If \(p(x)=x^2-4\sqrt{2}x+8\), in which form can it be written?
Answer and explanation
Correct answer: \((x-2\sqrt{2})^2\)
This is a perfect-square trinomial because \((x-2\sqrt{2})^2 = x^2 -2\cdot(2\sqrt{2})x + (2\sqrt{2})^2 = x^2 -4\sqrt{2}x +8\). Option (x+2\sqrt{2})^2 would give +4\sqrt{2}x (wrong sign). Option (x-\sqrt{2})^2 has constant term 2, and (x-4\sqrt{2})^2 has constant term 32, so they do not match the given polynomial. Exam tip: use the identity \((x-a)^2 = x^2 -2ax + a^2\); find a from the middle coefficient and verify a^2 equals the constant term.
Frequently asked questions
What is the correct answer to this question?
\((x-2\sqrt{2})^2\)
Why is this the correct answer?
This is a perfect-square trinomial because \((x-2\sqrt{2})^2 = x^2 -2\cdot(2\sqrt{2})x + (2\sqrt{2})^2 = x^2 -4\sqrt{2}x +8\). Option (x+2\sqrt{2})^2 would give +4\sqrt{2}x (wrong sign). Option (x-\sqrt{2})^2 has constant term 2, and (x-4\sqrt{2})^2 has constant term 32, so they do not match the given polynomial. Exam tip: use the identity \((x-a)^2 = x^2 -2ax + a^2\); find a from the middle coefficient and verify a^2 equals the constant term.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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