Question

Factor completely and then place the factors in the proper location on the grid.
x2 + 13x + 36

Answer 1

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)

Answer 2

(x + 9)(x + 4)

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