Polynomials

Algebra 2 YOU WILL LEARN TO: Add and Subtract Polynomials Multiply Polynomials ADD and SUBTRACT POLYNOMIALS A polynomial is a ___________________________ or a sum of _________________________________. The monomials that make up a polynomial are called the _________________ of the polynomial. In a polynomial such as x2 + 2x + x +1, the two monomials 2x and x can be combined because they are _______________________________. The result is __________________________. The polynomial x2 + 3x +1 is a _________________________ because it has ________________ unlike terms. A polynomial such as xy + z3 is a ________________________ because it has two unlike terms. The degree of the polynomial is the degree of the degree of the ___________________________________ __________________________________________________________________. As an example, the degree of x2 + 3x +1 is ______, and the degree of xy + x3 is ______. EXAMPLE: Degree of a Polynomial Determine whether each expression is a polynomial. If it is a polynomial, state the degree of the polynomial. a. 2 6 65 34 y + y _____________________________________________________________________ b. m - 5 ______________________________________________________________________ c. 2 6 65 34 + y- y ______________________________________________________________________ To simplify a polynomial means to perform the operations indicated and ___________________________ ________________________________________. EXAMPLE: Subtract and Simplify (4x2 - 3x2 + 3xy)- (8xy + 3x2 ) = MULTIPLY POLYNOMIALS You can use the ___________________________ Property to multiply polynomials. EXAMPLE: Multiply and Simplify a. 2xy(3xy3 - 4xy + 2y4 ) = b. 3 (4 6 8 4 ) 21 a a - b + ab = The ______________________________ uses the Distributive Property to multiply _________________. FOIL Method for Multiplying Binomials The product of two binomials is the sum of the products of F _________________________________________________ O _________________________________________________ I _________________________________________________ L _________________________________________________ EXAMPLE: Multiply the Binomials a. (y -10)(y + 7) = b. (2a + 3b)(8a - 5b) = The “FOIL” method is only applicable when multiplying two binomials. In general, when multiplying polynomials, be sure to multiply ___________________________________ in one polynomial by _______________________________________ in the other polynomial. EXAMPLE: Multiply Polynomials (2x2 - xy + 4y2 )(3x2 + 5xy) =