Question 1183411
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(a) By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x. 


(b) Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1
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(a)  According to the remainder theorem, the remainder of  3(x+4)^2-(1-x)^3  when divided by x is the value 

     of this polynomial at x= 0.


     So, we substitute the value of 0 instead of  x  into the polynomial and calculate


           {{{3*(0+4)^2 - (1-0)^3}}} = {{{3*4^2 - 1^3}}} = 3*16 - 1 = 48 - 1 = 47.      <U>ANSWER</U>



(b)  According to the remainder theorem, the remainder of  (2x-1)^3+6(3+4x)^2-10  when divided by  (2x+1)  is the value 

     of this polynomial at x= -0.5,  which is the root of the binomial (2x+1).


     So, we substitute the value of  -0.5  instead of  x  into the polynomial and calculate


           {{{(2*(-0.5)-1)^3 + 6*(3 + 4*(-0.5))^2 - 10}}} = {{{(-2)^3 + 6*1^2 - 10}}} = -8 + 6 - 10 = -12.      <U>ANSWER</U>
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Solved.