What is a cubic polynomial function in standard form with zeros -2,3,-5

Question

Show all of the work using box method

 

Answer 1

A quadratic equation works like this.

x²+8x-20=0

(x+10)(x-2)=0

x+10=0 or x-2=0

x=-10 or x=2

 

So when you are given the zeroes, just work backwards. For example if your zeroes, or roots, are 5 and -3, that means

x=5 or x = -3 which comes from

x-5=0 or x+3=0 which comes from

(x-5)(x+3)=0 which multiplied out, which is what I think you're refering to when you say the box method, is

x²-2x-15=0

 

The same thing happens in a cubic equation or any other power for that matter.

your zeroes are -2, 3, -5 which means

x+2=0, x-3=0, or x+5=0 which comes from

(x+2)(x-3)(x+5)=0 so multiply that out to get

(x²-x-6)(x+5)=0 which equals

x³+4x²-11x-30=0

 

Again, I'm not sure what the box method is but your final answeer should match up with mine.

 

Hope this helped.

 

Answer 2

 

zeros -2,3,-5

(x+2)(x-3)(x+5)=0

(x²+2x-3x-6)(x+5)=0

(x²-x-6)(x+5)=0

x²(x+5)-x(x+5)-6(x+5)=0

x³+5x²-x²-5x-6x-30=0

x³+4x²-11x-30=0