Mathematics
Mathematics, 17.04.2020 18:59, mckinley2006

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Cedric completed the square for the quadratic expression 5x2βˆ’40x+15 in order to determine the minimum value of the expression, as shown.

Step 1: 5(x2βˆ’8x+3)
Step 2: 5(x2βˆ’8x+16βˆ’16+3)
Step 3: 5((x+4)2βˆ’16+3)
Step 4: 5((x+4)2βˆ’13)
Step 5: 5(x+4)2βˆ’65
What mistake, if any, did Cedric make?

A. In Step 3, he incorrectly wrote the square as (x+4)2. He should have written xβˆ’42.
B. In Step 1, he incorrectly factored out 5. He should have written 5(x2βˆ’8xβˆ’3).
C. In Step 5, he incorrectly distributed 5 from the parentheses. He should have written 5(x+4)2βˆ’13.
D. He did not make a mistake.
E. In Step 2, he incorrectly added 16 and βˆ’16. He should have written 5(x2βˆ’8x+64βˆ’64+3).

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