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

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

1 Answer
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