#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#