What are the steps to solving both parts correctly?

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1 Answer
Oct 18, 2017

color(blue)("PART 1"PART 1

f(x)=4x^3+16x^2-3x-45f(x)=4x3+16x23x45 Find f(-3)f(3)

Lets substitute all of xx with color(red)(-3)3

f(color(red)(-3))=4(color(red)(-3))^3+16(color(red)(-3))^2-3(color(red)(-3))-45f(3)=4(3)3+16(3)23(3)45

=f(color(red)(-3))=4*(-27)+16*9-(-9)-45=f(3)=4(27)+169(9)45

=f(color(red)(-3))=-108+144+9-45=f(3)=108+144+945

=f(color(red)(-3))=0=f(3)=0

color(blue)("PART 2"PART 2

f(x)=4x^3+16x^2-3x-45f(x)=4x3+16x23x45 Find f(x)=0f(x)=0

f(x)=4x^3+16x^2-3x-45=0f(x)=4x3+16x23x45=0

Factorize color(red)(4x^3+16x^2-3x-45->4x3+16x23x45

f(x)=(x+3)(2x−3)(2x+5)=0f(x)=(x+3)(2x3)(2x+5)=0

Set the factors equal to zero

color(green)(x+3=0x+3=0 or color(violet)(2x−3=02x3=0 or color(orange)(2x+5=02x+5=0

therefore color(green)(x=−3 or color(violet)(x=3/2 or color(orange)(x=−5/2