Ctrl+k

Evaluate polynomial expressions

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.

Detailed Explanation: Evaluate polynomial expressions

To evaluate a polynomial expression, replace each variable with its given value, then simplify using the order of operations:

  1. Substitute values using parentheses.
  2. Evaluate exponents.
  3. Multiply.
  4. Add or subtract.

Example

Evaluate

P(x,y)=2x2−3xy+y2−4P(x,y)=2x^2-3xy+y^2-4

when x=−2x=-2 and y=3y=3.

1. Substitute the values. Use parentheses around negative numbers:

P(−2,3)=2(−2)2−3(−2)(3)+(3)2−4P(-2,3)=2(-2)^2-3(-2)(3)+(3)^2-4

2. Evaluate the exponents.

(−2)2=4and32=9(-2)^2=4 \quad \text{and} \quad 3^2=9

So,

P(−2,3)=2(4)−3(−2)(3)+9−4P(-2,3)=2(4)-3(-2)(3)+9-4

3. Multiply.

The middle term is

−3(−2)(3)=18-3(-2)(3)=18

Therefore,

P(−2,3)=8+18+9−4P(-2,3)=8+18+9-4

4. Add and subtract.

P(−2,3)=31P(-2,3)=31

So, the value of the polynomial is

31\boxed{31}

Always use parentheses when substituting a negative value, especially when the variable has an exponent.

Learn by doing: Evaluate polynomial expressions

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

    Practice with unlimited practice problems

    Number Sequences - Polynomial, Specific Term

      ?