Question

(2 points)

A polynomial is divided by (x - 2), the quotient is (x – 6), and the remainder is -6
What is the original polynomial

Answer 1

Answer: x^2-8x+6

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Step-by-step explanation:

n = numerator polynomial = unknown (what we want to solve for)

d = denominator polynomial = x-2

q = quotient = x-6

r = remainder = -6

Based on that, we can say,

n/d = q + r/d

n = q*d + r ... multiply every term by d

n = (x-6)(x-2) + (-6) .... substitution

n = x^2-8x+12-6

n = x^2-8x+6

Dividing (x^2-8x+6) over (x-2) leads to a quotient of (x-6) and a remainder of -6.