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1. Polynomial Functions

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 2 nd degree and higher polynomials are non-linear functions

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1. Polynomial Functions

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  1. 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

  2. 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

  3. 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

  4. 3. Exponents Operations Review

  5. 4. 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 -15 Add up all the boxes -5 X2 – 2x – 15

  6. 4. 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) -7b b -12b 2b2 – 12b – 7b + 42 42 -6 Add up all the boxes 2b2 – 19b + 42

  7. 4. 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) 12c 3c -20c 15c2 – 20c + 12c – 16 -16 -4 Add up all the boxes 15c2 – 8c – 16

  8. 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 -4a2 8a 4a 12a2 4 -2a 2 Add up all the boxes 24a3 + 8a2 + 6a + 4

  9. 5. Factoring Polynomial Expressions Sum Product x2 + bx + c (x )( x )

  10. 5. Factoring Polynomial Expressions Example 1: Factor the polynomial Sum Product X2 + 6x + 8 (x + )( x + ) (x + 4)( x + 2)

  11. 5. Factoring Polynomial Expressions Example 2: Factor the polynomial Sum Product g2 + 7g – 18 (g + big)( x – ) (g + 9)(g – 2)

  12. 5. Factoring Polynomial Expressions Example 3: Factor the polynomial 2h2 – 22h + 48 2(h2 – 11h + 24) 2(h – )(h – ) 2(h – 8)(h – 3)

  13. 5. Factoring Polynomial Expressions Example 3: Factor the polynomial Sum Product 5m2 – 4h – 21 (5m – big)(m + ) (2h – 7)(h + 3)

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