Shelia is dividing x to the 4th power minus 4 x cubed plus 4 x squared minus 6 x plus 5 by x minus 1 using a division table. Shelia's Work Quotient Divisor x cubed negative 3 x squared plus x negative 5 x x to the 4th power negative 3 x cubed x squared cap A negative 1 negative x cubed 3 x squared cap b cap c What are the missing values in the table?
Answer
A
cap A is equal to 5 x ; cap b is equal to 1 x ; cap c is equal to 5
B
cap A is equal to negative 5 x ; cap b is equal to negative 1 x ; cap c is equal to 5
C
cap A is equal to negative 5 x ; cap b is equal to 1 x ; cap c is equal to 5
D
cap A is equal to 5 x ; cap b is equal to negative 1 x ; cap c is equal to 5
Explanation
Multiply each quotient term by both terms of the divisor, x − 1. The x row gives x⁴ − 3x³ + x² − 5x, so A = −5x. The −1 row gives −x³ + 3x² − x + 5, so b = −x and c = 5. These values match choice B.
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