Question

Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x2 − 8x − 4 are added?

a. 2x2 - 4x + 2 will be a polynomial
b. 2x2 - 4x + 2 may or may not be a polynomial
c. 2x2 - 12x - 10 will be a polynomial
d. 2x2 - 12x - 10 may or may not be a polynomial

Answer 1

in order for polynomials to be closed under addition, the sum of polynomials must also result in another polynomial (automatically narrowing us down to choices a and c)

to distinguish between a and c, simply add 4x + 6 and 2x2 − 8x − 4 and see which choice matches your result. remember to combine like terms.