Question

Find the difference of (3x^2 – 5x + 7) and (x^2+ 2x - 1).

a. Is 3x^2 – 5x + 7 a polynomial? If not, give an explanation.
b. Is x^2+ 2x – 1 polynomial? If not, give an explanation.
c. Is the difference a polynomial? If not, give an explanation.
d. If the difference is a polynomial, identify the constant term.

Answer 1

Explanation:

A polynomial is a mathematical expression in sum of powers with one or more variables multiplied by coefficients.

a) 3x² - 5x + 7 is a polynomial

b) x² + 2x - 1 is a polynomial

c) 3x² - 5x + 7 - [x² + 2x -1 ]= 3x² - 5x + 7 - x² - 2x + 1

{add like terms} = 3x² - x² - 5x - 2x +7 +1

= 2x² - 7x + 8

2x² - 7x + 8 is a polynomial

d) Constant term = 8

=