Factorise fully each of the following - Junior Cycle Mathematics - Question 9 - 2015
Question 9
Factorise fully each of the following.
(a)
7x - 21y
(b)
x² - 25
(c)
x² - x - 6
Worked Solution & Example Answer:Factorise fully each of the following - Junior Cycle Mathematics - Question 9 - 2015
Step 1
(a) 7x - 21y
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Answer
To factorise the expression, we first identify the common factor. In this case, the common factor is 7. Thus, we can factor out 7:
7(x−3y)
Step 2
(b) x² - 25
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Answer
The expression is a difference of squares, which can be factored using the formula a2−b2=(a+b)(a−b). Here, we can rewrite 25 as 52:
(x+5)(x−5)
Step 3
(c) x² - x - 6
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Answer
To factor the quadratic expression, we look for two numbers that multiply to -6 (the constant term) and add to -1 (the coefficient of x). The suitable numbers are -3 and 2. Therefore, we can write the factors as:
(x−3)(x+2)
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