Question

Jacob incorrectly factored 5x^2 - 11x + 2 using the following steps
Step 1. 5x^2 + (-10x - x) + 2
Step 2. (5x^2 -10x) + (x - 2)
Step 3. 5x(x -2) + 1(x-2)
Step 4. (5x + 1)(x - 2)
In which studies he make his first error

Answer 1

Jacob made a mistake in his factoring process in Step 1.

Let's look at the original expression: \( 5x^2 - 11x + 2 \).

In Step 1, he rewrites \(-11x\) as \(-10x - x\). While this looks fine structurally, it does not keep the equation balanced with respect to the original expression:

- Starting from \(5x^2 - 11x + 2\), transforming \(-11x\) into \(-10x - x\) gives \(5x^2 + (-10x - x) + 2\), which is fine.

However, moving to Step 2, he groups terms incorrectly. The correct grouping from Step 1 should have been:

\[ 5x^2 - 10x - x + 2 \]

Instead, he groups as \((5x^2 - 10x) + (x - 2)\) in Step 2, which is incorrect. The correct grouping should have been \((5x^2 - 10x) + (-x + 2)\).

This grouping leads to an incorrect factorization in later steps. Therefore, the first error occurs in the transition from Step 1 to Step 2.