Can u give me some information card that answers this question 1, What is a perfect square trinomial?
2. When do we say that a trinomial is a PST?
3. How to factor PST?

### Perfect Square Trinomial (PST) Information Card

#### 1. What is a Perfect Square Trinomial?
A **Perfect Square Trinomial (PST)** is a special form of a quadratic trinomial that can be expressed as the square of a binomial. In general, it takes the form:

\[ ax^2 + bx + c \]

where the trinomial is a perfect square if it can be factored into:

\[ (mx + n)^2 \]

Expanding this squared binomial gives:

\[ (mx + n)^2 = m^2x^2 + 2mnx + n^2 \]

So, a trinomial of the form \( ax^2 + bx + c \) is a PST if:

- \( a = m^2 \)
- \( b = 2mn \)
- \( c = n^2 \)

#### 2. When Do We Say That a Trinomial is a PST?
A trinomial \( ax^2 + bx + c \) is called a **Perfect Square Trinomial** if it meets the following conditions:

1. **Square Term**: The first term \( ax^2 \) must be a perfect square.
2. **Constant Term**: The last term \( c \) must be a perfect square.
3. **Middle Term Relationship**: The middle term \( b \) should be twice the product of the square roots of the first and last terms.

Mathematically, if \( a = m^2 \) and \( c = n^2 \), then \( b \) should equal \( 2mn \).

#### 3. How to Factor a Perfect Square Trinomial?
To factor a Perfect Square Trinomial, follow these steps:

1. **Identify the Square Roots**: Determine the square roots of the first term \( ax^2 \) and the last term \( c \).
2. **Check the Middle Term**: Ensure the middle term \( b \) is twice the product of these square roots.
3. **Write the Binomial**: Express the trinomial as the square of a binomial:
   \[
   ax^2 + bx + c = (mx + n)^2
   \]
   where \( m \) is the square root of the first term and \( n \) is the square root of the last term.

   **Example**: 
   Factor the trinomial \( x^2 + 6x + 9 \).
   
   - The square root of \( x^2 \) is \( x \).
   - The square root of \( 9 \) is \( 3 \).
   - The middle term \( 6x \) is twice the product of \( x \) and \( 3 \), confirming it's a PST.
   - Factor as \( (x + 3)^2 \).

### Want more details or have any questions?

### Related Questions
1. How can you identify a perfect square trinomial in a polynomial?
2. What are some examples of perfect square trinomials and their factorizations?
3. Can a perfect square trinomial have negative terms? How does that affect factoring?
4. How do perfect square trinomials relate to the difference of squares?
5. What is the difference between a perfect square trinomial and a general trinomial?

### Tip:
When factoring, always check if the trinomial can be rewritten as a square of a binomial first; it simplifies the problem and reduces errors.

Can u give me some information card that answers this question 1, What is a perfect square trinomial? 2. When do we say that a trinomial is a PST? 3. How to factor PST?

Explore the concept of perfect square trinomials, learn how to identify and factor them with step-by-step instructions. Ideal for students in Grades 8-10, this guide simplifies key algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation