Question

Select the factors of x2 - 12x + 36. (4 points)

(x-6)(x - 6)
(x + 6)(x + 6)
(x + 3)(x + 12)
(x - 3)(x - 12)

Answer 1

See a solution process below

Explanation:

Because the x 2 coefficient is 1 we know the coefficient for the x terms in the factor will also be 1 :

( x ) ( x )

Because the constant is a positive and the coefficient for the x term is also a positive we know the sign for the constants in the factors will both be positive:

( x + ) ( x + )

Now we need to determine the factors which multiply to 36 and also add to 12:

1 × 36 = 36 ; 1 + 36 = 37 <- this is not the factor

2 × 18 = 36 ; 2 + 18 = 20 <- this is not the factor

3 × 12 = 36 ; 3 + 12 = 15 <- this is not the factor

4 × 9 = 36 ; 4 + 9 = 13 <- this is not the factor

6 × 6 = 36 ; 6+ 6 = 12 <- this IS the factor

( x + 6 ) ( x + 6 )