# Determine If the Following Polynomial Has (X + 1) a Factor :- X3 + X2 + X + 1 - Mathematics

Sum

Determine if the following polynomial has (x + 1) a factor :-

x3 + x2 + x + 1

#### Solution

If (x + 1) is a factor of p(x) = x3 + x2 + x + 1, then p (−1) must be zero, otherwise (x + 1) is not a factor of p(x).

p(x) = x3 + x2 + x + 1

p(−1) = (−1)3 + (−1)2 + (−1) + 1

= − 1 + 1 − 1 + 1

= 0

Hence, x + 1 is a factor of this polynomial.

Concept: Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.
Is there an error in this question or solution?
Chapter 2: Polynomials - Exercise 2.4 [Page 43]

#### APPEARS IN

NCERT Class 9 Maths
Chapter 2 Polynomials
Exercise 2.4 | Q 1.1 | Page 43

Share
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}