Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
