Vocabulary

• Term– A term is the number of small expressions inside a big question  EX (4xy +6 – 5x) this expression would have 3 expressions, because there are 3 different parts 
• Coefficient– A coefficient is a number that goes before a variable in an algebraic question EX (4e + 6y) the coefficients in this expression would be the numbers 4, and 6
• Constant– A constant is a number without a variable in front of it, I like to refer to it as “the lonely number” because he has no friends in front of him EX  (37e – 14+2x -7) in this case the 14 would be considered a constant, because it doesn’t have a variable in front of it.
• Degree–  the degree of an algebraic question would be the exponent on a variable, and if there are more than one terms the degree would be the sum of all of the exponents together. EX  + the degree of this expression would equal 7, because it is only adding the exponents together
• monomial-  a monomial is a algebraic question consisting of  one term
• binomial- a binomial is an expression which has two terms
• trinomial- a trinomial is an algebraic question in which the expression includes three terms.

Algebraic questions + examples

ADDITION

Addition-  For addition of polynomials you may be asked to simplify an expression like ( 2x + 5y) + ( 3x – 2y) to solve this expression you can use the grouping method

Step 1) remove the brackets

2x + 5y + 3x – 2 y

Step 2) Grouping- group together the numbers with the same variable

2x + 3x +5y – 2y

Step 3) do the math to figure out the answer

2x + 3x +5y – 2y

= 5x + 3y

SUBTRACTION 

Subtraction – for the subtraction of polynomials you may be asked to simplify a question like (16x + 14) – ( + x – 9)

step 1) re-write the question without the use of brackets

16x + 14 – + x – 9

step 2) for the second term you need to change all of the numbers to their opposites, so if the number was originally a negative, it will be changes to a positive, and vise versa.

16x + 14 – – x +9

step 3) sort into variable groups

16x +14 – – x +9

=      16x -x       14+9

step 4) solve the expression

=

= 16x – x = 15x

= 14 + 9 = 23

FINAL SIMPLIFIED ANSWER 

• +15x +23

 

Brackets (Multiplication) 

Multiplication– for multiplication of polynomials you may be asked to simplify a question like this (5x – 2)( + 7a -2)

step 1) re-write your question without the brackets

5x – 2 + 7a – 2

Step 2) re-write using what you know about distribution, which is… you will take the 5x and multiply it with our trinomial, and do the same with the -2 so now you will have…

5x ( +7 – 2) -3( +7 – 2)

Step 3) the third step id to distribute our numbers

5x() =

5x(7)= 35

5x (-2)= -10

 

-2( + 7 -2)

= -2() = -20x

= -2(7)= -14

= -2 (-2)= 4

Step 3) merge like terms together

     35, -10, -14, 4= 15     -20x

FINAL SIMPLIFIED ANSWER 

• + 15 -20x

 

Division

Dividing polynomials- for division you may be asked to simplify a question like…  + 12x – 6

Step 1) divide all the numbers on top, with the 3 on the bottom                                                 3

+ 12x – 6

3

Start with / 3 = 5

12/3 = 4

6/3 = 2

Step 2) add the variables back in

+ 4x – 2

Step 3) add like terms… In this case we don’t have any like terms, but if you did you need to add them together