Writing Polynomial Equations

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What is a polynomial function?

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A polynomial function is a mathematical expression that involves a sum of powers in one or more variables multiplied by coefficients. The general form is: f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + 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 expression. For example, in the polynomial f(x) = 4x^3 + 3x^2 + 2, the degree is 3.

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What is a monomial?

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A monomial is a polynomial with only one term. It can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers. For example, 5x^2 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, 3x + 4 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 standard form of a polynomial?

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The standard form of a polynomial is when it is written in descending order of the degree of its terms. For example, 2x^3 + 3x^2 + x + 5 is in standard form.

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What are the roots of a polynomial?

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The roots of a polynomial are the values of x that make the polynomial equal to zero. They can be found by factoring the polynomial or using the quadratic formula for quadratic polynomials.

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What is the Factor Theorem?

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The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x). This helps in factoring polynomials.

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CCSS.HSA.APR.B.2

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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 this division is f(c). This can be used to evaluate polynomials quickly.

Tags

CCSS.HSA.APR.B.2

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How do you find the zeros of a polynomial?

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To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. This can involve factoring, using the quadratic formula, or synthetic division.