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A day full of math games & activities. Find one near you.
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.
⇒ 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.
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