Simplifying, 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

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

• -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.

• x³-3x²+5x-7x³-5x²+12

• Step 2: Combine Like Terms

• -6x³-8x²+5x+12

Multiple Choice

Simplify (-4m³-m+9)-(4m²+m-12)

• -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