# x + 1 is a factor of the polynomial

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

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

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

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

**Solution:**

By applying the remainder theorem

x + 1 = 0

x = -1

Let us substitute x = -1 in all the equations

a. x^{3} + x^{2} - x + 1 = (-1)^{3} + (-1)^{2} - (-1) + 1

= -1 + 1 + 1 + 1

= 2

b. x^{3} + x^{2} + x + 1 = (-1)^{3} + (-1)^{2} + (-1) + 1

= -1 + 1 - 1 + 1

= 0

c. x^{4} + x^{3} + x^{2} + 1 = (-1)^{4} + (-1)^{3} + (-1)^{2} + 1

= 1 - 1 + 1 + 1

= 2

d. x^{4} + 3x^{3} + 3x^{2} + x + 1 = (-1)^{4} + 3(-1)^{3} + 3(-1)^{2} + (-1) + 1

= 1 - 3 + 3 - 1 + 1

= 1

Therefore, x + 1 is a factor of the polynomial x^{3} + x^{2} + x + 1.

**✦ Try This: **If x + 1 is a factor of the polynomial 5x² + kx, then the value of k is

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 2

**NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 13**

## x + 1 is a factor of the polynomial a. x^{3} + x^{2} - x + 1, b. x^{3} + x^{2} + x + 1, c. x^{4} + x^{3} + x^{2} + 1, d. x^{4} + 3x^{3} + 3x^{2} + x + 1

**Summary:**

The standard form of a polynomial refers to writing a polynomial in the descending power of the variable. x + 1 is a factor of the polynomial x^{3} + x^{2} + x + 1

**☛ Related Questions:**

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