If the polynomial 2x³ + ax² + 3x - 5 and x³ + x² - 4x + a leave the same remainder when divided by x - 2, Find the value of a.

A polynomial is an algebraic expression that has constants, variables, and coefficients with a point where the value of the polynomial becomes zero as a whole.

Answer: The value of a is - 13/ 3.

Here's the step-by-step solution.

Explanation:

Let v( x ) = 2x³ + ax² + 3x - 5 and w( x ) = x³ + x² - 4x + a

Given that v( x ) and w( x ) when divided by x - 2 leaves the same remainder.

By remainder theorem,

⇒ v( 2 ) = w( 2 )

⇒ 2 × ( 2 )³ + a × ( 2 )² + 3 × ( 2 ) - 5 = ( 2 )³ + ( 2 )² - 4 × ( 2 ) + a

⇒ 16 + 4a + 6 - 5 = 8 + 4 - 8 + a

⇒ 17 + 4a = 4 + a

⇒ 4a - a = 4 + (- 17 )

⇒ 3a = - 13

⇒ a = - 13/ 3

Thus, the value of a is - 13/ 3.