Ex 2.4 solution

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

(i) x³+x²+x+1

Solution:

Let p(x) = x³+x²+x+1

The zero of x+1 is -1. [x+1 = 0 means x = -1]

p(−1) = (−1)³+(−1)²+(−1)+1

= −1+1−1+1

= 0

∴By factor theorem, x+1 is a factor of x³+x²+x+1

(ii) x⁴+x³+x²+x+1

Solution:

Let p(x)= x⁴+x³+x²+x+1

The zero of x+1 is -1. . [x+1= 0 means x = -1]

p(−1) = (−1)⁴+(−1)³+(−1)²+(−1)+1

= 1−1+1−1+1

= 1 ≠ 0

∴By factor theorem, x+1 is not a factor of x⁴ + x³ + x² + x + 1

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<a href="https://mycbseguide.com/blog/ncert-solutions-class-9-maths-exercise-2-4/" ping="/url?sa=t&source=web&rct=j&url=https://mycbseguide.com/blog/ncert-solutions-class-9-maths-exercise-2-4/&ved=2ahUKEwjZsuKznvLsAhVFwzgGHeNlBs8QFjADegQIBRAC" rel="noopener" target="_blank">NCERT Solutions for Class 9 Maths Exercise 2.4 ...</a>