Question

state the remainder theorem and the factor theorem for polynomials with real coefficients.
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Answer 1

Answer:

Reminder theorem: If you divide a polynomial f(x) by (x - h), then the remainder is f(h)

factor theorem: Suppose p(x) is a nonzero polynomial. The real number c is a zero of p if and only if (x - c) is a factor of p(x). The proof of The Factor Theorem is a consequence of what we already know. If (x - c) is a factor of p(x), this means p(x)=(x - c)q(x) for some polynomial q.

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Answer 2

Answer:

REMAINDER THEOREM:

If a polynomial p(x) is divided by linear polynomial g(x), quotient is q(x) and remainder is r(x).

=> p(x)= [g(x) × q(x)] + r(x)

FACTOR THEOREM:

If p(x) is a degree greater than 1 and 'a' is any real number then,

case1: (x-a) is a factor og p(x), if p(a)=0

then, x-a is a factor of p(x)

case2: If p(a)=0, if (x-a) is a factor of p(x).

p(a)= 0