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Class 9MathematicsExploring Algebraic IdentitiesQuadratic expressionsHard
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Which of the following quadratic trinomials is a perfect square?

Answer and explanation

Correct answer: \(x^2+6x+9\)

\(x^2+6x+9=x^2+2\cdot x\cdot3+3^2=(x+3)^2\), so option A is a perfect square. Option B is the closest distractor, but its constant term is \(8\); it must be \(9\) to form \((x+3)^2\). Exam tip: for \(x^2+bx+c\) to be a perfect square, check whether \(c=(b/2)^2\).

Related tags

Quadratic ExpressionsAlgebraic IdentitiesPerfect Square TrinomialClass 9 MathematicsPolynomialsExploring Algebraic IdentitiesMathematicsClass 9 Mcq
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10 more MCQs
  1. 1Which expression can be factorised using the difference-of-cubes identity?
  2. 2What will be the factorised form of (r^2-2rs+s^2)?
  3. 3Which expression can be factorised directly using the identity for the difference of two squares?
  4. 4Which expression can be factorised directly using the difference-of-squares identity \(a^2-b^2=(a-b)(a+b)\)?
  5. 5Which expression is a quadratic expression?
  6. 6Based on the powers of the variable \(x\) in the polynomial \(5x^2-3x+7\), what is the degree of this expression?
  7. 7If a, b and c are constants, which condition is necessary for \(ax^2+bx+c\) to be a quadratic expression in x?
  8. 8If a quadratic expression has the general form \(ax^2+bx+c\), which condition on \(a\) is necessary for it to be quadratic?
  9. 9Which of the following expressions represents the square of the difference of two terms?
  10. 10Which of the following quadratic expressions can be factorised using the identity for the difference of two squares?
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