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... 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 factor the quadratic expression x2+4x−5, we are given that one of the factors is (x+5). We can represent the expression in factorised form as:
x2+4x−5=(x+5)(x−1).
This is derived by finding a pair of numbers that multiply to −5 (the constant term) and add to 4 (the coefficient of x). The numbers are 5 and −1.
Step 2
Using your factors from part (a), or otherwise, solve the equation: $x^2 + 4x - 5 = 0$
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Answer
Using the factored form (x+5)(x−1)=0, we can set each factor equal to zero:
x+5=0 implies that x=−5.
x−1=0 implies that x=1.
Thus, the solutions are x=−5 and x=1.
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