use synthetic division to show that x is a solution of the third-degree polynomial equation and use the result to factor the polynomial completely. list all the real zeros of the function
x3-7x+6=0, x=2
+6251 If x=2 is a root of x3−7x+6 then (x−2) divides x3−7x+6
x3−7x+6=x2(x−2)+(2x2−7x+6)(2x2−7x+6)=2x(x−2)+(−3x+6)(−3x+6)=−3(x−2)x3−7x+6=(x−2)(x2+2x−3)
To find the rest of the zeros we have to factor x2+2x−3and this is easily done resulting in x2+2x−3=(x+3)(x−1)and thus the other zeros are x=−3,x=1
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