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

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

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

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Answer 1 · 2017-11-17T10:40:20

$"see explanation"$

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

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

1 Answer

Explanation:

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