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Unit 5 “ Polynomials”

Unit 5 “ Polynomials”. Math 9. 5.1 Modeling Polynomials – Using Algebra Tiles. We can use shapes or ‘ tiles ’ to represent various algebraic ‘ polynomials ’ , and certain tiles are matched to certain ‘ terms ’ .

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Unit 5 “ Polynomials”

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  1. Unit 5“Polynomials” Math 9

  2. 5.1 Modeling Polynomials – Using Algebra Tiles • We can use shapes or ‘tiles’ to represent various algebraic ‘polynomials’, and certain tiles are matched to certain ‘terms’. • We have to start by defining and naming the various ‘terms’ that we will be working with.

  3. What is a ‘term’? • A term is any number or variable or both that can be separated from another term by a positive or negative sign. Eg. -7 or +2x or x2 • A term without any variables is called a constant. Eg. -12 or +25 or +2.5 • ‘x’ can be anything but ‘4’ will always be ‘4’…it’s constantly ‘4’ • The rest of our terms will then need to be described too…

  4. What is a ‘term’? • A term is any number or variable or both that can be separated from another term by a positive or negative sign. Eg. -7 or +2x or x2 • But what are the parts called? -3x2 the exponent the sign the variable(s) the coefficient

  5. Coefficient – the numerical factor of a term. Coefficient 3 and –5 are the numerical coefficients of these 2 terms.

  6. What is a ‘term’? • What is the ‘sign’, ‘coefficient’, ‘variable’ and ‘exponent’ of the following terms? • -25a4 • 7.4b3

  7. What is a ‘term’ vs an ‘polynomial’? • A term is any number or variable or both that can be separated from another term by a positive or negative sign. A term can contain more than one variable. Eg. -7 or +2xy or x2 • A polynomial is made up of ‘terms’ separated by positive or negative signs. Eg. • x2 +5x -7 (3 terms) • 2a +3 (2 terms) • -13 (1 term)

  8. How do we name polynomials? • If a polynomial has one term in it, it is called a monomial. Eg. +15 or -5ab or x2 • If a polynomial has two terms in it, it is called a binomial. Eg. 6a -3 or 3x2 +8 • If a polynomial has three terms in it, it is called a trinomial. Eg. -4d2 +10d -7

  9. MONOmial- has ONEterm Ex. 3x2 4x ½ bc 7x2y • BInomial- TWO terms Ex. 3x + 7 2y2 - y ½ z3 - 4zy

  10. What do you think an expression with 3 terms would be called? Ex. 3x2 + 7x - 6 1 - 4x - 3y2 • TRInomial – THREE terms An algebraic expression that contains a term with a variable in the denominator, such as or the square root of a variable such as is NOT a polynomial.

  11. How do we name polynomials? • So what would each of these be called? • (3f -7) • (2xyz2) • (-6.7x) • (12a -3b +7c)

  12. How do we name polynomials? • The degree of a polynomial is determined by the term with the largest exponent. • We prefer to write expressions in order. • So we would write (-a3 +3a +9 –4a6 +10a2) as: • -4a6 –a3 +102 +3a +9 descending

  13. Using algebra tiles • We can start out by using tiles to represent constants. • A tile represents +1. • A tile represents -1. • The reason for this is that the dimensions of the tile are 1 by 1 = 1. (zoomed in) 1 1

  14. Using algebra tiles • So we can represent the following constants with the following tiles: • +6 • -3

  15. Using algebra tiles • Now on to the variables: • A tile represents +x. • A tile represents –x. • The reason for this is that the dimensions of the tile are 1 by x = 1x. (zoomed in) 1 x

  16. Using algebra tiles • So we can represent the following terms with the following tiles: • +6x • -3a

  17. Using algebra tiles • A tile represents +x2. • A tile represents –x2. • The reason for this is that the dimensions of the tile are x by x = x2. x x

  18. Using algebra tiles • So we can represent the following terms with the following tiles: • +3x2 • -3a2

  19. Write the expression represented by these tiles: -2x 5 3x2 = 3x2 – 2x + 5

  20. Represent each polynomial using algebra tiles… a) –3x2 + 1 b) 6 – x c) 3x2 – x – 4 d) 5

  21. Assignment • Page 214: 5 - 9, 12, 13, 15, 16, then 11,

  22. Classify the following as monomials, binomials, trinomials or polynomials:

  23. Polynomials: A polynomial is one term or the sum of terms whose variables have whole number exponents. • A term is a number, a variable, or the product of numbers and variables.Terms are separated by signs (+, -). • A Constant is a number whose value doesn’t change.

  24. If there are 2 they represent 2x. • If there is a , it represents -1. • Together, they would represent the expression 2x-1

  25. Some expressions contain terms such as “x2”. • We use a large square to represent these. These can also be negative as well. x2 -x2

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