Factor completely and then place the factors in the proper location on the grid.

x2 + 13x + 36

(x + 9) (x + 4)

Step-by-step explanation:

Given

x² + 13x + 36

Consider the factors of the constant term ( + 36) which sum to give the coefficient of the x - term ( + 13)

The factors are + 9 and + 4, since

9 * 4 = 36 and 9 + 4 = 13, hence

x² + 13x + 36 = (x + 9) (x + 4) ← in factored form

1. x^2 + 13x + 36 = 0

using powerful & time-sparing quadratic formula:

delta = 13^2 - 4*1*36 = 25 = 5^2

x1 and x2 = (-13 - / + 5) / 2 = - 9 and - 4

x^2 + 13x + 36 = (x+9) (x+4)

2. other way : complete the square

b^2 + 12b + 32 = b^2 + 2*6b + 6^2 - 6^2 + 32

b^2 + 12b + 32 = (b+6) ^2 - 4

b^2 + 12b + 32 = (b+6-2) (b+6+2) = (b+4) (b+8)

3. other way : - 4 "ovious" solution : (-4) ^2 - (-4) - 20 = 0

so the other is : - 4. a2 = - 20/1 - --> a2 = 5

a^2 - a - 20 = (a-5) (a+4)