Question

Factor the quadratic expression: x^2 + 13x + 42. Option 1: (x + 6)(x + 7) Option 2: (x - 6)(x - 7) Option 3: (x + 5)(x + 8) Option 4: (x - 5)(x - 8)

Answer 1

option 1

Explanation:

given

x² + 13x + 42

consider the factors of the constant term (+ 42) which sum to give the coefficient of the x- term (+ 13)

the factors are + 6 and + 7 , since

+ 6 × + 7 = + 42 and + 6 + 7 = + 13

use these factors to split the x- term

x² + 6x + 7x + 42 ( factor the first/second and third/fourth terms )

= x(x + 6) + 7(x + 6) ← factor out (x + 6) from each term

= (x + 6)(x + 7) ← in factored form