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, where he rewrote \(-11x\) as \(-10x - x\).
The correct factoring of \(5x^2 - 11x + 2\) should not have involved splitting \(-11x\) that way since it disrupts the balance of the expression. The correct way to factor it would be to find two numbers that multiply to \(5 \cdot 2 = 10\) and add to \(-11\), which would not be achieved by \(-10\) and \(-1\) as he has done.
Therefore, the correct answer is:
A. In Step 1 because the -11x was rewritten as -10x - x.
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