How to Add & Factor Polynomials

Mathematics can prove challenging for many people. Polynomials are expressions that you can add, subtract and multiply but not divide. They have constants, variables and exponents that are whole numbers. Being able to add and factor polynomials is a valuable skill. It makes a huge difference when working with graphs and doing algebra.

Instructions

Adding

1. Make sure the polynomials you want to add have the same variables. For example, if you need to add (3x^2+4x-6)+(x^2+4), adjust the second polynomial so it reads x^2+0x+4, since 0x is the same as 0.

2. Stack the polynomials above each other so the variables line up.

   3x^2 + 4x-6
   +x^2 + 0x+4

3. Add the constants for each variable that are alike through the problem. Make sure you account for signs, since subtracting six within the polynomial is the same as adding negative six when you add both polynomials together.

   3x^2 + 4x-6
   +x^2 + 0x+4

   =4x^2 +4x -2

Factoring

1. Pull out any common multiples from the polynomial. 2x^2+16x+30 has a common multiple of 2, so you can simplify it to 2(x^2+8x+15).

2. Multiply the first variable by the last constant. For 2(x^2+8x+15), multiply x^2 by 15 to get 15x^2.

3. Split the result from Step 2 to get two x variables that add up to the second variable in the problem: 15x^2= 3x*5x. 3x+5x=8x.

4. Bring down the first and last part of the polynomial: x^2+3x+5x+15

5. Group the first two variables together and the last variable with the constant:
   (x^2+3x)+(5x+15)

6. Pull out the common multiples: x^2+3x=x(x+3) and 5x+15=5(x+3)
   Notice how two of the groupings are the same. Add the common multiples for one of the factors, and the other factor is the grouping that is the same.
   (x+5)(x+3)

7. Remember the common multiple from Step 1. The factors for the polynomial are
   2(x+5)(x+3).

References

• Purplemath: Adding Polynomials
• Grade A Math Help.com: How to Factor Polynomials
• Math Is Fun: Polynomial

Resources

• Mathway