Properties of Polynomials. Polynomials are sums of "variables and exponents" expressions. Each piece of the polynomial that is being added, is called.

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Presentation on theme: "Properties of Polynomials. Polynomials are sums of "variables and exponents" expressions. Each piece of the polynomial that is being added, is called."— Presentation transcript:

1 Properties of Polynomials

2 Polynomials are sums of "variables and exponents" expressions. Each piece of the polynomial that is being added, is called a "term". – Monomials3, 4x, 3x 2, 7x 2 y, 18xyz the terms can be single or they can be a product of more than one there are no addition or subtraction signs – Binomials 3x+6, 4xy + 7z, 7x 2 y - 18xyz Two terms are separated by an addition or subtraction sign – Polynomials 4xy + 7z - 7x 2 y - 18xyz More than two terms are separated by addition and/or subtraction signs

3 Polynomial terms have variables which are raised to whole-number exponents (or else the terms are just plain numbers); – there are no square roots of variables, – there are no fractional powers – there are no variables in the denominator of any fractions.

4 6x –2 This is NOT a polynomial term the variable has a negative exponent. This is NOT a polynomial term the variable is inside a radical. 4x 2 This IS a polynomial term it obeys all the rules. This is NOT a polynomial term the variable is in the denominator. 1 x 2

5 The exponent on a term tells you the "degree" of the term. The leading term in the above polynomial is a "second-degree term" or "a term of degree two". The second term is a "first degree" term. The degree of the leading term tells you the degree of the whole polynomial; the polynomial above is a "second-degree polynomial". This polynomial has four terms, including a fifth-degree term, a third-degree term, a first- degree term, and a constant term. The degree of the leading term tells you the degree of the whole polynomial. This is a fifth-degree polynomial. Give the degree of the following polynomial: 2x 5 – 5x 3 – 10x + 9

6 Simplify (5x 2 )(–2x 3 ) Simplify –3x(4x 2 – x + 10) Simplify (x + 3)(x + 2) Multiply coefficients Multiply variables (add exponents) Distribute the monomial through the trinomial Multiply coefficients and then multiply variables (add exponents) WATCH YOUR SIGNS FOIL OR multiply one above the other

7 Simplify (4x 2 – 4x – 7)(x + 3) Simplify (x + 2)(x 3 + 3x 2 + 4x – 17)

8 Simplify (3x 2 – 9x + 5)(2x 2 + 4x – 7) Simplify (x 3 + 2x 2 + 4)(2x 3 + x + 1)


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