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Polynomials

Remainder Theorem

If deg(P) ≥1 then     P(x) = (x -cQ + R,     where R is a constant.

Substituting x = c into the equation we see that R = P(c)

Hence (x -c) is a factor of P(x) if P(c) = 0.

Example 7.

Study these examples. Click on "Next Example" to see a new example. Then click on "P(c)" to see the polynomial P evaluated at c. Finally, click on "Is (x - c) a factor of P?"


P(x)
c
x2 + x +

 


Exercise 10.

Now try a few exercises on your own:


P(x)
c
x2 + x +

 

P(c)
(x - c ) a factor of P?
    
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