Question

if polynomials has (x+1) as a factor.
(i) x4 – x3 + x2 - x+1​

Answer 1

SOLUTION

Given, x+1 as a factor.

=)x+1= 0

x+1= 0=)x= -1

So, putting the value in this equation:

$= > {x}^{4} - {x}^{3} + {x}^{2} - x + 1 \\ = > { - 1}^{4} - ( { - 1)}^{3} + ( - 1) {}^{2} - ( - 1) + 1 \\ = > 1 + 1 + 1 + 1 + 1 \\ = > 5$

hope it helps ☺️⬆️

Answer 2

The zero of x + 1 is -1.

(i) Let p (x) = x4 + x3 + x2 + x + 1

∴ P(-1) = (-1)4 + (-1)3 + (-1)2 + (-1)+1

= 1 – 1 + 1 – 1 + 1

⇒ P (-1) ≠ 1

So, (x + 1) is not a factor of x4 + x3 + x2 + x+ 1.