Question

Use long division to find the quotient below.

(x ^2 −5x−14)÷(x−2)
a) x−12
b) x+7
c) x−7
d) x+12

Answer 1

The quotient of the polynomial division (x^2 −5x−14)÷(x−2) is x−7 with a remainder of −20, making the correct answer (c) x−7.

Step-by-step explanation:

To find the quotient of the given polynomial division (x2 −5x−14)÷(x−2), we perform long division. Start by asking what we must multiply x by to get x2, which is x. Multiplying (x−2) by x yields x2 − 2x, which we subtract from the original polynomial to get (−5x−14) − (x2 − 2x) leading to −3x−14.

Now, determine what to multiply x by to get −3x, which is −3. Multiplying (x−2) by −3 gives −3x + 6. Subtract this from −3x−14 to get −20, which is our remainder.

The final answer is the quotient with remainder: x − 7 with a remainder of −20, hence the answer is (c) x−7.