Question

Can (x - 1) be the remainder on division of a polynomial p(x) by (x + 3)? Justify
your answer.​

Answer 1

(x - 1) and (x + 3) has equal degree. In polynomial division, the remainder degree must be below the divisor.

• Divisor Degree of (x + 3) is 1.

• Remainder Degree of (x - 1) is 1.

Therefore the division cannot have remainder of degree 1 which is (x - 1).

Division

• 1. Numbers

It is needed that remainder belongs here: $\sf{0\leq r<(dividend)}$

• 2. Polynomials

It is required that the degree remainder belongs here:-

$\sf{0\leq (remainder\:degree)<(divisor\:degree)}$