Question

Pick the expression that matches the given description: A polynomial of the 5th5th degree with a leading coefficient of 77 and a constant term of 66.

a) 6x5+x4+76x5+x4+7
b) 7x5+2x2+67x5+2x2+6
c) 6x7−x5+56x7−x5+5
d) 7x6−6x4+57x6−6x4+5

Answer 1

The correct polynomial that matches the description is b) 7x^5+2x^2+6, as it is a 5th-degree polynomial with a leading coefficient of 7 and a constant term of 6.

Step-by-step explanation:

The student is asking for a polynomial of the 5th degree which implies the highest exponent should be 5. The leading coefficient is the coefficient of the term with the highest exponent which should be 7, and the constant term is the term without a variable, which should be 6.

Considering these criteria, the correct expression is b) 7x^5+2x^2+6. This polynomial satisfies all requirements: it is a 5th-degree polynomial, has a leading coefficient of 7, and has a constant term of 6.