Question

show that -1 is the zero of the polynomial {x^3-3x^2-x+3}
PLEASE SHOW WORKINGS FOR YOUR ANSWER!!!!!

Answer 1

let's first give a name to the polynomial

$p(x) = x^3-3x^2-x+3$

ok, so what's a zero of a polynomial?

the zero is simply defined as z if p(z) = 0

so, let's put -1 inside p(x) and se what happens

if x = -1

$p(x) = p(-1) = (-1)^3-3(-1)^2-(-1)+3\\\\=-1-3+1+3\\\\=0$

so, this shows that p(-1) = 0 translating to -1 is a zero of p(x)

h/w idea: the degree (highest power of x in p(x) ) is 3, that means there two more zeros of this polynomial, try to find them

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