Question

Box Method

"X Method
x²–5x+6
x²–5x+6
x²-6x –lx+6
x
-1
%(2-6)-1(2-6)
2
XX
1-12
-61-6x+6
(x-1)(x-6)
(x-1)(x-6)
3 points
In the problem above, the student solved the problem but made a
mistake! Using your preferred method of factoring (box method or 'X'
method), identify the student's mistake in words (1-2 complete sentences)
AND then give the correct answer.

Answer 1

(x - 2)(x - 3)

Explanation:

The student factored the expression as (x - 1)(x - 6)

The error made is that - 6x and - 1x to not sum to - 5x

Given

x² - 5x + 6

Consider the factors of the constant term (+ 6) which sum to give the coefficient of the x- term (- 5)

The factors are - 2 and - 3, since

- 2 × - 3 = + 6 and - 2 - 3 = - 5, thus

x² - 2x - 3x + 6

= x(x - 2) - 3(x - 2)

= (x - 2)(x - 3)