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If \(p(x)=x^2-8x+16\), what is the value of \(p(4+t)\)?
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Answer and explanation
Correct answer: \(t^2\)
The polynomial can be written as \(p(x)=x^2-8x+16=(x-4)^2\). Therefore, \(p(4+t)=((4+t)-4)^2=t^2\). Option C gives only a linear term and misses the squaring step. In an exam, factoring into a perfect square is the quickest method here.
Frequently asked questions
What is the correct answer to this question?
\(t^2\)
Why is this the correct answer?
The polynomial can be written as \(p(x)=x^2-8x+16=(x-4)^2\). Therefore, \(p(4+t)=((4+t)-4)^2=t^2\). Option C gives only a linear term and misses the squaring step. In an exam, factoring into a perfect square is the quickest method here.
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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