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# Polynomials

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### Polynomials

1. 1. POLYNOMIALS
2. 2. JOURNAL ENTRY: DESCRIBE THE RULES FOR THE FOLLWOING <ul><li>Power of a Power Property : </li></ul><ul><li>Power of a Product Property : </li></ul><ul><li>Power of Quotient: </li></ul>
3. 3. MULTIPLYING MONOMIALS <ul><li>(-2x 4 y 2 ) (-3xy 2 z 3 ) = </li></ul><ul><li>(-2)(-3)(x 4 x )(y 2 y 2 ) z 3 </li></ul><ul><li>6x 5 y 4 z 3 </li></ul><ul><li>(-2x 3 y 4 ) 2 (-3xy 2 ) </li></ul><ul><li>(-2 ) 2 x 3∙2 y 4∙2 ) (-3xy 2 ) </li></ul><ul><li>(4)(-3)(x 6 x) (y 8 y 2 ) </li></ul><ul><li>-12x 7 y 10 </li></ul>
4. 5. MULTIPLYING AND DIVIDING MONOMIALS <ul><li>Monomial – an expression that is either a numeral, a variable or a product of numerals and variables with whole number exponents. </li></ul><ul><li>Constant – Monomial that is a numeral. Example - 2 </li></ul>
5. 6. POLYNOMIALS <ul><li>Polynomial – a monomial or a sum of monomials. Each monomial in a polynomial is referred to as a term </li></ul><ul><li>Special types of Polynomials </li></ul><ul><li>Monomial – an expression that is a number, a variable, or a product of numbers and or variables </li></ul><ul><li>Binomial – a polynomial with exactly two terms. </li></ul><ul><li>Trinomials – a polynomial with exactly three terms. </li></ul><ul><li>Coefficient – The numeric factor of a term. </li></ul>
6. 7. TELL WHETHER EACH EXPRESSION IS A POLYNOMIAL AND STATE WHAT KIND. <ul><li>4x + 9x +4 </li></ul><ul><li>Trinomial </li></ul><ul><li>xy + 3xy³ </li></ul><ul><li>Binomial </li></ul>
7. 8. IDENTIFY THE TERMS AND GIVE THE COEFFICIENT OF EACH TERM <ul><li>4x³y² - 3z² + 5 </li></ul><ul><li>Term 4x³y² has a coefficient of 4 </li></ul><ul><li>Term -3xz² has a coefficient of -3 </li></ul><ul><li>Term 5 has a coefficient of 5 </li></ul>
8. 9. COLLECTING LIKE TERMS <ul><li>2x²y³ + 3x³y² - 4x²y³ + 6x³y² </li></ul><ul><li>2x²y³ + - 4xy + 3x³y² - 4x²y³ - 8xy + 6x³y² </li></ul>
9. 10. IDENTIFY THE DEGREE OF A POLYNOMIAL <ul><li>The degree of a term is the sum of the exponents of the variables . The degree of a polynomia l is the highest degree of its terms. </li></ul><ul><li>Example: </li></ul><ul><li>3a²b³ + 3x³y³ + 2 </li></ul><ul><li>The degree of 3a²b³ is 5 </li></ul><ul><li>The degree of 3x³y³ is 6 </li></ul><ul><li>The degree of 2 is 0 </li></ul><ul><li>The term with the highest degree is called the leading term.. The coefficient of the leading term is called the leading coefficient. </li></ul>
10. 11. IDENTIFY THE DEGREE OF EACH TERM AND THE DEGREE OF THE POLYNOMIAL <ul><li>2xy³ + 3x³y - 4x²y³ </li></ul><ul><li>2x²y³ + - 4xy + 3xy² - 4x²y² </li></ul>
11. 12. DESCENDING ORDER <ul><li>The polynomial 3x 3 y 4 +2x 2 y 3 -xy 5 -7 is written in descending order for the variable x. The term with the greatest exponent for x is first, the term with the next greatest exponent for x is second and so on. </li></ul><ul><li>The polynomial 7 -xy 5 +2x 2 y 3 + 3x 3 y 4 is written in ascending order for the variable x. The term with the least exponent for x is first, the term with the next larger exponent for x is second and so on. </li></ul>
12. 13. Collect like terms and Arrange each polynomial in descending order for x <ul><li>3x²y³ + - 2xy + 3x³y² - 5x²y³ - 8xy + 4x³y² </li></ul><ul><li>7x³y² - 2x²y³ -10xy </li></ul><ul><li>Collect like terms and Arrange each polynomial in descending order for b </li></ul><ul><li>4a 3 + 7a 2 b + b 3 - 3ab 2 + b 3 - a 3 + 3a 2 b </li></ul>