Determine $(x + 1)$ is a factor of $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$ or not.

Open in App

Solution

Applying remainder theorem, we get
$x + 1 = 0$
$x = - 1$

Now,
$x^{4} + 3 x^{3} + 2 x^{2} + x + 1$

Replacing $x$ with $- 1$ , we get
$= (- 1)^{4} + 3 \times (- 1)^{3} + 2 \times (- 1)^{2} + (- 1) + 1$
$= 1 - 3 + 2 - 1 + 1$
$= 0$

Hence, $(x + 1)$ is a factor of polynomial $(x^{4} + 3 x^{3} + 2 x^{2} + x + 1) .$

Suggest Corrections

Similar questions

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

X⁴+3x³+3x²+x+1

x + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

x^{3} + x^{2} - x + 1

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

(x + 1)

x^{3} + x^{2} + x + 1

x^{4} + x^{3} + x^{2} + x + 1

x^{4} + 3 x^{3} + 3 x^{2} + x + 1

x^{3} - x^{2} - (2 + \sqrt{2}) x + \sqrt{2}

Join BYJU'S Learning Program