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Sagot :
The value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.
What is polynomial equation?
Polynomial equations is the expression in which the highest power of the unknown variable is n (n is real number).
The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.
The given polynomial equation in the problem is,
[tex]2x^3 +18x^2 - 18x - 162[/tex]
The factor of the polynomial equation are given as,
[tex]2(x+ k)(x - k)(x +9)[/tex]
First find out the factors to compare and find the value of k.The above equation has the unknown variable x and the highest power of this unknown variable is 3.
Take out the highest common factor 2, which can divide each term of the above equation (2, 18, -18, -162). Thus,
[tex]2(x+ k)(x - k)(x +9)=2(x^3 +9x^2 - 9x - 81)[/tex]
Take out the highest common factor to make the groups as,
[tex]2(x+ k)(x - k)(x +9)=2(x^2( x+9) - 9(x + 9))\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 9)\\2(x+ k)(x - k)(x +9)=2( x+9) (x^2 - 3^2)[/tex]
Use the property of difference of the square for the (x²-3²) term as,
[tex]2(x+ k)(x - k)(x +9)=2( x+9) (x+3)(x-3)\\2(x+ k)(x - k)(x +9)=2 (x+3)(x-3)( x+9)[/tex]
On comparing the two equation, we get the value of k as 3. Thus, the value of the constant 'k' in the factored form factorization the provided polynomial equation is 3.
Learn more about factor of polynomial here;
brainly.com/question/24380382
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