A student was asked to use grouping to solve 2x2−9x+10=0.

Question

Select the step where the student first made an error.



Given: 2x2−9x+10=0
Step 1: I need two numbers that multiply to 20 and add to -9. The numbers are -4 and -5.

Step 2: 2x2−4x−5x+10=0
Step 3: 2x(x−2)−5(x−2)=0
Step 4: (2x+5)(x−2)=0
Step 5: 2x+5=0 and x−2=0
Step 6: x=−52 and x=2(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 error occurs in Step 1.

The student correctly identifies that they need two numbers that multiply to 20 (the product of \(2 \times 10\)) and add to -9; however, the numbers they chose, -4 and -5, do not multiply to 20. Instead, they multiply to 20 when using the factored form of -4 and -5 as positive values (i.e., \(-4 \times -5 = 20\)). The correct pairs of numbers that multiply to 20 and add to -9 should instead be -4 and -5, but for the coefficient in front of \(x^2\) in the equation, which is 2.

The correct focus should have been on factoring the expression \(2x^2 - 9x + 10\) differently, leading to a different factoring approach.

Therefore, the first error occurs in Step 1.