Question

(b). Apply the remainder’s theorem to determine the remainder in the following:
(i) (2x3 + 3x4 – x +4) ÷ (x +2)
(ii) (3x3 + 11x2 + 10x - 12) ÷ (x - 3)

Answer 1

(i) (2x³ + 3x⁴ - x +4) ÷ (x +2)

$3x^3 -4x^2-8x+15 +(\frac {-26}{x+2} )$

$(-26)$ - remainder

(ii) (3x³ + 11x² + 10x - 12) ÷ (x - 3)

$3x^2+20x+70+ (\frac {198}{x-3} )$

$198$  - remainder