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Answer 1

Answer:

see the attachment

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Answer 2

Answer:

$\mathtt{1)g(x) = x + 1 = 0}$

$\mathtt{x = - 1}$

Now put the value of x is -1 in given polynomial.

$\mathtt{ = 2 {x}^{3} + {x}^{2} - 2x - 1}$

$\mathtt{ = 2 { (- 1)}^{3} + {( - 1)}^{2} - 2( - 1) - 1}$

$\mathtt{ = - 2 + 1 + 2 - 1}$

$\mathtt{ = 0}$

Yes this is the factor of given polynomial.

$\mathtt{2)g(x) = x + 2 = 0}$

$\mathtt{x = - 2}$

$\mathtt{ = {x}^{3} + {3x}^{2} + 3x + 1 }$

$\mathtt{ = {( - 2)}^{3} + 3{( - 2)}^{2} + 3( - 2) + 1}$

$\mathtt{ = ( - 2) + 6 - 6 + 1}$

$\mathtt{ = - 2 + 1}$

$\mathtt{ = - 1}$

No this is not the factor of given polynomial.

$\mathtt{3) g(x) = x - 3 = 0}$

$\mathtt{x = 3}$

$\mathtt{ = {x}^{3} - {4x}^{2} + x + 6 }$

$\mathtt{ = {3}^{3} - 4 {(3)}^{2} + 3 + 6 }$

=27-36+9

=0

Yes this is not the factor of this polynomial.

$\fbox \pink{i \: hope \: this \: helps \: you}$