Question 193258: If P(x) =3x to the 3rd power + 7x squared - 2x +6, use the remainder theorem to find the remainder when this polynomial is divided by the following binomials.
x - 3
x + 2
x + 1
x - 5
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! P(x)=3x^3+7x^2-2x-6
(x-3)
3|, 3,,7,,-2,,,,6
,,,,,,,,,,9,,,48,,138
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,,,,,3,,16,,46,,144,,,,,REM 144
P(3)= 3*3^3+7*3^2-2*3+6
p(3)=81 +63-6+6=144
(x+2)
-2|,,,,3,,,,7,,,,-2,,,,6
,,,,,,,,,,,,,,,-6,,,-2,,,8
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,,,,,,,,,3,,,,,1,,,,-4,,,14 ,,,,,rem14
P(-2)= 3(-2)^3+7(-2)^2-2(-2)+6
P(-2)=-24+28+4+6=14
(x+1)
-1|,,,,,3,,,,7,,,,,-2,,,,6
,,,,,,,,,,,,,,,-3,,,,-4,,,,6
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,,,,,,,,,,3,,,,4,,,,,-6,,,12,,,,,REM12
P(-1)= 3(-1)^3+7(-1)^2-2(-1)+6
P(-1)+ -3=7=2=6=12
(x-5)
5|,,,,3,,,,,7,,,,,-2,,,,6
,,,,,,,,,,,,,15,,,110,,,540
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,,,,,,,3,,,,22,,,,108,,546,,,,,,REM 546
P(5)= 3(5)^3=7(5)^2-2(5)+6
P(5)=375+175-10+6=546
instructor probably just wanted you to recognize remainder theorem, and calc P(x)
please excuse all the commas, just trying to allign numbers
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