Question 391606
+-1.+-2,+-4 are the possible roots.
The whole purpose of the sythetic division is to break the polynomial into smaller pieces so as to find the other roots and solve the equation. In this case if we can get one root then we will have a quadratic left and our troubles are over.
x^3-2x^2-7x-4 / x-4 = x^2+2x+1 This is the quotient.
x^2+2x+1=(x+1)(x+1)
So (x+1)(x+1)(x-4)=0
x=-1 and x=4 These are the zeros of the equation.
-1, -1, and 4 are the roots of the equation. It cannot have more than three roots because x^3 has the exponent 3.
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Ed
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{{{graph(500,500,-10,10,-10,10,x^3-2x^2-7x-4)}}}