x+10)=0\) has the correct product but a sum of \(3+10=13\), so it does not match the middle coefficient. Exam tip: to factor quickly, match the product (constant) and the sum (middle coefficient) before expanding.
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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