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Understanding and Evaluating Polynomials with Synthetic Substitution in Precalculus

Learn to recognize and evaluate polynomials using synthetic substitution. Understand polynomial structure, degrees, and roots. Practice with examples and solve problems in this precalculus section.

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Understanding and Evaluating Polynomials with Synthetic Substitution in Precalculus

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  1. Precalculus Section 2.1Recognize and evaluate polynomials using synthetic substitution. A polynomial is an expression that can be written in the form axn + bxn-1 + c xn-2 + …dx2 + ex + f, where n is a positive integer. “a” is the leading coefficient, and f is the constant. “n” is the degree of the polynomial. Polynomial Degree 0 1 2 3 4 5 Name Constant Linear Quadratic Cubic Quartic quintic Example 6 3x – 2 x2 + 2x – 5 x3 -3x4 + x3 – 2x2 + 7x – 1 6x5 - 9

  2. The root (zero) of a function is a value for which the polynomial equals zero. Find the zeros of g(x) = 2x2 – 3x Find the zeros of 2x3 – 32x

  3. Use synthetic substitution to evaluate Find h(-1) when h(x) = 2x2 – 5x + 6 Find g(1/2) when g(x) = 2x3 + 3x2 + 7 Find f(1+i) when f(x) = 2x2 – 5x + 3

  4. assignment Page 56 Problems 2-12 even, 16,19,20,22,26

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