factor this polynomial: x^2+12x+27

Given the quadratic function:

f(x) = x^2 + 12x - 27

a = 1

b = 12

c= 27

Find the factor.

Solution:
In order to solve for the roots or the factors of an equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is 12, and when multiplied, the answer is 27. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(12) ± √((12)^2 − 4(1)(27))/2(1)

x = −12 ± √(144 − 108)/2

x = −12 ± √(36)/2

x = −12 ± √(36)/2

x = −12 ± 6/2

Solve for ± separately

x = -12 + 6 /2
x = -6/2
x = -3

x = -12 - 6/2
x = -18/2
x = -9

Final answer:

x = -3

x = -9