Question 157666: Given that (x-2)^2 is a factor of the polynomial a(x^3) + b(x^2) + 7x + 4, find a and b and the other factor. Thank you. Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website! (x-2)^2
=x^2-4x+4 we have to divide this into the number below:
a(x^3) + b(x^2) + 7x + 4
The last number of the quotient has to be 1 so that when it is multiplied by +4 the result is 4. There can be no remainder.
The 1st number when multiplied by 4 has to equal 11 so that when it is subtracted from 7 it equals -4. 4z=11...z=11/4=2.75
==========___________2.75x+1___________
x^2-4x+4 /2.75x^3-10x^2+7x+4
==========2.75x^3-11x^2+11x
_______________________________
====================x^2-4x+4
====================x^2-4x+4
_______________________________
==========================0
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So a=2.75, b=-10 and the other factor is 2.75x+1
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Ed
