### About Adding Polynomials:

When we first encounter polynomials, we begin with addition and subtraction. We can add or subtract two or more polynomials by combining like terms. Recall that like terms are terms that have the same variable(s) raised to the same power(s).

Test Objectives

- Demonstrate an understanding of the definition of a polynomial
- Demonstrate the ability to add two or more polynomials
- Demonstrate the ability to subtract two polynomials

#1:

Instructions: Perform each indicated operation.

a) (k^{3} - 2k^{2}) - (4k^{3} - 2k)

b) (3p^{3} - 5) - (3p^{3} + 4)

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#2:

Instructions: Perform each indicated operation.

a) (5x + 3) + (1 + 3x)

b) (3n^{3} + 9n^{2} + 14) + (-4 + 12n^{4} - 12n^{2})

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#3:

Instructions: Perform each indicated operation.

a) (7m^{5} + 6m^{3} + 14m^{4}) + (-3m^{5} + 9m^{4} - 11m^{3})

b) (5b^{3} - 14b^{2} - 6b) + (3b + 6b^{2} + 7b^{3})

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#4:

Instructions: Perform each indicated operation.

a) (-4x^{4}y + 10xy^{4}) - (-2xy^{2} - 12x^{2} - 4x^{4}y - 14xy^{4}) - (14x^{2} - 9x^{4}y)

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#5:

Instructions: Perform each indicated operation.

a) (x^{3}y^{4} - 7) - (6x^{3}y^{5} - 11 + 10y^{5} - 5x^{2}y^{2}) - (-9x^{3}y^{4} + 11y^{5})

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Written Solutions:

#1:

Solutions:

a) -3k^{3} - 2k^{2} + 2k

b) -9

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#2:

Solutions:

a) 8x + 4

b) 12n^{4} + 3n^{3} - 3n^{2} + 10

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#3:

Solutions:

a) 4m^{5} + 23m^{4} - 5m^{3}

b) 12b^{3} - 8b^{2} - 3b

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#4:

Solutions:

a) 9x^{4}y + 24xy^{4} + 2xy^{2} - 2x^{2}

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#5:

Solutions:

a) -6x^{3}y^{5} + 10x^{3}y^{4} - 21y^{5} + 5x^{2}y^{2} + 4