Question

show that x-1, x+1 and 2 x+1 are factors of 2x3+x2+2x-1

Answer 1

* multiplication
x-1=0
x=1
2*1*3+2*1+2*1-1
6+2+2-1
10-1
9


x+1=0
x= -1
2*-1*3+2*-1+2*-1*-1
6-2+2
4+2
6

2x+1=0
2x=-1
x=-1/2
similarly do as solved above two....

Answer 2

Hey there !!!!!

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If p(x) is a polynomial then x-a is said to be a factor of p(x) if p(a) = 0

So

According to question p(x)=2x³+x²+2x-1

x-1=0

x=1

p(1) = 2+1+2-1=4

x-1 is not a factor of p(x) as p(1)≠0

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x+1

x = -1

p(-1) = -2+1-2-1 =0

x+1 is a factor of p(x) as p(-1) = 0 

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2x+1 = 0

x = -1/2

p(-1/2) = 2(-1/2)³+(-1/2)²+2(-1/2) -1

           =-2/8+1/4-1-1

           =-1/4+1/4-1-1
 
          =-2

p(-1/2)≠0 so 2x+1 is not a factor of p(x)

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Hope this helped you...............