Question

i. State the remainder theorem and indicate where you need to apply it.

ii. Find the remainder when x^3 + 4x^2 - x + 3is divided by (x+2).

(please answer asap)

Answer 1

Step-by-step explanation:

Let us consider polynomials to prove the remainder theorem formula.

You know that Dividend = (Divisor × Quotient) + Remainder

If r(x) is the constant then, p(x) = (x-c)·q(x) + r

Let us put x=c

p(c) = (c-c)·q(c) + r

p(c) = (0)·q(c) + r

p(c) = r

Hence, proved.

Answer 2

(i) The remainder theorem definition states that when a polynomial f(x) is divided by the factor (x -a) when the factor is not necessarily an element of the polynomial, then you will find a smaller polynomial along with a remainder. The resultant obtained is the value of the polynomial f(x) where x = a and this is possible only if f(a) = 0. In order to factorize polynomials easily, the remainder theorem is applied.

(ii) the reminder is 13

hope it helps