Exponents, Radicals, Polynomials…

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Presentation transcript:

Exponents, Radicals, Polynomials… Unit 2 Exponents, Radicals, Polynomials…

Exponent Rules & Monomials Multiplying powers Dividing powers Power to a power Negative exponents Zero as an exponent Use 5-1 sheet

Polynomials Non-Examples: 10/x, 5x-5 – 3x Rules for polynomials Monomials (variables attached to numbers—no negative or fraction exponents) connected by addition or subtraction Examples: 5xy , 10x³y + ½ yz – 2xyz Non-Examples: 10/x, 5x-5 – 3x

Adding Polynomials-Combine Like Terms Add the following polynomials: (3a2 + 3ab - b2) + (4ab + 6b2) (4x2 - 2xy + 3y2) + (-3x2 - xy + 2y2) (9y - 7x + 15a) - (-3y + 8x - 8a) (7a - 10b) - (3a + 4b)

Multiplying Polynomials 3x(3x² + 5xy³) Distribute!!! (7x – 3)(-2y + 5x) FOIL!!! (2x – 4)(x² + 3x – 5) Double distribute!!! Use sheet 5-2

Dividing Polynomials Polynomial by a monomial 5a²b – 15ab³ + 10a³b4

On your own… 6k²m – 12k³m² + 9m³ 2km²

Long Division of polynomials (x² - 2x – 15) divided by (x – 5)

(a² - 5a + 3)(2 – a)-1 Hint: put the variable in the front…

(4y4 – 5y² + 2y + 4) / (2y – 1)

Synthetic Division When do we use synthetic division? (x³ - 4x² + 6x – 4) / (x – 2) Set binomial = 0 and solve for x. 2| 1 -4 6 -4 2 -4 4 1 -2 2 |0 ---remainder So…the bottom row are the coefficients x² - 2x + 2

How do we know… When to just “cancel” terms? When to use long division? When to use synthetic division?