Find the degree of the given polynomial ? #(x^2+9)(5-x^2)#

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Answer 1 · 2018-05-18T06:55:44

Polynomial is of degree 4

#P = (x^2+9)(5-x^2)#

The degree of a polynomial is the exponent of highest power term.

In this case we can see by inspection that the highest power will be #x^2 xx -x ^2=-x^4# Hence, the polynomial will be of degree 4.

To show this more clearly.

#P = 5x^2-x^4 +45-9x^2#

#= -x^4-4x^2+45#

Since the highest power term in #x# is #-x^4# then P is of degree 4.

Answer 2 · 2018-05-18T07:25:30

#color(blue)4#

#(x^2+9)(5-x^2)#

#=>x^2(5-x^2)+9(5-x^2)#

#=>5x^2-x^4+45-x^2#

#=>-x^4+4x^2+45#

Since the highest power of the variable in the polynomial is #4#,

#therefore# The degree of the polynomial is #color(blue)(4#.

~Hope this helps! :)