### About Adding and Subtracting Polynomials:

When we add polynomials, we are simply combining like terms. Like terms are terms that have the exact same variable parts raised to the exact same powers. We can combine like terms using the distributive property: 5x + 2x = x(5 + 2) = 7x. When we subtract with polynomials, we change the operation to addition of the opposite.

Test Objectives

- Demonstrate the ability to find the degree of a polynomial
- Demonstrate the ability to add two or more polynomials together
- Demonstrate the ability to subtract polynomials

#1:

Instructions: Give the degree and type of polynomial.

a) 10n

b) -4n^{7}x^{3} + 9nx - 4

c) -12x^{3}y^{7}z^{4}

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#2:

Instructions: Perform each indicated operation.

a) (n^{5} + n + 4 + n^{4}) - (6 + 2n - 6n^{4} + 7n^{5}) - (4n^{4} - 8n^{3} + 8n - 6)

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#3:

Instructions: Perform each indicated operation.

a) (2n^{5} + 5n^{3} - 4n^{4} + 5n^{2}) - (2n^{5} + 8n^{3} - n^{2} - 3) - (8n^{3} - 3n^{2} - 5 - 4n^{4})

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#4:

Instructions: Perform each indicated operation.

a) (9x^{3}y^{2} - x^{5}y^{3} - 6x^{5}y^{2} + 7x^{4}y^{4}) + (4x^{4}y^{4} - x^{5}y^{3} + 5x^{5} + 7x^{3}y^{2}) - (9x^{5}y^{2} - 4x^{4} y^{4} + 7x^{3}y^{2} + x^{5})

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#5:

Instructions: Perform each indicated operation.

a) (8x^{5} - 7x^{5}y^{4} - 4x^{3}y^{5}) + (x^{3} - 4x^{5} + 6x) + (10x^{5}y^{4} - 8x^{3}y^{5} - 8x^{3})

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Written Solutions:

#1:

Solutions:

a) Degree is 1, monomial

b) Degree is 10, trinomial

c) Degree is 14, monomial

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#2:

Solutions:

a) -6n^{5} + 3n^{4} + 8n^{3} - 9n + 4

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#3:

Solutions:

a) -11n^{3} + 9n^{2} + 8

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#4:

Solutions:

a) 15x^{4}y^{4} - 2x^{5}y^{3} - 15x^{5}y^{2} + 9x^{3}y^{2} + 4x^{5}

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#5:

Solutions:

a) 3x^{5}y^{4} - 12x^{3}y^{5} + 4x^{5} - 7x^{3} + 6x