How do you find the degree of y = (1/4)(t-1)^2(t+3)(4-t)?

1 Answer
Jun 7, 2018

y is of degree 4

Explanation:

The degree of a polynomial of a single variable is the value of the highest exponent of the variable.

In our example:

y = (1/4)(t-1)^2(t+3)(4-t)

In this case the variable is t

We could go to the bother of expanding y to find the highest exponent of t. However, in this case there is a much simpler way.

Since y is the product of terms we can simply find the degree of each term and sum each to find the degree of y.

Taking each term in turn:

1/4 = 1/4t^0 ->Degree 0

(t-1)^2 -> Degree 2

(t+3) -> Degree 1

(4-t) -> Degree 1

Hence, degree of y = 0+2+1+1 =4

NB: This only works because y is the product of terms.

We are actually using the property of exponents:

t^a xx t^b = t^(a+b)