### R01520 Algrebra Factor Theorem

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In algebra, if we divide a polynomial P(x) by a polynomial D(x) (where the degree of D is less than the degree of P), we would find

P(x) = Q(x)· D(x) + R(x).

The Factor theorem

If the polynomial p(x) is divided by cx - d and the remainder, given by p(d/c) p(dc), is equal to zero, then cx - d cxd is a factor of p(x)

Converse: if (cx -d) is a factor of p(x),   thenp(d/c)= 0 p(dc)=0 .

The Remainder Theorem and the Factor Theorem are similar and deal with dividing a polynomial by a linear function.

Mathplanet  Pre Algebra

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