Adding Polynomials

Once you know how to simplify polynomials, adding them is very easy. You simply combine any like terms from both polynomials.

For example: (9x2-2x+3)+ (4x2+5x-8)

The parenthesis are not serving any function except to make the problem easier to read, so we can ignore them. : 9x2-2x+3 + 4x2+5x-8

Next, we need to identify which terms are like terms (remember, that means they have the same variables with the same exponents). Let's color them: 9x2-2x+3 + 4x2+5x-8

Now, add each set of like terms to get 13x2+3x-5

There are no more like terms, so what we have to do is make sure the polynomial is in standard form (highest exponent first then descending order and ending with the constant). It is, so we are finished. Final answer: 13x2+3x-5

No matter how many terms each polynomial has, you simply need to combine any like terms. Terms that cannot be combined are just brought down into the answer.

For example: (3y2-5y+10)+(4y2-8).

We only have two like terms to combine so we do that: 7y2+2. But we cannot forget to bring down the -5y as well. Thus, we get 7y2+2-5y.

There are no more like terms to combine, but this is not in standard form. Arrange your final answer in standard form: 7y2-5y+2

Practice: Add the polynomials

1) (6x2-5x+8)+(-2x2+3x-1)
2) (3y-11)+(y2-5y+1)
3) (x+5)+(3x-11)
4) (3y4-2y2+6y-8)+(y4-3y3+4y2-8y+3)
5) (4a2-9a-1)+(2a2+3a)+(4a2-7a+6)

Answers: 1) 4x2-2x+7 2) 4y2-2y-10 3) 4x-6 4) 4y4-3y3+2y2-2y-5 5) 10a2-13a+5

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