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CertifiedKey Concepts
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Definition and Terminology: Defining a polynomial, its terms, coefficients, and variables. Understanding that exponents must be non-negative integers.
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Degree of a Polynomial: The highest power of the variable.
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Types of Polynomials: Based on terms (monomial, binomial, trinomial) and degree (linear, quadratic, cubic).
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Zeroes of a Polynomial: Finding the value(s) of the variable for which the polynomial equals zero.
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Factorization of Polynomials:
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Splitting the middle term for quadratic polynomials.
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Using the Factor Theorem for cubic polynomials.
Expected Questions
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Classification and Degree: Identifying the degree, coefficient, and type of a given polynomial.
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Finding Zeros: Evaluating $P(a)$ to check if $a$ is a zero of $P(x)$.
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Applying Theorems:
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Finding the remainder without actual division using the Remainder Theorem.
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Using the Factor Theorem to find the value of an unknown coefficient (e.g., finding $k$ if $x-1$ is a factor of a polynomial).
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Factorization:
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Factoring quadratics by splitting the middle term.
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Factoring cubics using the Factor Theorem to find the first factor, followed by long division or synthetic division.
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Application of Identities: Expanding, simplifying, and factoring expressions using the new and old identities.
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