Question

What are the steps to solving both parts correctly?

Answer 1

`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`