Evaluating a polynomial expression means replacing each variable with a specified numerical value and applying grouping, nonnegative integer exponents, multiplication, and addition or subtraction in the correct order to obtain a single number. The process applies to one- or multivariable polynomials with integer, rational, or other specified real inputs, including careful handling of negative substitutions; it does not include solving polynomial equations or advanced symbolic methods, and supports later work with functions and algebraic models.
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Detailed Explanation: Evaluate polynomial expressions
To evaluate a polynomial expression, replace each variable with its given value, then simplify using the order of operations:
- Substitute values using parentheses.
- Evaluate exponents.
- Multiply.
- Add or subtract.
Example
Evaluate
when and .
1. Substitute the values. Use parentheses around negative numbers:
2. Evaluate the exponents.
So,
3. Multiply.
The middle term is
Therefore,
4. Add and subtract.
So, the value of the polynomial is
Always use parentheses when substituting a negative value, especially when the variable has an exponent.
Learn by doing: Evaluate polynomial expressions
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Practice:
Number Sequences - Polynomial, Specific Term
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Download/Modify Free Grade 10 'Evaluate polynomial expressions' Worksheet
Print this free 'Evaluate polynomial expressions' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Number Sequences - Polynomial, Specific Term
- Algebraic Function Variable Substitution - Bracketed Terms (Negatives)
- Algebraic Function Variable Substitution - Simple Terms (Negatives)
- Algebraic Function Variable Substitution - Simple Terms
- Order of Operations - Add, Subtract, Multiply no Parentheses (5 Numbers)
- Order of Operations - Add, Subtract, Multiply with Parentheses (5 Numbers)
- Algebraic Functions - Variable Substitution to Equation - Bracketed Terms
- Order of Operations - Add, Subtract with Parentheses (5 Numbers)
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Evaluate polynomial expressions) through scaffolded problems that grow in difficulty as concepts are understood.