Jacob incorrectly factored 5x² - 11x + 2 using the following steps:
Step 1: 5x² + (-10x - x) + 2
Step 2: (5x² - 10x)+(x - 2)
Step 3: 5x (x - 2) + 1(x - 2)
Step 4: (5x + 1)(x - 2)
In which step did he make his first error?
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A. In Step 1 because the -11x was rewritten as -10x - x.
B. In Step 2 because the sign on x should be negative and the sign on 2 should be positive.
C. In Step 3 because there is no need to multiply (x - 2 ) by 1.
D. In Step 4 because (x - 2) should be written first.
1 answer
Jacob's first error occurred in Step 1. The expression \(5x^2 - 11x + 2\) is incorrectly rewritten as \(5x^2 + (-10x - x) + 2\). The correct way to factor \(-11x\) would not involve breaking it down into \(-10x - x\) as this makes it incorrect since it doesn't preserve the equality of the original quadratic equation.
Therefore, the correct answer is:
A. In Step 1 because the -11x was rewritten as -10x - x.
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