POLYNOMIALS LESSON OBJECTIVES: Determine the highest degree of a polynomial. Writing polynomials in standard form.

Review Let’s review some vocabulary Coefficient Coefficient – The number in front of the variable. Constant Constant – A number without a variable. Terms Terms – Any number, variable, or product or quotient of a number and variable. (always separated by + or – signs)

Polynomial These are examples of polynomials: 5X² - 2X + 3 – 3X³ + 7X - 4

Degree of a Polynomial The degree of a polynomial is calculated by finding the largest exponent in the polynomial.

Degree of a Polynomial

Largest exponent is 1

Degree of a Polynomial Largest exponent is 1 degree 1

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3 Largest exponent is n

Degree of a Polynomial Largest exponent is 1 degree 1 Largest exponent is 2 degree 2 Largest exponent is 3 degree 3 Largest exponent is n degree n

Example 1 Answer the following questions about this polynomial: 1. What is the degree of the polynomial? 6

Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 6

Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 6 11

Example 1 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 3.What is coefficient of third degree term?

Example 2 Answer the following questions about this polynomial: 1.What is the degree of the polynomial? 2.What is the constant? 3.What is coefficient of second degree term? 4 – 5 17

Standard Form of Polynomials When you write polynomials, you write them with the exponents in decreasing order.

Example 3 Write this polynomial in standard form. What term has the largest exponent?

Example 3 Write this polynomial in standard form. What term has the next largest exponent?

Example 3 Write this polynomial in standard form. What term has the next largest exponent?

Example 3 Write this polynomial in standard form. What term has the next largest exponent?

Example 3 Write this polynomial in standard form. What term has the next largest exponent?

Example 3 Write this polynomial in standard form. What is the last term?

TRY THESE: Copy them onto notebook paper first, then re-write in standard form. 1. 4x – 3x x – 3x – 7x z 2 – 11z 3 + 5z – 5 5. y – 7y y 8 6. c 2 – 2 + 4c SOLUTIONS: 1. -3X 2 + 4X 2. 4X + 9 (stay same) 3. -7x 2 – 3x z 3 + 9z 2 + 5z – y 8 – 7y 5 + y 6. c 2 + 4c - 2

continued q 4 – 8q + 3q x 9. 2x 3 – x x 4 – 2 – 2x 3 + 7x – 2x 12. 3x 6 – 4 + 2x x + 5 – 4x 2 + x 3 SOLUTIONS: 7. 4q 4 + 3q 2 – 8q – x – x 4 + 2x x 4 – 2x 3 + 7x – x x 6 + 2x 2 – x 3 – 4x 2 – 2x + 5

INDEPENDENT PRACTICE (classwork or homework – follow teacher instructions) Copy and re-write in standard form. 1. 6x – 9x y – 9 – y v 4. 2x + 7x x 2 – 2x – x 3 – x x z 3 – z 8. 3 – 3x – 4x 2 – 6x x + 2x y + 18y 8 – 3y x – 4 – 3x 2 - 6x y – 9y 3 + 9y 2