polynomials

Definition: an expression containing many terms EX:5,-bx,3x²+2x-b

Standard form= must be written in alphabetical order with the highest exponent first

EX: 3x+1+2x² → 2x²+3x+1 ( the 2 comes first because it has the highest exponent and then the 3x because it’s the next highest then 1 because it has no degree)

Degree(Exponent ^/ 1²)

• 0 = constant (Ex 1)

• 1 = linear (EX 1x)

• 2 = quadratic (EX 1x²)

• 3 = cubic (EX 1x³)

4 = quartic (EX 1x^4)

idk why it stoped working

Number of terms

• 1 = monomial

• 2 = binomial

• 3 = trinomial

• 4 = Polynomial

EX:

6-constant mononomial

2x-linear mononomial

7p+1-linear binomial

V²+2v-5 -quadratic trinomial

4a³-8 -cubic binomial

2m^4-7m²-5m+1 -quartic polynomial

If a polynomial has more than one term to decide what categories (constant/ linear/ quadratic/ cubic/ quartic) it fits in you always pick the highest exponent to determine it and number of terms determine the (mono/bi/tri/poly) part is pretty straightforward you count how many terms are in there polynomial

SOLVING(add/subtract) A POLYNOMIAL

To solve a polynomial you must know how to solve you average equation I learned this in 6-7th grade it’s like the cross out and add and divide to get x= 7 baloney and you need to know slope as well as how to add/ subtract

ADDITION EX

(X+5)+(4x-7)

First add x+4x =5x

Next add 5+-7=-2

Then put them together to get 5x-2( linear binomial)

SUBTRACTION EX

(4x²+5x) - (7x+3x² + 1)

First 4x²-3x² =1x²

Next 5x-7x = -2x

Last mash it together and put the one back into the equation 1x²-2x+1

And boom you did it

MULTIPLY BINOMIALS

For multiplying you need to know about foil not like aluminum foil F.O.I.L which stands for First, Outer, Inner, last

First Outer Inner Last

(A+B)(C+D)= ac+ad+bc+bd

Ex

(X+2)(x+4)

• X • X = X² F

• X • 4 = 4X O

• 2 • X = 2X I

• 2 • 4 = 8 L

X²+4X+2X+8 (simplify)→ X²+6X+8

DIVISION OF MONO & POLLYNOMIAL