Question

The work below shows how to use long division to find (y2 – 6y + 9) (y – 4).



Which statements are correct? Check all that apply.

The remainder over the divisor is .
The remainder over the divisor is .
The remainder over the divisor is .
To check the answer, multiply the quotient by the remainder, and verify that it equals the divisor.
To check the answer, multiply the quotient by the divisor, and verify that it equals the dividend.

Answer 1

Divide y^2 − 6y + 9 by y − 4: quotient = y − 2 and remainder = 1. So

(y^2 − 6y + 9)/(y − 4) = (y − 2) + 1/(y − 4).

Correct choices:
- The remainder over the divisor is 1/(y − 4).

Incorrect choices:
- Any choice saying the remainder over the divisor is something else.
- "To check the answer, multiply the quotient by the remainder, and verify that it equals the divisor." — false.
- "To check the answer, multiply the quotient by the divisor, and verify that it equals the dividend." — incomplete/false here; the correct check is (quotient × divisor) + remainder = dividend, i.e. (y − 2)(y − 4) + 1 = y^2 − 6y + 9.