Question

Determine which of the following polynomials has (x + 1) as a factor.
1) x^3-x^2-x+1
2) x^4-x^3+x^2-x+1
3) x^4+2x^3+2x^2+x+1
4) x^3-x^2-(3-√3)x+√3
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Answer 1

Answer:

3 OPTION IS CORRECT

Step-by-step explanation:

Answer

Given polynomial is x

4

+2x

3

+2x

2

+x+1.

To find out: Whether (x+1) is a factor of the given polynomial or not.

Let the given polynomial be p(x).

According to the factor theorem, if (x−a) is a factor of f(x), then f(a)=0.

Hence, (x+1) will be a factor of the given polynomial if p(−1)=0.

Let's check for that:

Substituting x as −1, we get,

p(x)=x

4+2x3+2x

2+x+1

p(−1)=(−1)

4+2(−1)

3+2(−1)

2+(−1)+1

p(−1)=1−2+2−1+1p(−1)=1.

∴ p(−1)

=0

Hence, (x+1) is not a factor of the polynomial x

4+2x 3+2x2+x+1

HOPE THIS HELPED U :)