Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and the leading coefficient. If the function is not a polynomial, state why. f(x)=(2x+3)^2(3x+5)^2This is not a polynomial function because there is no leading coefficient.This is a polynomial function of degree 4 with a leading coefficient of 36.This is a polynomial function of degree 4 with a leading coefficient of −36.This is not a polynomial function as the factors are not all linear.

Answer:The correct option is 2. The given function is a polynomial of degree 4 with a leading coefficient of 36.Step-by-step explanation:A polynomial function is defined as[tex]P=a_0x^n+a_1x^{n-1}+....+a_{n-1}x+a_n[/tex]The given function is[tex]f(x)=(2x+3)^2(3x+5)^2[/tex]Using perfect square trinomial property.[tex]f(x)=(4x^2+12x+9)(9x^2+30x+25)[/tex]        [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]Using distributive property, we get[tex]f(x)=4x^2(9x^2+30x+25)+12x(9x^2+30x+25)+9(9x^2+30x+25)[/tex][tex]f(x)=36x^4+120x^3+100x^2+108x^3+360x^2+300x+81x^2+270x+225[/tex][tex]f(x)=36x^4+228x^3+541x^2+570x+225[/tex]The given function is a polynomial of degree 4 with a leading coefficient of 36.Therefore the correct option is 2.