2nd Degree Polynomial Function 1. Polynomial Functions Polynomial functions have multiple terms with bases raised to different powers The degree of the polynomial function is the highest exponent in the equation 2nd degree and higher polynomials are non-linear functions F(x) means the output of the function when the input is x. f(x) = y = h(x) = g(x) 2nd Degree Polynomial Function Term “Function of x” “f of x” Output when input is x Exponent f(x) = 5x2 + 15x + 30 Coefficient Base

Include the sign before the number when you combine like terms 2. Adding and Subtracting Polynomial Expressions Example 1: Simplify the polynomial expression using distributive property and by combining like terms 2x2 + 6x + 4x2 – 20x 2x2 + 6x + 4x2 + -20x Include the sign before the number when you combine like terms 6x2 – 14x

THEN, Combine Like Terms 2. Adding and Subtracting Polynomial Expressions Example 2: Simplify the expression using distributive property and by combining like terms 4( x3 – 5x2) – ( x3 + 3x2) Distribute FIRST THEN, Combine Like Terms 4( 1x3 + -5x2 ) + -1( 1x3 + 3x2) 4x3 + -20x2 + -1x3 + -3x2 3x3 – 23x2

Subtract the exponents 3. Exponents Operations Review Polynomial Operation Exponent Operation Adding/Subtracting (+ / - ) Stays the same Multiplying (*) Add the exponents Dividing (/) Subtract the exponents

4. (x – 5)(x + 3) (x – 5)(x + 3) X2 + 3x – 5x - 15 X2 – 2x – 15 Multiplying Polynomial Expressions Example 1: Multiply the polynomial (x – 5)(x + 3) Box Method Distribution Method (FOIL) x 3 Each box is a product (multiply) x2 3x (x – 5)(x + 3) x -5x X2 + 3x – 5x - 15 Add up all the boxes -15 -5 X2 – 2x – 15

4. (2b – 7)(b – 6 ) (2b – 7)(b – 6) 2b2 – 19b + 42 2b2 – 12b – 7b + 42 Multiplying Polynomial Expressions Example 2: Multiply the polynomial (2b – 7)(b – 6 ) Box Method Distribution Method (FOIL) 2b -7 Each box is a product (multiply) 2b2 (2b – 7)(b – 6) b -7b -12b 2b2 – 12b – 7b + 42 42 -6 Add up all the boxes 2b2 – 19b + 42

4. (5c + 4)(3c – 4 ) (5c + 4)(3c – 4) 15c2 – 8c – 16 Multiplying Polynomial Expressions Example 3: Multiply the polynomial (5c + 4)(3c – 4 ) Box Method Distribution Method (FOIL) 5c 4 Each box is a product (multiply) 15c2 (5c + 4)(3c – 4) 3c 12c -20c 15c2 – 20c + 12c – 16 -16 -4 Add up all the boxes 15c2 – 8c – 16

4. Multiplying Polynomial Expressions Example 4: Multiply the polynomial (4a + 2)(6a2 – a + 2) Box Method 6a2 -a 2 Each box is a product (multiply) 24a3 4a -4a2 8a 12a2 4 -2a 2 Add up all the boxes 24a3 + 8a2 + 6a + 4

5. x2 + bx + c (x )( x ) Polynomial Terms Signs in Factored Form +, + Factoring Polynomial Expressions Sum Product x2 + bx + c (x )( x ) Polynomial Terms Signs in Factored Form +, + (x + ), (x + ) +, - (x + big), (x - ) -, + (x - ), (x - ) -, - (x + ), (x - big)

5. X2 + 6x + 8 (x + )( x + ) (x + 4)( x + 2) Polynomial Terms Factoring Polynomial Expressions Example 1: Factor the polynomial Sum Product X2 + 6x + 8 (x + )( x + ) (x + 4)( x + 2) Polynomial Terms Signs in Factored Form +, +

5. g2 + 7g – 18 (g + big)( x – ) (g + 9)(g – 2) Polynomial Terms Factoring Polynomial Expressions Example 2: Factor the polynomial Sum Product g2 + 7g – 18 (g + big)( x – ) (g + 9)(g – 2) Polynomial Terms Signs in Factored Form +, - + (bigger) , -

5. 2h2 – 22h + 48 2(h2 – 11h + 24) 2(h – )(h – ) 2(h – 8)(h – 3) Factoring Polynomial Expressions Example 3: Factor the polynomial 2h2 – 22h + 48 2(h2 – 11h + 24) 2(h – )(h – ) 2(h – 8)(h – 3) Polynomial Terms Signs in Factored Form -, + -, -

5. 5m2 – 4h – 21 (5m – big)(m + ) (2h – 7)(h + 3) Polynomial Terms Factoring Polynomial Expressions Example 3: Factor the polynomial Sum Product 5m2 – 4h – 21 (5m – big)(m + ) (2h – 7)(h + 3) Polynomial Terms Signs in Factored Form -, - +, - (bigger)