Question

Jacob incorrectly factored 5x^2-11x +2
Step 1 5x^2 + (-10x-x)+2
Step2. (5x^2-10x)+(x-2)
Step 3. 5x(x-2) + 1(x-2)
Step 4. (5x +1)(x-2)
Which step did he make his first error

Answer 1

Let's analyze Jacob's steps to find out where he made the first error in factoring the quadratic expression \(5x^2 - 11x + 2\).

**Step 1:**
He rewrites the equation as:
\[ 5x^2 + (-10x - x) + 2 \]
This is correct since \(-10x - x = -11x\).

**Step 2:**
He rewrites it as:
\[ (5x^2 - 10x) + (x + 2) \]
Here, he incorrectly grouped the terms. He should group it as \[ (5x^2 - 10x) + (-x + 2) \] to maintain the correct expression. This is the first error.

**Step 3:**
He factors out from the first group:
\[ 5x(x - 2) + 1(x - 2) \]
This part is correct since \((5x^2 - 10x) = 5x(x - 2)\) and \((x - 2) = 1(x - 2)\).

**Step 4:**
He combines terms to arrive at the final factors:
\[ (5x + 1)(x - 2) \]
This part is mathematically correct based on his grouping but incorrect based on the original polynomial \(5x^2 - 11x + 2\). The original quadratic cannot be factored to this product.

In conclusion, Jacob made his **first error in Step 2** when he incorrectly grouped the terms. The correct grouping should have been \((5x^2 - 10x) + (-x + 2)\).