Question
$(x + 1)$ is a factor of $x^n +1$ only if.
✓
Answer
The linear polynomial $(x - 1)$ is a factor of $xn + 1,$ only if,
$f(-1) = (-1)^n + 1 = 0$
If n is odd integer$,$ then $f(-1) = -1 + 1 = 0$
$f(-1) = (-1)^n + 1 = 0$
If n is odd integer$,$ then $f(-1) = -1 + 1 = 0$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $8^{x+1} = 64,$ what is the value of $3^{2x+1}$?
→If ABC is an arc of a circle and $\angle\text{ABC} = 135^\circ,$ then the ratio of arc $\widehat{\text{ABC}}$ to the circumference is:
→Each of the points (-2, 2), (0, 0), (2, 2) satisfies the linear equation:
Which one of the following is not the graphical representation of statistical data:
- Bar graph.
- Histogram.
- Frequency polygon.
- Cumulative frequency distribution.
In a sphere the number of faces is:
If a solid sphere of radius 10cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is:
Let $\bar{\text{x}}$ be the mean of $x_1, x_2, ..., x_n$ and $\bar{\text{y}}$ be the mean of $y_1, y_2, ..., y_n$. If $\bar{\text{z}}$ is the mean of $x_1, x_2, ..., x_n, y_1, y_2, ..., y_n$ then $\bar{\text{z}}=?$
→→
If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is:
→- $\frac{1}{3}\pi\text{r}^3$
- $\frac{2}{3}\pi\text{r}^3$
- $3\pi\text{r}^3$
- $9\pi\text{r}^3$
A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is: