Question

Which statement shows that when two polynomials 5x − 6 and 6x + 2 demonstrates the closure property when multiplied? a. 30x2 − 26x − 12 may or may not be a polynomial b. 30x2 − 11x − 12 may or may not be a polynomial c. 30x2 − 26x − 12 is a polynomial d. 30x2 − 11x − 12 is a polynomial

Answer 1

Answer: a. 30x^2 − 26x − 12

First write the equation in a form to better help visualize.

(5x - 6)(6x + 2)

Then use distributive property on the second binomial from the first binomial.  You multiply 5x by 6x and 2, then multiply -6 by 6x and 2.

5x * 6x = 30x^2 (The answer is raised to the power of 2 because you're adding the invisible exponents, aka exponents of 1)

Then multiply 5x by 2

5x * 2 = 10x

Then you repeat the process but with -6 instead of 5x.

-6 * 6x = -36x  (It is not raised to a power of 2 because -6 does not have a variable to include the invisible exponent)

-6 * 2 = -12

Now take all of your answers and put them into 1 equation by the order you did them.  

30x^2 + 10x - 36x -12

But wait! The answer can still be simplified.  All you have to do is combine like terms.  However 30x^2 can't be combined with 10x because 10x isn't raised to the second power, terms can only be combined if they have the same variable and exponent.

30x^2 + (10x - 36x) - 12

30x^2 - 26x - 12

Answer 2

  The statement that shows that when two polynomials 5x − 6 and 6x + 2 demonstrates the closure property when multiplied is
. 30x2 − 26x − 12 is a polynomia
 Because its the correct one among all
hope it helps