Polynomials Honors Math – Grade 8. Explore Find the area of the figure. The total area is the area of the rectangle plus the area of the triangle. 5x.

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Presentation transcript:

Polynomials Honors Math – Grade 8

Explore Find the area of the figure. The total area is the area of the rectangle plus the area of the triangle. 5x 8x x2x2 Rectangle FormulaTriangle Formula This represents the total area of the figure.

Poly-what? Polynomial a monomial or sum of monomials Examples: 2x 2 + 3x – 1 15a 2 b – c 2 Non-example: Made up of monomials called terms Terms are combined by addition. Polynomials with two terms are binomials and those with three terms are trinomials.

Identify Polynomials State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial or trinomial. ExpressionPolynomial?Identification? YES. 2x – 3yz = 2x+(-3yz), the sum of two monomials. NO. Not a monomial YES. -8 is a real number and all are monomials. YES. The expression simplifies to 4a 2 + 6a + 9, so it is the sum of three monomials. Binomial None Monomial Trinomial

Write a Polynomial GEOMETRY Write a polynomial to represent the area of the shaded region. c b The area of the shaded region is the area of the rectangle minus the area of the circle. The length of the rectangle is b. The width of the rectangle is 2c. The radius of the circle is c. The polynomial representing the area of the shaded region is:

The degree of a monomial is the sum of the exponents of all its variables. MonomialDegree = =8

PolynomialTermsDegree of eachDegree of poly 33 4, 2, 04 1,2,3,03 2,1,02 The degree of a polynomial is the greatest degree of any term in the polynomial. 2,4 4

Arrange Polynomials in Ascending Order Arrange the terms of each polynomial so that the powers of x are in ascending order. The terms of a polynomial are usually arranged so that the powers of one variable are in ascending (increasing) order or descending (decreasing) order. Compare powers of x. 0 < 2 < 4 Compare powers of x. 0 < 1 < 2 < 3 x 0 = 1 x 0 = 1 and x = x 1

Arrange Polynomials in Descending Order Arrange the terms of each polynomial so that the powers of x are in ascending order. Compare powers of x. 3 > 2 > 1 > 0 Compare powers of x. 5 > 2 > 1 > 0 x 0 = 1 x 0 = 1 and x = x 1