 Simplify the following…  2(4 + x)  x(x – 3x 2 + 2)  5x – 2 + 6x  2x 2 + 5x – 11x 2 + 1  8x(4x 2 )

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Presentation transcript:

 Simplify the following…  2(4 + x)  x(x – 3x 2 + 2)  5x – 2 + 6x  2x 2 + 5x – 11x  8x(4x 2 )

Adding, Subtracting and Multiplying Polynomials

 Polynomial – A monomial or sum of monomials.  Monomial – A number, variable, or product of a number and 1 or more variables.  5x  Binomial – The sum of two monomials.  2x  Trinomial – The sum of three monomials.  x 3 – 10x + 4

 Degree of a Polynomial – The greatest degree of any term in the polynomial.  Degree 0 = Constant  Degree 1 = Linear  Degree 2 = Quadratic  Degree 3 = Cubic  Example: 5x 3 + 6x 2 – 2 Degree is 3 (Cubic)

ExpressionIs it a Polynomial? What is the degree? Monomial, Binomial, or Trinomial? 4x – 5yz a b 6x 3 + 4x + x + 3

 Write the terms in order from greatest to least degree.  4x 3 – 5x 2 + 2x – 7  Your Turn… Write these in standard form. 1. 3x 2 + 4x 5 – 8x 2. x + 5x 3 – 2x 2 – 7x

 Method 1: Combine Like Terms!!!  (2x 2 + 5x – 7) + (3 – 4x 2 + 6x)  Method 2: Align and Combine!!!  (3x + x 3 – 5) + (4x 2 – 4x + 2x 3 + 8)

 Method: Distribute the negative. Then, solve by adding.  (3 – 2x + 2x 2 ) – (4x – 5 + 3x 2 )  (7x + 4x 3 – 8) – (3x – 9x)

 -3x 2 (7x 2 – x + 4)

 2x(-4x 2 + 5x) – 5(2x )

 2x(5x – 2) + 3x(2x + 6) + 8 = x(4x + 1) + 2x(6x – 4) + 50  x(x + 3) – x(x – 4) = 9x – 16