Factorise x
2
+5x−14.
- A(x−7)(x+2)
- B(x−1)(x+14)
- C(x+7)(x−2)
- D(x−14)(x+1)
Solution & Step-by-step Explanation
To factorise the quadratic expression x
2
+5x−14, we need to split the middle term into two numbers whose sum is 5 and product is −14.
These two numbers are 7 and −2 because:
7+(−2)=5
7×(−2)=−14
Now, rewriting the middle term:
x
2
+7x−2x−14
Group the terms to take common factors out:
x(x+7)−2(x+7)
Taking (x+7) as a common factor:
(x+7)(x−2)
2
+5x−14, we need to split the middle term into two numbers whose sum is 5 and product is −14.
These two numbers are 7 and −2 because:
7+(−2)=5
7×(−2)=−14
Now, rewriting the middle term:
x
2
+7x−2x−14
Group the terms to take common factors out:
x(x+7)−2(x+7)
Taking (x+7) as a common factor:
(x+7)(x−2)