MCQ
Write the correct answer in the following: $x + 1$ is a factor of the polynomial.
- A$x^3+x^2-x+1$
- ✓$x^3+x^2+x+1$
- C$x^4+x^3+x^2+1$
- D$-x^4+3 x^3+3 x^2+x+1$
✓
Answer
Correct option: B.
$x^3+x^2+x+1$
Let assume $(x+1)$ is a factor of $x^3+x^2+x+1$
So, $x=-1$ is zero of $x^3+x^2+x+1$
$(-1)^3+(-1)^2+(-1)+1=0$
$\Rightarrow-1+1-1+1=0$
$\Rightarrow 0=0$
Hence, our assumption is true.
So, $x=-1$ is zero of $x^3+x^2+x+1$
$(-1)^3+(-1)^2+(-1)+1=0$
$\Rightarrow-1+1-1+1=0$
$\Rightarrow 0=0$
Hence, our assumption is true.
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