230 likes | 401 Views
Polynomials. Lesson 3.3 Factoring. Polynomials. A math equation consisting of one to many terms. Examples: 6, x , 6x, -1/2xy , 2y + x, x 2 – 5x - 9 Polynomials cannot have a variable as a denominator nor negative exponents. Are the following polynomials? 7/a ¼ xy – 10
E N D
Polynomials Lesson 3.3 Factoring
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.
Are the following polynomials? • 7/a • ¼ xy – 10 • 3pq1/2 • √7 x4 – x3 • 8-2
Polynomials with • one term are called monomials • 5x3, 8, x2, etc • two terms are called binomials • 3x – 1, 2x2 + 8, etc • three terms are called trinomials • 2x2 – 4x + 9
Variables – a letter that represents one or more numbers • 4y = y is the variable • Coefficient – number in front of a variable • 4y = 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.
Example 1 • State the degree, coefficient’s and constant term of the polynomial. • 5x3 + x2 – 7x + 9
Example 2 • State the degree, coefficient and constant term of the polynomial. • 6a – 4a2 - 3
Adding and Subtracting polynomials • Find like terms and combine them in order to simplify polynomials. • 4x – 2x2 + 3 – 6x2 + 5 – x
Try the following • a2b – ab2 + 4a3b – 7ab2 + 5a2b • (3a – 4b + c) + (3b – 5c – 3a)
Be Careful with subtraction • (4x2 – 9x + 6) – (2x2 – 3x – 1)
Factoring Linear polynomials • Just as natural numbers can be factored so can polynomials. • Find the GCF in each term and then factor.
Factoring Examples • 4m + 12 • GCF = 4 • = 4 (m + 3)
6 – 15a • GCF = 3 • = 3 (2 – 5a)
Try the following • 6n + 9 = • 6c + 4c2 = • 3g + 6 = • 8d + 12d2 =
Factoring Trinomials • ax2 + 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)
Examples • 18a2 – 12a + 6 • 9 + 27x – 45x2
Factoring with more than one variable • Find all GCF’s, numbers and letters. • -12 x3y – 20xy2 – 16x2y2 • GCF for numbers = 4 • GCF for letters = 1x and 1y • 4xy (-3x2 – 5y – 4xy)