Remainder

Algebra Level 2

When x 3 + a x^3+a is divided by x + 2 x+2 , the remainder is 15 -15 . Find the numerical value of a a .


The answer is -7.

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1 solution

By remainder theorem,

f ( x ) = x 3 + a f(x)=x^3+a

f ( 2 ) = ( 2 ) 3 + a = 15 f(-2)=(-2)^3+a=-15

It follows that

8 + a = 15 -8+a=-15

a = 15 + 8 a=-15+8

a = 7 a=-7 answer \boxed{\large\color{#D61F06}\text{answer}}

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