Finding depressed equation without a divisor

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I've been given

$$4x^3 -2x^2 + x - 3 = 0$$

and I want to convert it into a depressed equation. A depressed equation is an equation that results from reducing the number of roots in a given equation with one unknown by dividing the original equation by the difference of the unknown and a root. However; I know for a fact that you need some sort of divisor in order to do this. The correct answer is:

$$4x^2 + 2x + 3$$

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1 Answer

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HINT: By inspection I see that $x=1$ is a solution to the original equation. What binomial factor does that guarantee for the cubic?

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