Find the remainder (without division) on dividing f(x) by (x - 2) where

(i) f(x) = 5x² - 7x + 4

(ii) f(x) = 2x³ - 7x² + 3

(i) By remainder theorem, on dividing f(x) by (x - a) , remainder = f(a)

∴ On dividing, f(x) = 5x² - 7x + 4 by (x - 2)

Remainder = f(2)

$= 5(2)^2 - 7(2) + 4 \\[0.5em] = 5(4) - 14 + 4 \\[0.5em] = 20 - 10 \\[0.5em] = 10.$

Hence, the value of remainder is 10.

(ii) By remainder theorem, on dividing f(x) by (x - a) , remainder = f(a)

∴ On dividing, f(x) = 2x³ - 7x² + 3 by (x - 2)

Remainder = f(2)

$= 2(2)^3 - 7(2)^2 + 3 \\[0.5em] = 2(8) - 28 + 3 \\[0.5em] = 16 - 28 + 3 \\[0.5em] = -9.$

Hence, the value of remainder is -9.