State the degree, the number of terms, and describe the long‐run behavior?
y=(x+4)(2x-3)(5-x)
y=(x+4)(2x-3)(5-x)
1 Answer
Nov 17, 2017
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#