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

Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5?

−2x2 + 2x + 1 may or may not be a polynomial
2x2 − 2x − 1 will be a polynomial
−2x2 + 2x + 1 will be a polynomial
2x2 − 2x − 1 may or may not be a polynomial

Answer 1

1) Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6?

3x^2+2x-6-(x+5)=3x^2+2x-6-x-5=3x^2+x-11
Answer: Second option: 3x^2 + x − 11 will be a polynomial

2) Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5?

x^2+2x+5-(3x^2+4)=x^2+2x+5-3x^2-4=-2x^2+2x+1
Answer: Third option −2x^2 + 2x + 1 will be a polynomial