Which of the following polynomials can be expressed as the square of a binomial?
Answer and explanation
Correct answer: \(x^2+10x+25\)
In option A, \(x^2+10x+25=x^2+2(x)(5)+5^2=(x+5)^2\), so it is a perfect-square polynomial. In option B, the constant term is 20, whereas 25 is required to complete the square for \(x^2+10x\). In option C, the middle term is 5x instead of the required 10x, and option D has a negative constant term. In an exam, check the identities \(a^2+2ab+b^2=(a+b)^2\) and \(a^2-2ab+b^2=(a-b)^2\).
Frequently asked questions
What is the correct answer to this question?
\(x^2+10x+25\)
Why is this the correct answer?
In option A, \(x^2+10x+25=x^2+2(x)(5)+5^2=(x+5)^2\), so it is a perfect-square polynomial. In option B, the constant term is 20, whereas 25 is required to complete the square for \(x^2+10x\). In option C, the middle term is 5x instead of the required 10x, and option D has a negative constant term. In an exam, check the identities \(a^2+2ab+b^2=(a+b)^2\) and \(a^2-2ab+b^2=(a-b)^2\).
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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