M3 Polynomials

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, P(x) = 2x^3 - 4x^2 + 3x - 5 is a polynomial.

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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 P(x) = 4x^5 + 3x^3 - 2, the degree is 5.

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How do you find the y-intercept of a polynomial function?

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To find the y-intercept of a polynomial function, substitute x = 0 into the function and solve for f(0).

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What is a zero of a polynomial?

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A zero of a polynomial is a value of x for which the polynomial evaluates to zero. For example, if P(x) = x^2 - 4, then the zeros are x = 2 and x = -2.

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What is the Factor Theorem?

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The Factor Theorem states that if P(c) = 0 for a polynomial P(x), then (x - c) is a factor of P(x).

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What is the Greatest Common Factor (GCF) of a polynomial?

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The GCF of a polynomial is the largest polynomial that divides all terms of the polynomial without leaving a remainder.

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How do you factor a quadratic polynomial?

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To factor a quadratic polynomial of the form ax^2 + bx + c, find two numbers that multiply to ac and add to b, then rewrite the polynomial using these numbers.

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What is synthetic division?

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Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor of the form (x - c).

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What is the Remainder Theorem?

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The Remainder Theorem states that the remainder of the division of a polynomial P(x) by (x - c) is equal to P(c).

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How do you determine the number of zeros of a polynomial?

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The number of zeros of a polynomial is determined by its degree. A polynomial of degree n can have up to n real zeros.