Question

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

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

Answer 1

`"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`