Question

Which of the following option is a polynomial whose factor is (x-1/a) , if (x-a), where a>0, is a factor of the given polynomial
q(x) = 4$\sqrt{2x^2 }$ - $\sqrt{2}$

Answer 1

Answer:

Apply remainder theorem  

x+1=0

x=−1

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

(i) x  

3

+x  

2

+x+1=(−1)  

3

+(−1)  

2

+(−1)+1=−1+1−1+1=0

Then x+1 is the factor of equation

(ii) x  

4

+x  

3

+x  

2

+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) x  

4

+3x  

3

+3x  

2

+x+1=(−1)  

4

+3(−1)  

3

+3(−1)  

2

+(−1)+1=1

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

(iv)x  

3

−x  

2

−(2+  

2

​

)x+  

2

​

=(−1)  

3

−(−1)  

2

−(2+  

2

​

)(−1)+  

2

​

=−1−1+2−  

2

​

+  

2

​

=0

This is zero. Then x+1 is the factor of equation

Step-by-step explanation: