if x-3 and x-1/3 are the factors of the polynomial px3+3x+r, show that p=r
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if x-3 is the factor of p(x),
then p(3)=0
p3³+3x3+r=0
27p+9+r=0
27p+r=-9------------(1)
if x-1/3 is a foctor,p(1/3)=0
p(1/3)³+1+r=0
p/27+1+r=0
multiply by 27,
p+27+27r=0
p+27r=-27----------(2)
by (1)and(2),
28p+28r=-36
14p+14r=-18
14(p+r)=-18
p+r=-9/7------------(3)
thus p=r
then p(3)=0
p3³+3x3+r=0
27p+9+r=0
27p+r=-9------------(1)
if x-1/3 is a foctor,p(1/3)=0
p(1/3)³+1+r=0
p/27+1+r=0
multiply by 27,
p+27+27r=0
p+27r=-27----------(2)
by (1)and(2),
28p+28r=-36
14p+14r=-18
14(p+r)=-18
p+r=-9/7------------(3)
thus p=r
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