Question 916411
{{{h(x) = (2x+6)(x-3)^2(x+1)^3 }}}


 y-int = (0,54) 
 x-int = (-3,0)(3,0)(-1,0) 


to determine what the degree is, multiply  first

{{{h(x) = (2x+6)(x-3)(x-3)(x+1)(x+1)(x+1) }}} when you multiply all this, you will get

{{{h(x) =2x^6-30x^4-16x^3+102x^2+144x+54}}}

the degree is: {{{6}}}

the coefficient of the term with the highest degree is called the leading coefficient, and you have {{{2}}}

a tangent is a "straight line" which touches a graph of function

or the tangent line to a curve is a straight line that just touches a curve

{{{drawing( 600, 600, -10, 10, -60, 60,circle(-1,0,.2),locate(-1,2.9,p(-1,0)), circle(3,0,.2),locate(3.3,2.7,p(3,0)), circle(-3,0,.2),locate(-3,2.8,p(-3,0)), circle(0,54,.2),locate(0,54,p(0,54)), graph( 600, 600, -10, 10, -60, 60,(2x+6)(x-3)^2(x+1)^3, (2x+6)(x-3)^2(x+1)^3)) }}}