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Algebra

Question 6 of 9

Factorising Quadratic Equations

Question

Factorise \(4m(m + 2) - 2(m^2 - 1) = 5 + 3m\)

Show solution Hide solution Fully worked — 5 steps
  1. Find the product of the expressions
    \[ 4m(m + 2) - 2(m^2 - 1) = 5 + 3m \]
    \[ 4m^2 + 8m - 2m^2 + 2 = 5 + 3m \]
  2. Add \(-5 - 3m\) to both sides
    \[ 2m^2 + 5m - 3 = 0 \]
  3. Factorise
    \[ (2m - 1)(m + 3) = 0 \]
  4. Using the zero-factor theorem, equate each factor to 0

    Then either

    \[ 2m - 1 = 0 \Rightarrow m = \frac{1}{2} \]

    or

    \[ m + 3 = 0 \Rightarrow m = -3 \]
  5. State the solutions

    The solutions are \(m = \frac{1}{2}\) or \(m = -3\). That is, \(m\) is one half and \(m\) is minus three.