State the degree, the number of terms, and describe the long‐run behavior?

y=(x+4)(2x-3)(5-x)

1 Answer
Jim G.
Nov 17, 2017

#"see explanation"#

Explanation:

#"we are going to have to expand the factors since we"#
#"require the number of terms"#

#"expand the first pair using Foil and multiply the result"#
#"by the third factor"#

#rArr(x+4)(2x-3)=2x^2+5x-12#

#rArr(2x^2+5x-12)(5-x)#

#=-2x^3+5x^2+37x-60#

#"the degree of the polynomial is determined by the term"#
#"with the largest "color(blue)"exponent of the variable"#

#"that is "-2x^(color(red)(3))rArr"degree is 3"#

#"the polynomial has 4 terms"-2x^3,5x^2,37x" and "-60#

#"the long-run behaviour is determined by the "color(blue)"leading term"#

#"that is "-2x^3#

#"which is of odd degree with negative leading coefficient"#

#• " as "xto+oorarr,yto-oodarr#

#• " as "xto-oolarr,yto+oouarr#

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