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

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Answer 1 · 2018-06-07T05:38:07

#y# is of degree #4#

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)#