P.3 Polynomials and Special Products

Unit P:Prerequisites for Algebra 5-Trig

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.

Standard Form

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

Operations with Polynominials

• You can add and subtract polynomials by combining like terms.

• To find the product you must distribute.

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

Application