Question

The polynomials ax^3 + 3x² - 13 and 2x³ - 5x + 1 are divided by x + 2. If the remainder in each case is the same, then the value of a is​

Answer 1

x+2 = 0

x     = -2

p(x) = $ax^{3} + 3x^{2} - 13$

p(-2) = $-8a + 3(-2^{2}) -13$

s(x) = 2x³ - 5x + 1

s(-2) = 2(-2³) - 5(-2) + 1

therefore:

                 -8a + 3(-2^{2}) -13 = 2(-2³) - 5(-2) + 1

                                   -8a - 1 = -16 + 11

                                       -8a = -5+1

                                           a = -4/-8 =

                                           a = 1/2