Question

Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6?
3x2 + x − 11 may or may not be a polynomial
3x2 + x − 11 will be a polynomial
3x2 + x − 1 will be a polynomial
3x2 + x − 1 may or may not be a polynomial

Answer 1

For this case we have the following polynomials:
 $P = 3x ^ 2 + 2x - 6 Q = x + 5$
 By subtracting both polynomials we have:
 $P - Q = (3x ^ 2 + 2x - 6) - (x + 5)$
 What we must do is subtract terms of the same degree.
 We have then:
 $P - Q = 3x ^ 2 + (2x - x) + (-6 - 5) P - Q = 3x ^ 2 + x - 11$
 Answer:
 $3x ^ 2 + x - 11$ will be a polynomial