polynomials lesson 3.3 factoring. polynomials a math equation consisting of one to many terms....
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POLYNOMIALS
A math equation consisting of one to many terms.
Examples:
6, x, 6x, -1/2xy, 2y + x, x2 – 5x - 9
Polynomials cannot have a variable as a denominator nor negative exponents.
Polynomials with • one term are called monomials5x3, 8, x2, etc• two terms are called binomials3x – 1, 2x2 + 8, etc• three terms are called trinomials2x2 – 4x + 9
• Variables – a letter that represents one or more numbers
4y = y is the variable• Coefficient – number in front
of a variable4y = coefficient is 4
DEGREES OF A POLYNOMIAL
The degree of a polynomial is the degree of the term with the highest exponent.
Constant term: term without a variable.
2x – 1 = degree of 1 Constant term of -1 These are called a linear.
2x2 + 8 = degree of 2 Constant term of 8 These are called quadratic.
2x3 – 5 = degree of 3 Constant term of -5 These are called cubic.
ADDING AND SUBTRACTING POLYNOMIALS
Find like terms and combine them in order to simplify polynomials.
4x – 2x2 + 3 – 6x2 + 5 – x
FACTORING LINEAR POLYNOMIALS
Just as natural numbers can be factored so can polynomials.
Find the GCF in each term and then factor.
FACTORING TRINOMIALSax2 + bx + c
5 – 10z – 5z2
Find the GCF of all three terms. In this example the GCF is 5.
Factor out a 5 from each and write as a product.
5 ( 1 – 2z – z2)
FACTORING WITH MORE THAN ONE VARIABLE
Find all GCF’s, numbers and letters.
-12 x3y – 20xy2 – 16x2y2
GCF for numbers = 4GCF for letters = 1x and 1y
4xy (-3x2 – 5y – 4xy)