TRINOMIAL

Trinomial

Definition Of Trinomial

A trinomial is a polynomial with three terms.

A polynomial with three terms is called a trinomial.

Example of Trinomial

x² + 5x - 2, - x² - 2x - 3, x² + 9x + 6, x² - 6x + 2, - x² - 4x + 5

Video Examples: Factoring Trinomials

Solved Example on Triangle Proportionality Theorem

Ques: What term should be added to the expression x² + 8x, to make it a perfect square trinomial?

Choices:

A. -16
B. 64
C. 16
D. 4
Correct Answer: C

Solution:

Step 1:x² + 8x [Original expression.]
Step 2: To complete the square of the expression x² + bx, add the square of half the coefficient of x, that is, add = (b/2)²
Step 3: The coefficient b = 8, so add (b/2)² = (8/2)² = 16, to the expression.
Step 4:x² + 8x + 4² = x² + 8x + 16 = (x + 4)².
Step 5: 16 should be added to the expression, x² + 8x, to create a perfect square trinomial.

Quick Summary

A trinomial has three terms.
Terms can include variables, coefficients, and constants.
Trinomials are a type of polynomial.

\[ ax^2 + bx + c \]

🍎 Teacher Insights

Emphasize the importance of identifying terms correctly. Use visual aids to differentiate between monomials, binomials, and trinomials. Incorporate factoring techniques to demonstrate practical applications of trinomials.

🎓 Prerequisites

Polynomials
Variables
Coefficients
Exponents

Check Your Knowledge

Q1: Which of the following is a trinomial?

x + y 3x^2 2x^2 + 5x - 3 4

Q2: How many terms does the expression 5x^3 - 2x + 7 have?

1 2 3 4

Frequently Asked Questions

Q: What is the difference between a trinomial and a binomial?
A: A trinomial has three terms, while a binomial has two terms.

Q: Can a trinomial have terms with the same variable and exponent?
A: Yes, but like terms should be combined to simplify the expression before identifying it as a trinomial.