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

What is a coefficient?

• The number in front of a variable.

• The exponent of a variable.

• A constant.

• A variable.

Multiple Choice

What are like terms?

• The same coefficients.

• The same variables with different exponents.

• Terms with the same variable and exponents combination.

• Different variables with same exponents.

Two monomials

x+y

3-a²

2x+4y​

​Binomial:

​Monomial:

Fractions are NOT monomials!

​Trinomial:

Three monomials

x+y+z

3+a-b

2x²-4y​+5z

​Polynomial:

Multiple Choice

$$4y-5xz$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$x^3-10x+1$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$5x$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$5x$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Multiple Choice

$$6x^3+4x+y+3$$  

• Monomial

• Binomial

• Trinomial

• Polynomial

Match

Match the following:

• Monomial

• Binomial

• Trinomial

• Polynomial

( )

()

()

( )

• ( $$-2x$$ )

• ( $$3x^2+7$$ )

• ( $$5x^2+7x-10$$ )

• ( $$8x^4+7x^2+3x-9$$ )

9+5x²+x⁴-3x³+x-2x⁶

Put this polynomial in standard form:

​4x⁴+2x+3

Standard Form: terms in order from greatest to least degree

​3y³-y²+12y

​y⁸+8y³+2y²-y+7

Adding Polynomials is the same as combining like terms.

• Find like terms and add their coefficients.

Make a Real World Connection

• Look at each term and think of a real-world application

• RULE - Add the coefficients when the bases are the same. Keep the base.

• REMEMBER, the variables must have the same exponent!

• Rewrite all terms that can not be combined

Multiple Choice

(4x³-5x²+3x)+(-2x³-x²+6x)

• 2x³-6x²-9x
• 2x³+6x²+9x
• -2x³-6x²+9x
• 2x³-6x²+9x

Multiple Choice

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

• 2x² + 3x +1
• -2x² - 11x -4
• 2x² + 5x -7
• -2x² + 11x -4

Multiple Choice

$$Add:\ (9x^3+5x^2−3x)+(4x^3−8x^2+7x)$$  

• undefined

• undefined 

• undefined 

• undefined 

Multiple Choice

$$Add:\ \ \left(-4k^4+14+3k^2\right)+\left(-3k^4-14k^2-8\right)$$  

•  

  undefined

•  

  undefined 

• undefined 

• undefined 

Multiple Choice

$$Subtract:(3r^4+4r^3)−(r^4−5r^3)$$  

• undefined 

• undefined 

• undefined

• undefined 

Multiple Choice

$$Subtract:\ \ \left(13a^2-6a^5-2a\right)-\left(-10a^2-11a^5+9a\right)$$  

•  

  undefined

• undefined 

• undefined 

• undefined 

Multiple Choice

$$Subtract:\ \ \left(6x^4-5x^3+2x^2-8x\right)\ -\ \left(4x^4+5x^3+3x^2+12x\right)$$  

•  

  undefined

• undefined 

• undefined 

• undefined 

Multiple Choice

(3x + 4y - 3z) - (2x - 6y + 7z)

• x + 10y - 10z
• -x +10y - 10z
• x -10y - 10z
• -x -10y - 10z