Question

Consider the trinomial x^2+10x+24

answer (a) and (b) individually

(a) on a test a student wrote the factored form as (x+2)(x+12) because they noticed that the product of 2 and 12 is 24. the teacher marked the answer wrong. why?

(b) what is the correct factored form of this trinomial? explain how you know this answer is correct

Answer 1

see explanation

Explanation:

(a)

(x + 2)(x + 12) ← expand using FOIL gives

x² + 14x + 24 ≠ x² + 10x + 24

(b)

consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (+ 10)

the factors are + 6 and + 4 , since

6 × 4 = 24 and 6 + 4 = 10 , then

x² + 10x + 24 = (x + 6)(x + 4)