Simplify The Expression: $4x^2 - 13x + 9$

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Introduction

In algebra, simplifying expressions is a crucial step in solving equations and inequalities. It involves rewriting an expression in a simpler form, often by combining like terms or factoring out common factors. In this article, we will simplify the expression $4x^2 - 13x + 9$ using various algebraic techniques.

Understanding the Expression

The given expression is a quadratic expression in the form of $ax^2 + bx + c$. Here, $a = 4$, $b = -13$, and $c = 9$. To simplify this expression, we need to examine the coefficients of the terms and look for opportunities to combine like terms or factor out common factors.

Factoring the Expression

One way to simplify the expression is to factor it. Factoring involves expressing the expression as a product of simpler expressions. In this case, we can try to factor the quadratic expression by finding two numbers whose product is $4 \times 9 = 36$ and whose sum is $-13$. These numbers are $-12$ and $-3$, since $-12 \times -3 = 36$ and $-12 + (-3) = -15$, which is close to $-13$.

However, we can try to factor the expression by grouping the terms. We can group the first two terms together and factor out the common factor of $4x$. This gives us:

$$4x^2 - 13x + 9 = (4x^2 - 13x) + 9$$

Now, we can factor out the common factor of $x$ from the first two terms:

$$4x^2 - 13x + 9 = x(4x - 13) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

This is still not in the simplest form, as we can see that the expression can be further simplified by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

However, we can simplify this expression further by factoring out the common factor of $4x - 13$ from the first two terms:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

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Q&A: Simplifying the Expression

Q: What is the first step in simplifying the expression $4x^2 - 13x + 9$? A: The first step in simplifying the expression is to examine the coefficients of the terms and look for opportunities to combine like terms or factor out common factors.

Q: Can we factor the expression $4x^2 - 13x + 9$? A: Yes, we can factor the expression by grouping the terms. We can group the first two terms together and factor out the common factor of $4x$. This gives us:

$$4x^2 - 13x + 9 = (4x^2 - 13x) + 9$$

Q: How do we factor out the common factor of $4x$ from the first two terms? A: We can factor out the common factor of $4x$ from the first two terms by dividing each term by $4x$. This gives us:

$$4x^2 - 13x + 9 = x(4x - 13) + 9$$

Q: Can we simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final simplified form of the expression $4x^2 - 13x + 9$ is:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: Can we simplify the expression further? A: Yes, we can simplify the expression further by factoring out the common factor of $4x - 13$ from the first two terms. This gives us:

$$4x^2 - 13x + 9 = (4x - 13)(x) + 9$$

Q: What is the final simplified form of the expression $4x^2 - 13x + 9$? A: The final