POLYNOMIALS

LESSON 3

.3 FA

CTORIN

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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.

Are the following polynomials?7/a¼ xy – 103pq1/2

√7 x4 – x3

8-2

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.

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)

Work on Handout

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 + 12GCF = 4

= 4 (m + 3)

6 – 15aGCF = 3

= 3 (2 – 5a)

TRY THE FOLLOWING

6n + 9 =

6c + 4c2 =

3g + 6 =

8d + 12d2 =

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)

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 = 4GCF for letters = 1x and 1y

4xy (-3x2 – 5y – 4xy)

5ab2 + 10a2b3 – 15a2b4

- 20c4d - 30c3d2 – 25cd

Work on textbook questions # 6, 7, 8, 9, 10, 14.