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Operations with Polynomials

1.Add the polynomials.

(x^3+4x^2+2x-3) + (-x^3-3x^2-3x+2)

2.Perform the indicated operation.
(2 - 3x + x^3) - (-1 - 4x + x^2)

3.Find the product .

-2ab*7a^5*b^4

4.Find the opposite of the polynomial.

-2r^2 - r + 3

5.Multiply:

(-4 - a)^2

6.Find the quotient and the remainder

(x^4-2x^2+3) / (x+1)

7.Simplify.

[4z(z^4)^4] / [24z^5(z^2)^3]

8.Write without negative exponents:

(3xy^2)^-1

Note:
Hello, please help me with the above. I want to be able to use them as samples to solve other problems so if you can show me step by step how it works it would great. Thanks so much for all your help.

Solution Preview

1.Add the polynomials.

(x^3+4x^2+2x-3) + (-x^3-3x^2-3x+2)

When you add polynomials, the most important thing to remember is to keep like terms (the same exponent) together.

(X^3+4x^2+2x-3)+ (-x^3-3x^2-3x+2)
1) Rewrite with like terms together: (x^3 + -x^3) + (4x^2+-3x^2)+(2x+-3x)+(-3+2)
2) Perform the addition: (0)+(x^2)+(-x)+(-1)
3) Simplify to eliminate parentheses: x^2-x-1

2.Perform the indicated operation.
(2 - 3x + x^3) - (-1 - 4x + x^2)

This is the same as number 1; the only difference is that since it is subtraction you need to remember to use the opposite signs.
1) Rewrite with like terms together: ...

Solution Summary

Here are several worked-out answers for adding, subtracting, multiplying, dividing polynomials.

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