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Factorise the quadratic expression $x^2 + 2x - 3$ - Junior Cycle Mathematics - Question 14 - 2021

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Question 14

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Factorise the quadratic expression $x^2 + 2x - 3$. $x^2 + 2x - 3 = (x )(x )$ Factorise fully $3ps - pr + 3qs - qr.$

Worked Solution & Example Answer:Factorise the quadratic expression $x^2 + 2x - 3$ - Junior Cycle Mathematics - Question 14 - 2021

Step 1

Factorise the quadratic expression $x^2 + 2x - 3$

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Answer

To factorise the expression x2+2x−3x^2 + 2x - 3, we look for two numbers that multiply to −3-3 (the constant term) and add up to 22 (the coefficient of the xx term).

The numbers 33 and −1-1 satisfy these conditions:

  • 3imes−1=−33 imes -1 = -3
  • 3+(−1)=23 + (-1) = 2

Thus, we can write:

x2+2x−3=(x+3)(x−1)x^2 + 2x - 3 = (x + 3)(x - 1)

Step 2

Factorise fully $3ps - pr + 3qs - qr$

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Answer

To factorise the expression 3ps−pr+3qs−qr3ps - pr + 3qs - qr, we can group the terms:

(3ps−pr)+(3qs−qr)(3ps - pr) + (3qs - qr)

From the first group, we can factor out pp:

p(3s−r)p(3s - r)

From the second group, we can factor out qq:

q(3s−r)q(3s - r)

So we have:

p(3s−r)+q(3s−r)p(3s - r) + q(3s - r)

Now we can factor out (3s−r)(3s - r):

(3s−r)(p+q)(3s - r)(p + q)

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