Combine like terms for:
4x3 - 9x2 + 7y - 9z + w - f + 6
Evaluate the x3 terms:
4x3 ← There is only one x3 term
Evaluate the x2 terms:
-9x2 ← There is only one x2 term
Evaluate the y terms:
7y ← There is only one y term
Evaluate the z terms:
-9z ← There is only one z term
Evaluate the w terms:
w ← There is only one w term
Evaluate the f terms:
-f ← There is only one f term
Evaluate the constants:
6 ← There is only one constant
Combine like terms
4x3 - 9x2 + 7y - 9z + w - f + 6
Analyze the 7 terms of the polynomial 4x3 - 9x2 + 7y - 9z + w - f + 6
Analyze Term 1
Term 1 is 4x3
Our coefficient/constant is 4
Our variable piece is x
Raise our variable to the power of 3
Analyze Term 2
Term 2 is -9x2
Our coefficient/constant is -9
Our variable piece is x
Raise our variable to the power of 2
Analyze Term 3
Term 3 is 7y
Our coefficient/constant is 7
Our variable piece is y
No exponent exists for this term
Analyze Term 4
Term 4 is -9z
Our coefficient/constant is -9
Our variable piece is z
No exponent exists for this term
Analyze Term 5
Term 5 is w
Since there is no coefficient
our coefficient is 1
Our variable piece is w
No exponent exists for this term
Analyze Term 6
Term 6 is -f
Since our term starts with a minus sign
our coefficient is -1
Our variable piece is f
No exponent exists for this term
Analyze Term 7
Term 7 is 6
Our coefficient/constant is 6
This term has no variable, so it is a constant
No exponent exists for this term
Determine the Degree of the Polynomial:
Highest exponent for x = 3
Common Core State Standards In This Lesson
What is the Answer?
Our variable piece is x
Raise our variable to the power of 3
Our coefficient/constant is -9
Our variable piece is x
Raise our variable to the power of 2
Our coefficient/constant is 7
Our variable piece is y
No exponent exists for this term
Our coefficient/constant is -9
Our variable piece is z
No exponent exists for this term
Since there is no coefficient
our coefficient is 1
Our variable piece is w
No exponent exists for this term
Since our term starts with a minus sign
our coefficient is -1
Our variable piece is f
No exponent exists for this term
Our coefficient/constant is 6
This term has no variable, so it is a constant
No exponent exists for this term
How does the Polynomial Calculator work?
It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.
This calculator has 1 input.
What 2 formulas are used for the Polynomial Calculator?
Variables can be any letter but e or i.
What 6 concepts are covered in the Polynomial Calculator?
- constant
- a value that always assumes the same value independent of how its parameters are varied
- exponent
- The power to raise a number
- expression
- finite combination of symbols
- polynomial
- an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
- term
- a single number or variable, or numbers and variables multiplied together
- variable
- Alphabetic character representing a number
