Question

andy divides (2x4 – 3x3 – 3x2 + 7x – 3) by (x2 – 2x + 1) as shown below. What error does Randy make?

x squared minus 2 x + 1 StartLongDivisionSymbol 2 x Superscript 4 Baseline minus 3 x cubed minus 3 x squared + 7 x minus 3 EndLongDivisionSymbol. minus 2 x Superscript 4 Baseline minus 4 x cubed + 2 x squared to get a remainder of x cubed minus 5 x squared + 7 x. minus x cubed minus 2 x squared + x to get a remainder of negative 3 x squared + 6 x minus 3. minus negative 3 x squared + 6 x minus 3 to get a remainder of 0 and a quotient of 2 x squared + x + 3.
He makes a subtraction error.
He makes an error writing the constant term in the quotient.
He makes an error choosing the x-term in the quotient.
He makes an error rewriting the problem in long division.

Answer 1

He wrote the constant term wrong in the quotient.

Correctly dividing gives quotient 2x^2 + x - 3 (not +3). The last step should be adding the term -3 (since (-3)(x^2 - 2x + 1) = -3x^2 + 6x - 3), which produces remainder 0. Randy wrote +3 instead of -3.