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