O PERATIONS WITH P OLYNOMIALS & F UNCTIONS AS Maths.

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Presentation transcript:

O PERATIONS WITH P OLYNOMIALS & F UNCTIONS AS Maths

An expression constructed from variables and constants. Uses only addition, subtraction and multiplication. Powers must be non-negative whole numbers.

Powers should always be written in descending order, starting with the highest power and ending with the smallest. The degree of a polynomial is the highest power. What is the name of a polynomial with…..  Degree 0  Degree 1  Degree 2  Degree 3  Degree 4 constant linear quadratic cubic quartic

Is this polynomial written in standard form? What is the degree of this polynomial? What is the -7 called? yes 5 a constant

Write the polynomials in standard form and identify the polynomial by degree. (a) (b)

Question (a) Question (b) This is a 2 nd degree or quadratic polynomial This is a 3 rd degree or cubic polynomial.

Add: (x 2 + 3x + 1) + (4x 2 +5) Step 1: Underline like terms: Step 2: Add the coefficients of like terms, do not change the powers of the variables: (x 2 + 3x + 1) + (4x 2 +5) Notice: ‘3x’ doesn’t have a like term. x2 x2 + 4x 2 + 3x x 2 + 3x + 6

Some people prefer to add polynomials by stacking them. If you choose to do this, be sure to line up the like terms! (x 2 + 3x + 1) + (4x 2 +5) 5x 2 + 3x + 6 (x 2 + 3x + 1) + (4x 2 +5) Stack and add these polynomials: (2a 2 + 3ab + 4b 2 ) + (7a 2 + ab – 2b 2 ) (2a 2 + 3ab + 4b 2 ) + (7a 2 + ab – 2b 2 ) 9a 2 + 4ab + 2b 2

Add the following polynomials; you may stack them if you prefer:

Subtract: (3x 2 + 2x + 7) - (x 2 + x + 4) Step 1: Change subtraction to addition by distributing the negative throughout the second bracket. Step 2: Underline like terms or stack. (3x 2 + 2x + 7) + ( - x x + - 4) (3x 2 + 2x + 7) + (- x x + - 4) 2x 2 + x + 3

Subtract the following polynomials :

x²x²3x3x-2 2x²2x² -x-x 4 Multiply x ² + 3 x – 2 by 2 x ² – x + 4 Method 1: Draw out a grid Simplify

Multiply x ² + 3 x – 2 by 2 x ² – x + 4 Method 2: Distribute Simplify

1) (4 – 7x)(2 + 5x – x 2 ) 2) (x 2 + x – 3)(2x 2 – x + 4) 3) (x 3 + 2x 2 – 3x +1)(3x 2 + 2x – 3 )

Expand one pair of brackets first. Then expand this answer by the final bracket.

Functions can be added, subtracted, multiplied, and divided! Make sure you are only adding & subtracting “like terms”! Given Find (a) (b) (c)

Y OU TRY ! Given Find (a) (b) (c) Solutions:

I NDEPENDENT S TUDY Core 1 & 2 Advanced Mathematics ORC Textbook, Pg. 135, Exercise 9 #1 – 7 Copy & complete all questions in your notebook Mark all questions & correct those you got wrong DUE: Next Lesson!