SOLUTION: Please help me.The question is:- The expressions {{{ x^3-ax+a^2 }}} and {{{ ax^3+x^2-17 }}} have the same remainder when divided by x-2, find the possible value of a and find th

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me.The question is:- The expressions {{{ x^3-ax+a^2 }}} and {{{ ax^3+x^2-17 }}} have the same remainder when divided by x-2, find the possible value of a and find th      Log On


   

Question 557557: Please help me.The question is:-
The expressions +x%5E3-ax%2Ba%5E2+ and +ax%5E3%2Bx%5E2-17+ have the same remainder when divided by x-2, find the possible value of a and find the remainder.
I tried to solve it but got stuck:-
+f%28x%29=+x%5E3%2Ba%5E2-ax+ ; +f%28x%29=+ax%5E3%2Bx%5E2-17+
+Divisor+=+x-2+ ; Therefore x-2=0 ; =>x=-2
+f%282%29=+2%5E3%2Ba%5E2-a%282%29+ ; +f%282%29=+a%282%29%5E3%2B2%5E2-17+
+f%282%29=8+%2B+a%5E2+-2a+%3B+ => +a%5E2+-+2a+%2B+8+ ; +f%282%29=+8a%2B4-17+ ; => 8a-13
Since the remainders are the same, The equation is :-
+a%5E2+-+2a+%2B+8++=+8a+-13+
+a%5E2+-+2a+-+8a+=+-13+-8+
+a%5E2++-++10a+++=+++-21++
+a+%28+a+-+10+%29++=+++-21++
And I'm stuck.....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're doing great so far. I'm going to pick up where you left off.


+a+%28+a+-+10+%29++=+++-21++


+a%5E2-+10a++=+++-21++


+a%5E2-+10a%2B21+=+0++


+%28a-7%29%28a-3%29+=+0++


+a-7=0 or a-3+=+0++


+a=7 or a=3


Now use these values of 'a' to find the remainder.

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