A student was asked to use grouping to solve 3x2+13x+4=0 .

Question

Select the step where the student first made an error.



Given: 3x2+13x+4=0
Step 1: I need two numbers that multiply to 12 and add to 13. The numbers are 1 and 12.

Step 2: 3x2+1x+12x+4=0
Step 3: x(3x+1)+4(3x+1)=0
Step 4: (x+4)(3x+1)=0
Step 5: x+4=0 and 3x+1=0
Step 6: x=4 and x=13 (1 point)
Responses

Step 1
Step 1

Step 2
Step 2

Step 3
Step 3

Step 4
Step 4

Step 5
Step 5

Step 6

Answer 1

The first error occurs in Step 1.

The student incorrectly states that they need two numbers that multiply to 12 (which is derived from multiplying the leading coefficient of 3 by the constant term 4) and add to 13. However, the correct product of the two numbers should actually be the product of 3 (the coefficient of \( x^2 \)) and 4 (the constant term), which is 12. But the numbers needed should multiply to 3 multiplied by 4 (which is 12) and add to 13.

The numbers that multiply to 12 and add to 13 actually do not exist. The correct way to factor the quadratic equation involves a different approach or recognizing it cannot be factored nicely with integers.

Thus, the correct answer is Step 1.