8 1 ADDING AND SUBTRACTING POLYNOMIALS Goals Add

8 -1 ADDING AND SUBTRACTING POLYNOMIALS Goals: • Add and subtract polynomials. Eligible Content: • A 1. 1. 1. 5. 1

VOCABULARY � Polynomial – a mathematical expression consisting of a sum of terms. Each term is the product of a constant and one or more variables raised to a positive or zero power. � Examples:

VOCABULARY � Standard Form – the terms are in descending order of exponents.

VOCABULARY � Degree – the largest exponent in the polynomial.

VOCABULARY � Constant � Linear – degree is zero. – degree is one. � Quadratic � Cubic – degree is two. – degree is three. � Quartic – degree is four.

VOCABULARY � Leading coefficient – the coefficient of the first term when the polynomial is in standard form.

VOCABULARY � Monomial � Binomial � Trinomial � Anything – polynomial with one term. – polynomial with two terms. – polynomial with three terms. bigger – polynomial

EXAMPLES Give the degree and classify the polynomial by degree and number of terms. Ø 0, constant, monomial 1. -5 Ø 1, linear, monomial 2. ¼ x Ø 1, linear, binomial 3. -9 x+2 Ø 2, quadratic, binomial 4. x 2 – 6 Ø 3, cubic, trinomial 5. -x 3 +2 x + 1 6. 3 x 4 +2 x 3 – x 2 +5 x – 8 Ø 4, quartic, polynomial

ADDITION � Add like terms! � Put your answer in Standard Form!!

EXAMPLES 1. 2.

Find (3 x 2 + 2 x – 1) + (– 5 x 2 + 3 x + 4). A. – 2 x 2 + 5 x + 3 B. 8 x 2 + 6 x – 4 C. 2 x 2 + 5 x + 4 D. – 15 x 2 + 6 x – 4

Find (4 x 3 + 2 x 2 – x + 2) + (3 x 2 + 4 x – 8). A. 5 x 2 + 3 x – 6 B. 4 x 3 + 5 x 2 + 3 x – 6 C. 7 x 3 + 5 x 2 + 3 x – 6 D. 7 x 3 + 6 x 2 + 3 x – 6

SUBTRACTION � Distribute the negative sign! � Add like terms and put your answer in Standard Form!!

EXAMPLES 1. 2.

Find (3 x 3 + 2 x 2 – x 4) – (x 2 + 5 x 3 – 2 x 4). A. 2 x 2 + 7 x 3 – 3 x 4 B. x 4 – 2 x 3 + x 2 C. x 2 + 8 x 3 – 3 x 4 D. 3 x 4 + 2 x 3 + x 2

Find (8 y 4 + 3 y 2 – 2) – (6 y 4 + 5 y 3 + 9). A. 2 y 4 – 2 y 2 – 11 B. 2 y 4 + 5 y 3 + 3 y 2 – 11 C. 2 y 4 – 5 y 3 + 3 y 2 – 11 D. 2 y 4 – 5 y 3 + 3 y 2 + 7

PRACTICE � Page 468 #1 -18

HOMEWORK � Pages 468 -469 #20 – 42 even