How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -5, 2, -2?

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Answer 1 · 2017-02-28T08:53:05

#x^3+5x^2-4x-20=0#

#" if the zeros are" -5,2,-2, " we write down the corresponding factors and multiply them"#

#x=-5=>(x+5)=0#

#x=2=>(x-2)=0#

#x=-2=>(x+2)=0#

the polynomial is:

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

multiplying out.

#(x+5)(x^2-4)=0" (difference of squares)"#

#x^3-4x+5x^2-20=0#

tidying up

#x^3+5x^2-4x-20=0#