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Factorise $5x - 15$ and $2x - 6$ - Junior Cycle Mathematics - Question 2 - 2015

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Factorise $5x - 15$ and $2x - 6$. If A and B are variable quantities, we say that A is proportional to B if the fraction \( \frac{A}{B} \) is a constant.

Worked Solution & Example Answer:Factorise $5x - 15$ and $2x - 6$ - Junior Cycle Mathematics - Question 2 - 2015

Step 1

Factorise $5x - 15$

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Answer

To factorise 5x−155x - 15, we can factor out the greatest common factor, which is 5:

5x−15=5(x−3)5x - 15 = 5(x - 3)

Step 2

Factorise $2x - 6$

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Answer

Similarly, for 2x−62x - 6, we factor out the greatest common factor, which is 2:

2x−6=2(x−3)2x - 6 = 2(x - 3)

Step 3

Show that $5x - 15$ is proportional to $2x - 6$

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Answer

From part (a), we can express the factors:

We found:

  • 5x−15=5(x−3)5x - 15 = 5(x - 3)
  • 2x−6=2(x−3)2x - 6 = 2(x - 3)

Now, to show proportionality, we take the ratio:

5(x−3)2(x−3)=52\frac{5(x - 3)}{2(x - 3)} = \frac{5}{2}

Since this fraction is a constant, it proves that 5x−155x - 15 is proportional to 2x−62x - 6.

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