Question

Determine if x-1 is a factor of x4+3x3+3x2+x+1​

Answer 1

Step-by-step explanation:

If x-a is a factor of p(x) then p(a)=0................... factor theorem

Here p(x)=x⁴+3x³+3x²+x+1

and x-a=x-1....... a=1

p(a)=p(1)=(1)⁴+3(1)³+3(1)²+1+1

p(a)=1+3+3+1+1

p(a)=9

p(a) is not equal to zero

So x-1 is not a factor of p(x)

Answer 2

Answer✍

Apply remainder theorem 

x+1=0

x=−1

Put the value of x=−1 in all equations. 

(i) x3+x2+x+1=(−1)3+(−1)2+(−1)+1=−1+1−1+1=0

Then x+1 is the factor of equation

(ii) x4+x3+x2+x+1=(−1)4+(−1)3+(−1)2+(−1)+1=1−1+1−1+1=1

This is not zero.Then x+1 is not the factor of equation

(iii) x4+3x3+3x2+x+1=(−1)4+3(−1)3+3(−1)2+(−1)+1=1

XxBrainlyRajxX

This is not zero.Then x+1 is not the factor of equation

(iv)x3−x2−(2+2)x+