Question

the polynomial ax^3+3x^2-13 and 2x^3-5x+a are divided by x+2, if the remainder in the each case is same find a

Answer 1

Please mark it as a brainlist..

Answer 2

Answer:

Let

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

and

$\\ \boxed{ \sf q(x) = 2 {x}^{3} - 5x + a}$

be the given polynomials. The remainder when p(x) and q(x) are divided by (x+2) are p(-2) and q(-2) respectively.

By the given condition, we have

$\\ \qquad \sf \: p( - 2) = q( - 2) \\ \\ \\ \implies \sf \: a {( - 2)}^{3} + 3 {( - 2)}^{2} - 13 = 2 {( - 2)}^{3} - 5 \times \\ \\ \sf \: - 2 + a \\ \\ \\ \implies \sf - 8a + 12 - 13 = - 16 + 10 + a \\ \\ \\ \implies \sf - 8 a - 1 = a - 6 \\ \\ \\ \implies \sf - 9 = - 5 \\ \\ \\ \implies\boxed{ \sf a = \frac{5}{9} }$