Ch7 Review - Polynomial Functions

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What is a polynomial function?

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A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The general form is: $$f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0$$ where $$a_n, a_{n-1}, ..., a_0$$ are constants and $$n$$ is a non-negative integer.

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial $$4x^3 - x + 5x^4 + 2x^2 - 8$$, the degree is 4.

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What is a monomial?

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A monomial is a polynomial with only one term. For example, $$3x^5$$ is a monomial.

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What is a binomial?

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A binomial is a polynomial with exactly two terms. For example, $$x^2 + 3x$$ is a binomial.

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What is a trinomial?

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A trinomial is a polynomial with exactly three terms. For example, $$x^2 + 3x + 2$$ is a trinomial.

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What is the Remainder Theorem?

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The Remainder Theorem states that if a polynomial $$f(x)$$ is divided by $$x - c$$, the remainder of that division is equal to $$f(c)$$.

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How do you find the remainder when dividing polynomials?

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To find the remainder when dividing a polynomial by a linear divisor, you can use synthetic division or the Remainder Theorem.

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What is synthetic division?

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Synthetic division is a simplified method of dividing a polynomial by a linear divisor of the form $$x - c$$. It is faster than long division.

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What is a factor of a polynomial?

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A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder. For example, $$x + 2$$ is a factor of $$x^2 - 4$$.

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What is the Factor Theorem?

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The Factor Theorem states that a polynomial $$f(x)$$ has a factor $$x - c$$ if and only if $$f(c) = 0$$.