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Algebra

Question 1 of 9

Factorising Quadratic Equations

Question

Factorise \(15x^2 + 7x = 2\)

Show solution Hide solution Fully worked — 4 steps
  1. Rearrange in the form \(ax^2 + bx + c = 0\)
    \[ 15x^2 + 7x = 2 \]
    \[ 15x^2 + 7x - 2 = 0 \]
  2. Factorise
    \[ (5x - 1)(3x + 2) = 0 \]
  3. Using the zero-factor theorem, equate each factor to 0

    Then either

    \[ 5x - 1 = 0 \Rightarrow x = \frac{1}{5} \]

    or

    \[ 3x + 2 = 0 \Rightarrow x = \frac{-2}{3} \]
  4. State the solutions

    The solutions are \(x = \frac{1}{5}\) or \(x = \frac{-2}{3}\). That is, \(x\) is one fifth and \(x\) is minus two thirds.