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Factorise $x^2 + 4x - 5$ - Junior Cycle Mathematics - Question 11 - 2017

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Question 11

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Factorise $x^2 + 4x - 5$. One of the factors is $(x + 5)$. $x^2 + 4x - 5 = (x + 5)( )$ Using your factors from part (a), or otherwise, solve the equation: $x^2 ... show full transcript

Worked Solution & Example Answer:Factorise $x^2 + 4x - 5$ - Junior Cycle Mathematics - Question 11 - 2017

Step 1

Factorise $x^2 + 4x - 5$

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Answer

To factorise the quadratic expression x2+4x−5x^2 + 4x - 5, we start with the given factor (x+5)(x + 5). We need to find the other factor.

Using polynomial identity: x2+4x−5=(x+5)(x−1)x^2 + 4x - 5 = (x + 5)(x - 1)

Thus, the complete factorisation is: x2+4x−5=(x+5)(x−1)x^2 + 4x - 5 = (x + 5)(x - 1)

Step 2

Using your factors from part (a), or otherwise, solve the equation:

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Answer

Now, substituting the factors into the equation to solve: (x+5)(x−1)=0(x + 5)(x - 1) = 0

Setting each factor to zero provides:

  1. x+5=0x + 5 = 0

    • Thus, x=−5x = -5

  2. x−1=0x - 1 = 0

    • Thus, x=1x = 1

The solutions to the equation x2+4x−5=0x^2 + 4x - 5 = 0 are therefore:

  • x=−5x = -5
  • x=1x = 1

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