Question

A student was asked to use grouping to solve 3x^2+5x−2=0.

Select the step where the student first made an error.

Given: 3x^2+5x−2=0

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

Step 2: 3x^2+6x−x−2=0

Step 3: 3x(x+2)−1(x+2)=0

Step 4: (3x−1)(x−2)=0

Step 5: 3x−1=0 and x−2=0

Step 6: x=1/3 and x=2

(1 point)

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Answer 1

Step 4.

Explanation: From Step 3 you get (x+2)(3x−1), not (3x−1)(x−2). The correct factorization is (3x−1)(x+2)=0, so the roots are x = 1/3 and x = −2.