Adding and Subtracting Polynomials

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

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

•  $-9x^2+4x$  

•  $x^2-6x$  

•  $14x^3y^2+x^2-6x$  

•  $14x^3y^2+19x^2-6x$