Question

determine which of the following polynomial has (x+)1) as a factor.
1) x³+x²+x+1
2) x³-x²-(2+√2)x+√2
3) 2x³-9x²+x+12​

Answer 1

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.

Answer 2

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