Adding and Subtracting Polynomials

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.

Multiple Choice

Which are like terms?

• $$3x^2y^3\ \ and\ -5x^2y^2$$

• $$2x^3y^4\ \ and\ \ -3x^3y^4$$

• $$5x^2y^2\ \ and\ \ 5x^3y^3$$

• $$2xy\ \ and\ \ 5ab$$

Multiple Choice

$$Add\ the\ following:\ \ 3x^2y^4\ +\ 7x^2y^4$$  

• $$10x^4y^8$$  

• $$21x^2y^4$$  

• $$21x^4y^8$$  

• $$10x^2y^4$$  

Adding Polynomials is the same as combining like terms.

• Find like terms and add their coefficients.

Example: (3x² + 5x - 8) + (7x² - 8x + 12)

• 3x² + 5x - 8 + 7x² - 8x + 12

• 3x² + 7x² + 5x - 8x - 8 + 12

• Final Answer: 10x² - 3x + 4

Multiple Choice

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

• $$5x^3-3x^2+4x$$  

• $$13x^3-13x^2+4x$$  

• $$13x^3-3x^2+4x$$  

• $$14x^6$$  

Multiple Choice

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

• $$-7k^4-11k^2+6$$  

• $$12k^4-11k^2+6$$  

• $$-7k^4+0-5k^2$$  

• $$-7k^4-11k+2$$  

Multiple Choice

$$Add:\ \ \left(9r^3+5r^2+11r\right)+\left(-2r^3+9r-8r^2\right)$$  

• $$21r^3+20r$$  

• $$7r^3+14r^2+3r$$  

• $$11r^3-3r^2+20r$$  

• $$7r^3-3r^2+20r$$  

Subtracting Polynomials

• Drop the first set of parentheses.

• Distribute the negative for the second set of parentheses.

• Combine like terms.

Example: (5x³ - 2x² + 4x) - (8x³ + 3x² - 8x)

• 5x³ - 2x² + 4x - 8x³ - 3x² + 8x

• 5x³ - 8x³ - 2x² - 3x² + 4x + 8x

• Final Answer: -3x³ - 5x² + 12x

Multiple Choice

$$Subtract:\ \ \left(3r^4+4r^3\right)-\left(r^4-5r^3\right)$$  

• $$2r^4-r^3$$  

• $$2r^4-5r^3$$  

• $$2r^4+9r^3$$  

• $$11r^7$$  

Multiple Choice

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

• $$10x^4-10x^3-x^2-20x$$  

• $$2x^4-10x^3-x^2-20x$$  

• $$2x^4-x^2-20x$$  

• $$2x^4-20x$$  

Multiple Choice

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

• $$-17a^5-23a^2-11a$$  

• $$15a^5-23a^2+11a$$  

• $$27a^7-11a$$  

• $$5a^5+23a^2-11a$$  

Multiple Choice

$$Subtract.\ \ \left(4x^2+7x^3y^2\right)-\left(-6x^2-7x^3y^2-4x\right)-\left(10x+9x^2\right)$$  

• $$-9x^2+4x$$  

• $$x^2-6x$$  

• $$14x^3y^2+x^2-6x$$  

• $$14x^3y^2+19x^2-6x$$  

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

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3

• 4y² + 3y³ - y + 3

• -y⁴ + 2y³ -y - 4

• 4y³ + 3y² -3y + 1

Multiple Choice

Find the difference. 
(3- 2x + 2x²) - (4x -5 +3x²)

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Multiple Choice

Add the polynomials.
(2x + 5y) + (3x - 2y)

• 3x + 5y

• 5x + 3y

• 5x + 7y

• 7xy + 1xy

Multiple Choice

Simplify the expression.
(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3 

• -7n² - 8n + 3 

• -6n² - 8n + 3

• -7n² - 4n + 3