color(blue)("PART 1"
f(x)=4x^3+16x^2-3x-45 Find f(-3)
Lets substitute all of x with color(red)(-3)
f(color(red)(-3))=4(color(red)(-3))^3+16(color(red)(-3))^2-3(color(red)(-3))-45
=f(color(red)(-3))=4*(-27)+16*9-(-9)-45
=f(color(red)(-3))=-108+144+9-45
=f(color(red)(-3))=0
color(blue)("PART 2"
f(x)=4x^3+16x^2-3x-45 Find f(x)=0
f(x)=4x^3+16x^2-3x-45=0
Factorize color(red)(4x^3+16x^2-3x-45->
f(x)=(x+3)(2x−3)(2x+5)=0
Set the factors equal to zero
color(green)(x+3=0 or color(violet)(2x−3=0 or color(orange)(2x+5=0
therefore color(green)(x=−3 or color(violet)(x=3/2 or color(orange)(x=−5/2