Question

A student was asked to use grouping to solve x^2−5x+6=0
.

Select the step where the student first made an error.




Given: x^2−5x+6=0

Step 1: I need two numbers that multiply to 6 and add to -5. The numbers are -2 and -3.

Step 2: x2−2x−3x+6=0

Step 3: x(x−2)−3(x−2)=0

Step 4: (x+3)(x−2)=0

Step 5: x+3=0 and x−2=0

Step 6: x=−3 and x=2



(1 point)

Answer 1

Step 4.

From x(x−2) − 3(x−2) you should factor (x−2) to get (x−2)(x−3) (or (x−3)(x−2)), not (x+3)(x−2). The correct solutions are x = 2 and x = 3.