Operations with Polynomials Review

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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!