Polynomial Naming and Classification
A Grade 12 math worksheet on naming and classifying polynomials by degree and number of terms, including real-world applications.
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Polynomial Naming and Classification
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Read each question carefully and follow the instructions to classify and name the given polynomials.
1. Which of the following best describes the polynomial \(3x^4 - 2x + 7\)?
Cubic binomial
Quartic trinomial
Quadratic monomial
Linear polynomial
2. A polynomial with a degree of 1 and two terms is called a:
Constant monomial
Linear binomial
Quadratic trinomial
Cubic monomial
3. The degree of the polynomial \(5x^3y^2 - 4x^2y^4 + 2xy^5\) is .
4. A polynomial with only one term is called a .
5. The polynomial \(7\) is classified as a monomial.
6. Classify the polynomial \(y = -2x^5 + x^3 - 8x + 1\) by its degree and number of terms.
7. Consider the polynomial \(P(x) = (3x^2 - 5x + 1)(2x + 4)\). Explain how you would determine its degree without fully expanding the expression.
Match each polynomial expression with its correct classification.
8. \(4x^2 - 3x + 9\)
a. Linear binomial
9. \(x^3 + 2\)
b. Quadratic trinomial
10. \(-5x\)
c. Cubic binomial
11. \(12\)
d. Constant monomial
12. The expression \(4x^{1/2} + 3\) is a polynomial.
True
False
13. A trinomial always has a degree of 3.
True
False
14. The path of a projectile can be modeled by the polynomial function \(h(t) = -16t^2 + v_0t + h_0\), where \(h(t)\) is the height at time \(t\), \(v_0\) is the initial velocity, and \(h_0\) is the initial height. What type of polynomial is this function (by degree and number of terms)? Explain your reasoning.