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Class 9MathematicsExploring Algebraic IdentitiesQuadratic expressionsHard
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The factorised form of (2x^2+mx+10) is ((2x+5)(x+2)). What is (m)?

Answer and explanation

Correct answer: 9

Expanding \((2x+5)(x+2)\) gives \(2x^2+4x+5x+10\). Therefore, the middle term is \(4x+5x=9x\). Comparing it with \(2x^2+mx+10\), we get \(m=9\). The values 4 and 5 are coefficients of the separate cross terms, whereas \(m\) is their sum. Exam tip: add both cross terms when finding the middle term in a product of two binomials.

Related tags

Quadratic ExpressionsAlgebraic IdentitiesBinomial ExpansionCoefficient ComparisonPolynomialsExploring 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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