To find the factors of the quadratic expression x² + 9x + 14, we can use the method of factoring by grouping or applying the quadratic formula. However, in this case, factoring by grouping is quite straightforward.
First, we’ll look for two numbers that add up to the coefficient of x (which is 9) and multiply to the constant term (which is 14). The numbers we are looking for are 7 and 2 because:
- 7 + 2 = 9
- 7 × 2 = 14
Now we can rewrite the quadratic expression using these numbers:
x² + 7x + 2x + 14
Next, we can group the terms:
=(x² + 7x) + (2x + 14)
Now, factor out the common factors in each group:
= x(x + 7) + 2(x + 7)
Now, we can see that (x + 7) is a common factor:
= (x + 7)(x + 2)
So, the final factored form of the quadratic expression x² + 9x + 14 is:
(x + 7)(x + 2)
This means that the factors of the expression are (x + 7) and (x + 2).