A student claims that dividing a polynomial by gives quotient and remainder
MATHEMATICS · Single correct · GCSE · Further Mathematics · Algebra and Proof · Algebra and Proof
Problem
A student claims that dividing a polynomial f(x) by g(x)=x2+4x+1 gives quotient 3x−2 and remainder x2+5. Which statement correctly evaluates this claim?
(a) It is invalid because the remainder should be a constant term when dividing by a quadratic.
(b) It is valid only if f(x) is of degree 4 so that the degrees align.
(c) It is invalid because the degree of the remainder must be less than the degree of the divisor.
(d) It is valid because the degree of the remainder is allowed to equal that of the divisor.