Area tiles show \(t^2+7t+12\). Which rectangle sides are correct?
Answer and explanation
Correct answer: \((t+3)\) and \((t+4)\)
To factor \(t^2+7t+12\), we need two numbers whose sum is \(7\) and product is \(12\). Since \(3+4=7\) and \(3\times4=12\), \(t^2+7t+12=(t+3)(t+4)\). Option C also gives constant term \(12\), but its middle term is \(8t\), not \(7t\). Exam tip: multiply the binomials or check both the sum and product before choosing an answer.
Frequently asked questions
What is the correct answer to this question?
\((t+3)\) and \((t+4)\)
Why is this the correct answer?
To factor \(t^2+7t+12\), we need two numbers whose sum is \(7\) and product is \(12\). Since \(3+4=7\) and \(3\times4=12\), \(t^2+7t+12=(t+3)(t+4)\). Option C also gives constant term \(12\), but its middle term is \(8t\), not \(7t\). Exam tip: multiply the binomials or check both the sum and product before choosing an answer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Visual models of identities.
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