Question

if p(x) = x³-5x²+4x-3 and g(x)=x-2, show that p(x) is not a multiple of g(x).​

Answer 1

"" ❤️ Answer ❤️ ""

Given,

P(x)=

x 3

5x

2

+

4x−

3

g(x)= x− 2

Put

g(x)=

0

⟹ x= 2

Now, p(2) should be 0 if p(x) is a multiple of

g(x)

so,

p(2)=

2 3

5(2)

2

+ 4(2)− 3

p(2)= 8− 20+ 8− 3

p(2)= 16− 23

p(2)= −7

since remainder is not zero,

p(x)

is a not multiple of

g(x)

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Answer 2

g(x)=x-2

     x=2

put x=2 in p(x)

p(x) = x³-5x²+4x-3

       =2³-5*2²+4*2-3

       =8-20+8-3

       =16-23

       =-7

thus ans is not zero the x-2 is not a multiple of x³-5x²+4x-3