If \(p(x)=x^2+4x+6\), what is the simplified form of \(p(x-1)\)?
Answer and explanation
Correct answer: \(x^2+2x+3\)
To find \(p(x-1)\), substitute the entire expression \((x-1)\) for \(x\): \(p(x-1)=(x-1)^2+4(x-1)+6=x^2-2x+1+4x-4+6=x^2+2x+3\). Therefore, option A is correct. Option B has an incorrect constant-term calculation, while option D results from mishandling the expansion of \(4(x-1)\). Exam tip: whenever the replacement contains a minus sign, keep the complete expression inside parentheses.
Frequently asked questions
What is the correct answer to this question?
\(x^2+2x+3\)
Why is this the correct answer?
To find \(p(x-1)\), substitute the entire expression \((x-1)\) for \(x\): \(p(x-1)=(x-1)^2+4(x-1)+6=x^2-2x+1+4x-4+6=x^2+2x+3\). Therefore, option A is correct. Option B has an incorrect constant-term calculation, while option D results from mishandling the expansion of \(4(x-1)\). Exam tip: whenever the replacement contains a minus sign, keep the complete expression inside parentheses.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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