Question

Consider the polynomial - 4 + 2y² + 3y + 8.

1) What is the constant term?
2) What is the exponent of the third term?

Answer 1

-4 + 2y^2 + 3y + 8

2y^2+3y+4

1) 4

2) 0

Answer 2

In the polynomial -4 + 2y² + 3y + 8, the constant term is 8, and the exponent of the term 3y is 1 because any variable without an exponent written is understood to be to the first power.

The student is working with a polynomial and has asked two questions about it. The given polynomial is -4 + 2y² + 3y + 8.

Firstly, they have asked about the constant term. The constant term in a polynomial is the term without any variables. In this polynomial, the constant term is 8.

Secondly, the question is regarding the exponent on the third term of the polynomial. The third term in the given polynomial is 3y.

The exponent for y in 3y is 1, even though it is not explicitly written. This is because any variable without an exponent shown is assumed to be to the first power.