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CLassifying Polynomials
Adding Polynomials
2x
3
3 x 4 x 3 x 5 x 2 x 7 2
3
2
Stack the polynomials
2 x 3x 4 x 3 3
2
x 5x 2 x 7 3
2
Combine Like Terms (Same Variable and Same Exponent)
2 x 3x 4 x 3 3
2
x 5x 2 x 7 3
2
3x 2 x 6 x 4 3
2
subtracting Polynomials
x
3
2 x 6 x 2 2 x 4 x x 4 2
3
2
Subtraction is the same as adding the opposite so change each sign in the second polynomial.
x
3
2 x 6 x 2 2 x 4 x x 4
x
3
2x 6x 2 2x 4x x 4
2
3
2
3
2
2
Now stack them and add.
x3 2 x 2 6 x 2 +2 x 4 x x 4 3
2
x 2 x 5x 2 3
2
Multiplying by a monomial 4 x 2 x 3x 1 2
2
Use the Distributive Property and multiply the monomial times each term in the parentheses.
4 x 2 x 3x 1 2
2
4 x 2 x ) 4 x (3x) 4 x (1 2
2
2
2
Multiply the coefficents and add the exponents.
8x 12x 4x 4
3
2
Multiplying Polynomials FOIL
2x 3 4x 5 Multiply
First terms Outer terms Inner terms Last terms
2 x(4 x) 2 x(5) 3(4 x) 3(5) 8 x 2 10 x 12 x 15 8 x 2 2 x 15 Remember to combine the like terms.
Factoring the GCF Find the largest number that will divide each of the terms. Also find the most common factors for each variable .
8 x 16 x 12 x 4
3
2
4x (2 x 4 x 3) 2
2
Multiply and see if you get what you started with. Be sure you have no common factors in the answer.
Factoring polynomials
x
2
3x 10
Find 2 numbers that multiply to be the last number and add to be the middle number.
The numbers are -5 and 2
x
2
3x 10
( x 5)( x 2) Always be careful that the signs are correct.
Factoring Difference of Squares
4x 9 2
Find what squared is the first term and what squared is the second term
(2 x) 4 x 2
2
and (3) 9 2
so
4x 9 2
(2 x 3)(2 x 3)
I hope this review helps. I know you will
ON THE TEST!