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Monomials and polynomials
Dynamic tasks on like terms, polynomial operations, degree, evaluation and algebraic vocabulary.
Questions: 10Estimated time: 17 minutes
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Question 1out of 10
Subtract the polynomial (x − 8) from (3x − 3).
When subtracting a polynomial, reverse the sign of every term inside its parentheses, then combine like terms. For example, (5x + 2) − (3x − 4) = 2x + 6.
Question 2out of 10
Add the like terms -8x and -3x.
Like terms have the same variables raised to the same powers. Add their coefficients and keep the variable part: 3x² + 5x² = 8x².
Question 3out of 10
How is 7x2 + 3x + 6 classified by its number of terms?
A polynomial with one, two or three terms is a monomial, binomial or trinomial respectively. The expression ax² + bx + c has three terms, so it is a trinomial.
Question 4out of 10
Multiply the monomials: 3x3 · 9x1.
Multiply the coefficients and add exponents of the shared base x: axᵐ × bxⁿ = abxᵐ⁺ⁿ. Check the coefficient sign separately.
Question 5out of 10
In the monomial 7x5, identify the coefficient and the exponent.
In axⁿ, a is the coefficient and n is the exponent of x. The degree of this nonzero one-variable monomial is n; the coefficient size does not change it.
Question 6out of 10
Evaluate P(x) = 4x2 + 2 when x = −1.
Substitute the given x value. Square x first, multiply by a, then add b. Put a negative x in parentheses: (−3)² = 9.
Question 7out of 10
Expand: (x + 8)(x + 3).
Multiply each term in the first parentheses by every term in the second. (x + a)(x + b) = x² + ax + bx + ab = x² + (a + b)x + ab.
Question 8out of 10
What is the degree of the monomial 3x5?
In axⁿ, a is the coefficient and n is the exponent of x. The degree of this nonzero one-variable monomial is n; the coefficient size does not change it.
Question 9out of 10
Evaluate P(x) = 4x2 − 5 when x = 1.
Substitute the given x value. Square x first, multiply by a, then add b. Put a negative x in parentheses: (−3)² = 9.
Question 10out of 10
Subtract the polynomial (x − 6) from (4x − 8).
When subtracting a polynomial, reverse the sign of every term inside its parentheses, then combine like terms. For example, (5x + 2) − (3x − 4) = 2x + 6.
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Sample questions
- Add the like terms ___ and ___.
- Subtract the polynomial (___) from (___).
- Multiply the monomials: ___x___ · ___x___.
- Expand: (x + ___)(x + ___).
- What is the degree of the monomial ___x___?
Monomials and polynomials
A monomial is a product of a number and powers of variables, while a polynomial is a sum of monomials. Like terms have identical variable parts, so only their coefficients are combined. When multiplying monomials, multiply coefficients and add exponents of equal variables.
Polynomial operations
When subtracting a polynomial, change the sign of every term in it. Expand brackets carefully before collecting terms. The degree of a monomial is the sum of its variable exponents; the degree of a simplified polynomial is the greatest degree of its terms.
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