Question

check whether (x+1) is a factor of x³-x²-(2+√2)x+√2
please urgent

Answer 1

No,(x+1) is not the factor of
${x}^{3} - {x}^{2} - ( 2 + \sqrt{2})x + \sqrt{2}$
, because:-
let p(x) be x+1
so x= -1
let g(x) be our polynomial
we use remainder theorem
g(x)=
${3}^{3} - {x}^{2} - (2 + \sqrt{2} )x + \sqrt{2}$
g(-1)=
$- 1 - 1 + 2 + \sqrt{2} + \sqrt{2}$
$- 2 + 2 + \sqrt{2}$
$2 \sqrt{2}$
hence ,the remainder is not zero so p(x) is not the factor of g(x).

Answer 2

Step-by-step explanation:

x

3

−x

2

−(2+

2

)x+

2

, because:-

let p(x) be x+1

so x= -1

let g(x) be our polynomial

we use remainder theorem

g(x)=

{3}^{3} - {x}^{2} - (2 + \sqrt{2} )x + \sqrt{2}3

3

−x

2

−(2+

2

)x+

2

g(-1)=

- 1 - 1 + 2 + \sqrt{2} + \sqrt{2}−1−1+2+

2

+

2

- 2 + 2 + \sqrt{2}−2+2+

2

2 \sqrt{2}2

2

hence ,the remainder is not zero so p(x) is not the factor of g(x).