If (p(x)=x-6) and (q(x)=3x+2), what is (2p(x)+q(x))?
Answer and explanation
Correct answer: \(5x-10\)
\(2p(x)+q(x)=2(x-6)+(3x+2)\). Using the distributive property, \(2(x-6)=2x-12\). Combining like terms gives \(2x-12+3x+2=5x-10\). Hence, \(5x-10\) is correct. The option \(4x-10\) results from incorrectly adding \(2x\) and \(3x\). Exam tip: multiply each polynomial by its coefficient first, then combine like terms.
Frequently asked questions
What is the correct answer to this question?
\(5x-10\)
Why is this the correct answer?
\(2p(x)+q(x)=2(x-6)+(3x+2)\). Using the distributive property, \(2(x-6)=2x-12\). Combining like terms gives \(2x-12+3x+2=5x-10\). Hence, \(5x-10\) is correct. The option \(4x-10\) results from incorrectly adding \(2x\) and \(3x\). Exam tip: multiply each polynomial by its coefficient first, then combine like terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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