Factor Theorem-4

The polynomials ax³ + 3x² - 13 and 2x³ -5x + a are divided by x + 2. If the remainder is same in each case, find the value of a.

Solution: Let f(x) =ax³ + 3x² - 13 and g (x) = 2x³ -5x + a

The remainders when f (x) and g (x) are divided by x + 2 are f (-2) and g (-2)

f (-2) = a(-2)³ + 3(-2)² - 13

= -8a + 12 - 13 = -8a - 1

g (-2) = 2.(-2)³ - 5(-2) + a = - 16 + 10 + a = -6 + a

Given, f (-2) = g (-2)

=> - 8a - 1 = - 6 + a

=> 6 - 1 = a + 8a

=> 5 = 9a

=> a = 5/9

Hence the value of a = 5/9