Answer:

Certainly! If '-4' is a zero of the polynomial \( p(x) = x^2 - x - 2(2 + 2k) \), it means that when \( x = -4 \), the polynomial evaluates to zero.

Substitute \( x = -4 \) into the polynomial and solve for \( k \):

\[ p(-4) = (-4)^2 - (-4) - 2(2 + 2k) \]

\[ 0 = 16 + 4 - 2(2 + 2k) \]

Now, simplify the equation:

\[ 0 = 20 - 4 - 4k \]

Combine like terms:

\[ 0 = 16 - 4k \]

Solve for \( k \):

\[ 4k = 16 \]

\[ k = 4 \]

So, the value of \( k \) is 4.

Please mark me as brainliest .

[tex]\huge{\bf{\purple{\underline{\colorbox{lavender}{\color{purple}{ɑׁׅ֮ꪀׁׅ꯱ׁׅ֒ᨰׁׅꫀׁׅܻꭈׁׅ}}}}}}[/tex]

If ( -4) is a zero of the polynomial

[tex]( p(x) = x^2 - x - 2(2+2k) )[/tex]

it means that when you substitute (x = -4) into the polynomial, the result is zero.

Let's substitute (x = -4) into the polynomial and set it equal to zero:

[tex][p(-4) =(-4)^2 -(-4)-2(2 + 2k)]

[/tex]

Simplify this expression and set it equal to zero:

[tex]\[ 16 + 4 - 2(2 + 2k) = 0 \][/tex]

Combine like terms:

[ 20 - 4(1 + k) = 0]

Now, solve for ( k):

[ 20 - 4 - 4k = 0]

Combine like terms:

[ 16 - 4k = 0 ]

Now, isolate ( k):

[-4k = -16]

[ k = 4]

Therefore, the value of ( k) is 4.