Question

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

MARKS: 20

i] x3 + x2 + x + 1
ii] x4 + x3 + x2 + x + 1
iii] x4 + 3x3 + 3x2 + x + 1
iv] 3x3 - 3x2 + x - 1​

Answer 1

(i)

The zero of x + 1 is -1

let put (x) = x3 + x2 x2 + x+ 1

= -1 + 1 -1+1

= P (-1) =0

so,(x+1) is a factor of x3 +x2 +x+1.

(ii)

x4+x3+x2+x+1

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

p (-1)=(-1)4+(-1)3+(-1)2+(-1)

=1-1+1-1+1

= p (-1) # 1

so, (x+1) is not factor of x4+x3+x2+x+1

(iii)

+3x3+3x2+ x+1

let p (x) = x4+3x3+3x2+x+1

= p (-1) =(1-) 4+3(-1) 3+3(-1) 2+(-1) +1

= 1 =3+3-1+1=1

so, (x+1) is not a factor a factor of x4+3x3+3x2+x+1

(iv)

x3-x2-(2+√2) x+√2

let the p (x) = x3= x2-(2+√2)

x+√2

= p(-1) =(-1) 3-(-1) 2-(2+√2)

(-1) +√2

= -1-1+2+√2+√2

= 2√2

= p(-1) # 0

so, (x+1) is not a factor of x3-x2-(2+√2) x+√2

hope it help uh!! ✌࿐

Answer 2

Step-by-step explanation:

hope it's help uhh dear