A polynomial is an algebraic expression made of variables and coefficients combined using addition, subtraction, and multiplication. Polynomials are f
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What is the Remainder Theorem and why is it useful?
The Remainder Theorem states that when P(x) is divided by (x minus r), the remainder is P(r). This is useful because you can find P(r) by just evaluating the polynomial rather than doing long division. It is also the basis for the Factor Theorem.
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How do you know how many zeros a polynomial has?
A polynomial of degree n has exactly n zeros counting complex numbers and multiplicities. Over real numbers, it has at most n real zeros. The actual number and nature of zeros depend on the specific polynomial.
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What is synthetic division and when is it used?
Synthetic division is a shortcut method for dividing a polynomial by a linear factor (x minus r). It is faster than long division but only works for linear divisors. It is often used to test if a value is a zero using the Remainder Theorem.
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