Question

How do you add and subtract polynomials?

Answer 1

In either case, you combine "like terms." This means: combine all terms that have x^2 in them, all terms that have x in them, all constants, and so on.
Invent or borrow a few examples and try working through them; I'd be glad to give you some follow-up attention.

Answer 2

Thanks!!

Answer 3

Examples:
1. Add the polynomials \(x^2 + 2x + 5\) and \(x^3 + 5x^2 - 3\).

Solution: You can only add like terms. Like terms are terms that have the same variable part. (Same variables with same exponents.)

\( (x^2 + 2x + 5 ) + (x^3 + 5x^2 - 3 ) \)

Since this is an addition, the parentheses are not needed, so just drop them.

\(= x^2 + 2x + 5 + x^3 + 5x^2 - 3 \)

Now add like terms. I will first group like terms together to make it easier to seeit. You can skip this step.

\( = x^3+ (x^2 + 5x^2) + 2x + (5 - 3) \)

\(= x^3 + 6x^2 + 2x + 2\)

This is the final answer.

Answer 4

2. Subtract the polynomials \((x^2 + 2x + 5)\) - \((x^3 + 5x^2 - 3)\).

Solution:
The parentheses around the first polynomial are unnecessary and can be dropped.
Since there is a negative sign to the left of the second polynomial, to get rid of the second set of parentheses, all signs inside the second set of parentheses change.

\(= x^2 + 2x + 5 - x^3 - 5x^2 + 3\)

Now you combine like terms like we did in the previous example.

\(= -x^3 -4x^2 + 2x + 8\)

This is the final answer.