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1 Answer
Jim G.
Dec 4, 2017

#"see explanation"#

Explanation:

#(1)color(white)(x)P(x)=2x^5-6x^3+x^2-2#

#"the degree of the polynomial is the value of the largest"#
#"exponent of the variable"#

#rArrP(x)" is of degree 5"#

#"the leading coefficient is the coefficient of the term"#
#"containing the largest exponent of the variable"#

#rArr"leading coefficient "=2#

#"to determine end behaviour we consider the term of "#
#"highest degree"#

#"that is "2x^5#

#• " odd degree with positive leading coefficient"#

#"as "xto+oo,P(x)to+oo#

#"as "xto-oo,P(x)to-oo#
graph{2x^5-6x^3+x^2-2 [-20, 20, -10, 10]}

#(2)color(white)(x)Q(x)=-4x^2+x-1#

#rArrQ(x)" is of degree "2#

#"with leading coefficient "=-4#

#• " even degree with negative leading coefficient"#

#"as "xto+-oo,Q(x)to-oo#
graph{-4x^2+x-1 [-40, 40, -20, 20]}

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