Adding and Subtracting Polynomials

Adding and Subtracting Polynomials

I can add and subtract polynomials by using the distributive property and combining like terms.

What is a polynomial?

• The root poly means many: polygon-many sides is another example we have seen.

• A polynomial is a mathematical expression with many terms

Naming Polynomials

This isn't too important to memorize, but we will use some of this vocabulary such as binomial and trinomial in the future.

The degree is the highest exponent in the polynomial.

Multiple Choice

Classify by number of terms:

3x² – 8x + 1

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Multiple Choice

Classify by number of terms:
9x

• Monomial
• Binomial
• Trinomial
• 4-Term Polynomial

Multiple Choice

Classify by number of terms:

3x³ – 6x

• Monomial

• Binomial

• Trinomial

• 4-Term Polynomial

Adding and Subtracting Polynomials

• Step 1: Distribute the "1s" to eliminate the parentheses.

• Step 2: Combine like terms

  • like terms have the same variables and same powers

    • 2x² and -5x² are like terms

    • -3x⁴ and -3x⁷ are NOT like terms

    • -6xy² and 13xy² are like terms

    • -4x²y and 10xy² are NOT like terms

Ex 1: (-7.1x²-180x+5800)+(21x²-140x+1900)

• Since the number in front of both sets of parentheses is 1, this eliminates the parentheses

  • The parentheses mean nothing when the sign between them is addition.

    • -7.1x²-180x+5800+21x²-140x+1900

• Combine like terms

  • 13.9x²-320x+7700

Ex 2: (x³-3x²+5x)-(7x³+5x²-12)

• Step 1: Notice there is a -1 in front of the 2nd set of parentheses. This changes the signs of the second polynomial. *Distribute the negative/subtraction sign into the second set of parentheses.

  • x³-3x²+5x-7x³-5x²+12

• Step 2: Combine Like Terms

  • -6x³-8x²+5x+12

Multiple Choice

Simplify (-4m³ - m + 9) - (4m² + m - 12)

** Don't forget to distribute the negative/subtraction sign. **

• -4m³-4m²-2m-21

• -4m³-4m²-2m+21

• -8m³-2m+21

• -4m³+4m²+2m+21

Multiple Choice

Simplify (8xy² + 6xy) + (-12x²y + 13xy²)

• 21xy² +12x²y+6xy

• 21xy² -12x²y-6xy

• 21xy² +12x²y-6xy

• 21xy² -12x²y+6xy

Multiple Choice

• 3x³ +8x

• x³+3x² +8x

• 2x² +8x

• x³-3x³ +8x²

Multiple Choice

• 4g²-2g

• 4g²+4g-6

• 6g²+2g+6

• 4g²+2g

Multiple Choice

• 3n²+4n

• -3n²+4n

• 3n²+20n

• 3n²-4n

Multiple Choice

• 3y⁴+3y³+7y²+4y

• 3y⁴+3y³+7y²+4y+6

• 3y⁴+3y³+7y²+6^

• 3y⁴+3y³+7y²+4y-6^

Multiple Choice

• 4w²-11w

• 2w²-11w

• 2w²+11w

• 4w²+w

Multiple Choice

• 2x²-13x-7

• 2x²+13x+7

• -2x²-13x-7

• -2x²+13x-7