Question

Suppose a(x), b(x), q(x), and r(x) are polynomials, and a(x) divided by b(x) is equal to q(x) with a remainder of r(x). Which of these expressions is equal to

a(x)
b(x)?

Answer 1

a(x) = b(x)*q(x) + r(x)

b(x) = [ a(x) - r(x) ] / q(x)

Explanation:

we see : a(x) / (b(x) = q(x) + r(x) / (b(x))

so..

a(x) = b(x)*q(x) + r(x)

and b(x) = ?

solve for b(x)

a(x) - r(x) = b(x)*q(x)

b(x) = [ a(x) - r(x) ] / q(x)