Count terms after simplification
A monomial has one term, a binomial two and a trinomial three. Terms are separated by addition or subtraction at the outer level. Their labels do not tell you the polynomial degree, which is the largest nonzero exponent.
For example, 2x³ − x + 4 is a trinomial of degree three. The expression 2x + 3x has two written pieces but simplifies to the monomial 5x.
Use the operation appropriate to the structure
Addition and subtraction combine coefficients of like powers. Multiplication distributes each term across the other expression. A power of a sum is not the sum of the powers.
The polynomial calculator uses one variable x and nonnegative whole-number exponents. Negative powers and variable denominators are rational expressions, outside this polynomial input model.
A constant does not have to be positive
In x² − 5x − 8, the constant term is −8. In 7 − 2x, the linear coefficient is −2 even though the terms are not written in descending order. Reordering terms is allowed as long as every sign travels with its term. A missing exponent on x means one, not zero.
LET’S WORK IT THROUGH
Expand (x + 3)(x + 2).
- Multiply x by both terms: x² + 2x.
- Multiply 3 by both terms: 3x + 6.
- Collect the linear terms.
THE ANSWERx² + 5x + 6.
YOUR TURN
A small check for understanding.
Is 4x² − 7 a quadratic binomial?
Reveal the answer
Yes. It has two terms and highest exponent two.
Now try your own numbers.
The polynomial calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Polynomial calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.