When #P(x) = x^3 + 2x + a# is divided by x - 2, the remainder is 4, how do you find the value of a?

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Answer 1 · 2015-07-28T10:31:50

Using the Remainder theorem.

#a=-8#

According to the Remainder theorem, if #P(x)# is divided by #(x-c)# and the remainder is #r# then the following result is true :

#P(c)=r#

In our problem,

#P(x)=x^3+2x+a" "# and

To find the value of #x# we have to equate the divisor to zero : #x-2=0=>x=2#

The remainder is #4#

Hence #P(2)=4#

#=>(2)^3+2(2)+a=4#

#=>8+color(orange)cancel(color(black)4)+a=color(orange)cancel(color(black)4)#

#=>color(blue)(a=-8)#