- This document discusses working with polynomials, including defining terms, writing polynomials, simplifying polynomials, adding and subtracting polynomials, multiplying polynomials using the FOIL method, and providing examples of each. - Key aspects of polynomials include terms consisting of a variable and its exponent and coefficient, writing polynomials in order of decreasing power with the leading and constant terms defined, and combining like terms when simplifying, adding, or subtracting polynomials. - To multiply polynomials, the FOIL method is used, which involves multiplying the First, Outer, Inner, and Last terms of binomial expressions.

1. -Elliott Brown Working With Polynomials

2. The Sum of Terms Terms Consist of A variable it’s exponent It’s coefficient Example: 3x2 What is a Polynomial?

3. In order of decreasing power Example: x5+3x4+x+2 Leading term=term of highest degree x5+x+2 Constant term=final term of degree zero x5+x+2 Writing Polynomials

4. Monomials: 2x Binomials: x+2 Trinomials: x2+x+2 Different Polynomials

5. Always simplify polynomials Combine like terms 2x+6x=8x 5x2+7x2=12x2 3x4+x+7x4-6x=10x4-5x Simplifying Polynomials

6. Combine like terms (just like simplifying) Example: (4x2-3x+7)+(2x2+6x-4) =4x2-3x+7+2x2+6x-4 =6x2+3x+3 Adding polynomials

7. Combine like terms… However remember order of operations Example: (3x2+7x+2)-(-2x2+4x+2) =3x2+7x+2+2x2-4x-2 =5x2+3x Subtracting polynomials

8. (x3+x-3)+(x3-x2-2x) (5x6-4x3+x+7)-(8x6-7x4+3x3-x+3) (3x5+7)+(4x2+x-6) (3x5+4x3+5x)-(-6x5-3x3+3x) More practice

9. (x3+x-3)+(x3-x2-2x) =2x3-x2-x-3 (5x6-4x3+x+7)-(8x6-7x4+3x3-x+3) =5x6-4x3+x+7-8x6+7x4-3x3+x-3 =-3x6+7x4-7x3+2x+4 solutions

10. (3x5+7)+(4x2+x-6) =3x5+4x2+x+1 (3x5+4x3+5x)-(-6x5-3x3+3x) =3x5+4x3+5x+6x5+3x3-3x =9x5+7x3+2x solutions

11. Multiply coefficients Add exponents (7x2)(-3x)=-21x3 Multiplying monomials

12. Monomial x Trinomial (2x2)(3x2+x-7) Distribute single term polynomial 6x4+2x3-14x2 Multiplying Polynomials

13. (x+2)(x+5) (x+2)(x)+(x+2)(5) x(x)+2(x)+x(5)+2(5) x2+2x+5x+10 x2+7x+10 Multiplying Binomials

14. (x+3)(x2+2x+2) (x+3)(x2)+(x+3)(2x)+(x+3)(2) x3+3x2+2x2+6x+2x+6 x3+5x2+8x+6 Binomials x Trinomials

15. Only used for multiplying two binomials (x+2)(x+5) Order of multiplying terms First Outer Inner Last Foil method

16. (x+2)(x+5) First: (x)(x)=x2 Outer: (x)(5)=5x Inner: (2)(x)=2x Last: (2)(5)=10 (x+2)(x+5)=x2+5x+2x+10 =x2+7x+10 Foil method