Question

Determine which of the following polynomials has (x+1) a factor

x^3-x^2-(2+√2)x+√2 . ​

Answer 1

Answer:

here is ur answer............

Answer 2

Answer:

x+1 is a factor so by dividing the polynomial by x+1, the remainder should be 0.

and to find the remainder put x+1=0, i.e. x=-1 in the polynomials; and check which polynomial is coming to zero.

for option a= (-1)^3+(-1)^2+(-1)+1

= -1+1-1+1

= 0

so option 'a' will be the right answer.

Now do the same for 2) polynomial, put x= -1;

= (-1)^3-(-1)^2-(2+√2)(-1)+√2

= -1-1+2+√2+√2

= -2+2+2√2

= 2√2

here this is not coming 0 that means x+1 is not a factor of 2nd polynomial.

now for 3)- put x=-1;

= 2(-1)^3-9(-1)^2+(-1)+12

= -2 -9 -1 +12

= -12 + 12

= 0

here 0 is coming so x+1 will be a factor of this polynomial.