What are the steps to solving both parts correctly?

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1 Answer
Oct 18, 2017

#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#