If \(p(x)=x^2-2x+3\), what is \(p(x+1)\)?
Answer and explanation
Correct answer: \(x^2+2\)
To find \(p(x+1)\), replace every occurrence of \(x\) in the polynomial with the complete expression \((x+1)\): \(p(x+1)=(x+1)^2-2(x+1)+3=x^2+2x+1-2x-2+3=x^2+2\). Hence, option A is correct. Option D fails to combine the \(-2x\) term correctly. Exam tip: keep the substituted binomial in parentheses, especially when it is squared.
Frequently asked questions
What is the correct answer to this question?
\(x^2+2\)
Why is this the correct answer?
To find \(p(x+1)\), replace every occurrence of \(x\) in the polynomial with the complete expression \((x+1)\): \(p(x+1)=(x+1)^2-2(x+1)+3=x^2+2x+1-2x-2+3=x^2+2\). Hence, option A is correct. Option D fails to combine the \(-2x\) term correctly. Exam tip: keep the substituted binomial in parentheses, especially when it is squared.
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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