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P.3 Polynomials and Special Products

P.3 Polynomials and Special Products. Unit P:Prerequisites for Algebra 5-Trig. Definition of a Polynomial in x. Let a 0 , a 1 , a 2 , …, a n be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form a n x n + a n-1 x n-1 + … + a 1 x + a 0

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P.3 Polynomials and Special Products

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  1. P.3 Polynomials and Special Products Unit P:Prerequisites for Algebra 5-Trig

  2. Definition of a Polynomial in x • Let a0, a1, a2, …, an be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form anxn + an-1xn-1 + … + a1x + a0 where an ≠ 0. The polynomial is of degree n, an is the leading coefficient, and a0 is the constant term.

  3. Standard Form • In standard form, a polynomial is written in descending powers of x.

  4. Operations with Polynominials • You can add and subtract polynomials by combining like terms. • To find the product you must distribute.

  5. Special Products • Sum and Difference of Same Terms • (a + b)(a – b) = a2 – b2 • Square of a Binomial • (a + b)2 = a2 + 2ab + b2 • (a – b)2 = a2 – 2ab + b2 • Cube of a Binomial • (a + b)3 = a3 + 3a2b + 3ab2 + b3 • (a – b)3 = a3 – 3a2b + 3ab2 – b3

  6. Application

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