Depressed Polynomials and Factor Theorem

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Depressed Polynomials
When you divide a polynomial by one of its binomial factors, the quotient is called a depressed polynomial.

Figure 1.

Above, we're dividing a polynomial by one of its factors (x - 4). Because we're dividing by a factor, we end up with a remainder of 0.

Factor Theorem
The binomial x – a is a factor of the polynomial if and only if f(a) = 0.