Which Of These Is A Trinomial?A. $2x - 7$ B. $x + 2y^2 - 7$ C. $5xy$ D. $2x^3 - 7y^3$

Understanding Trinomials

A trinomial is a type of polynomial that consists of three terms. It is a quadratic expression that can be factored into the product of two binomials. In other words, a trinomial is a polynomial with three terms, and it can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Identifying Trinomials

To identify a trinomial, we need to look for a polynomial with three terms. The terms can be added, subtracted, or multiplied, but they must be three distinct terms. For example, $2x^2 + 3x - 4$ is a trinomial because it has three terms: $2x^2$, $3x$, and $-4$.

Analyzing the Options

Now, let's analyze the options given in the problem:

Option A: $2x - 7$

This is a binomial, not a trinomial. It has only two terms: $2x$ and $-7$. Therefore, option A is not a trinomial.

Option B: $x + 2y^2 - 7$

This is a trinomial. It has three terms: $x$, $2y^2$, and $-7$. Therefore, option B is a trinomial.

Option C: $5xy$

This is a binomial, not a trinomial. It has only two terms: $5xy$ and $0$ (which is implied but not written). Therefore, option C is not a trinomial.

Option D: $2x^3 - 7y^3$

This is a binomial, not a trinomial. It has only two terms: $2x^3$ and $-7y^3$. Therefore, option D is not a trinomial.

Conclusion

Based on the analysis of the options, we can conclude that the only trinomial among the given options is option B: $x + 2y^2 - 7$.

Key Takeaways

• A trinomial is a type of polynomial that consists of three terms.
• To identify a trinomial, we need to look for a polynomial with three terms.
• A trinomial can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Examples of Trinomials

Here are some examples of trinomials:

• $2x^2 + 3x - 4$
• $x + 2y^2 - 7$
• $3x^2 - 2x + 1$

Why is it Important to Identify Trinomials?

Identifying trinomials is important because it helps us to factorize them into the product of two binomials. This can be useful in solving quadratic equations and other mathematical problems.

How to Factorize Trinomials

To factorize a trinomial, we need to find two binomials whose product is equal to the trinomial. This can be done by using the factoring method, which involves finding the greatest common factor (GCF) of the terms and then factoring out the GCF.

Conclusion

In conclusion, a trinomial is a type of polynomial that consists of three terms. It can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Identifying trinomials is important because it helps us to factorize them into the product of two binomials, which can be useful in solving quadratic equations and other mathematical problems.

Final Answer

The final answer is option B: $x + 2y^2 - 7$.

Understanding Trinomials

A trinomial is a type of polynomial that consists of three terms. It is a quadratic expression that can be factored into the product of two binomials. In other words, a trinomial is a polynomial with three terms, and it can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Q&A

Q: What is a trinomial?

A: A trinomial is a type of polynomial that consists of three terms. It is a quadratic expression that can be factored into the product of two binomials.

Q: How do I identify a trinomial?

A: To identify a trinomial, you need to look for a polynomial with three terms. The terms can be added, subtracted, or multiplied, but they must be three distinct terms.

Q: What is the difference between a trinomial and a binomial?

A: A binomial is a polynomial with two terms, while a trinomial is a polynomial with three terms.

Q: Can a trinomial be factored?

A: Yes, a trinomial can be factored into the product of two binomials. This can be done by using the factoring method, which involves finding the greatest common factor (GCF) of the terms and then factoring out the GCF.

Q: How do I factor a trinomial?

A: To factor a trinomial, you need to find two binomials whose product is equal to the trinomial. This can be done by using the factoring method, which involves finding the greatest common factor (GCF) of the terms and then factoring out the GCF.

Q: What are some examples of trinomials?

A: Some examples of trinomials include:

• $2x^2 + 3x - 4$
• $x + 2y^2 - 7$
• $3x^2 - 2x + 1$

Q: Why is it important to identify trinomials?

A: Identifying trinomials is important because it helps us to factorize them into the product of two binomials. This can be useful in solving quadratic equations and other mathematical problems.

Q: Can a trinomial have negative terms?

A: Yes, a trinomial can have negative terms. For example, $-2x^2 + 3x - 4$ is a trinomial with negative terms.

Q: Can a trinomial have fractional terms?

A: Yes, a trinomial can have fractional terms. For example, $\frac{1}{2}x^2 + \frac{3}{4}x - \frac{1}{4}$ is a trinomial with fractional terms.

Conclusion

In conclusion, a trinomial is a type of polynomial that consists of three terms. It can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Identifying trinomials is important because it helps us to factorize them into the product of two binomials, which can be useful in solving quadratic equations and other mathematical problems.

Final Answer

The final answer is that a trinomial is a type of polynomial that consists of three terms, and it can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable.

Key Takeaways

• A trinomial is a type of polynomial that consists of three terms.
• To identify a trinomial, you need to look for a polynomial with three terms.
• A trinomial can be factored into the product of two binomials.
• Identifying trinomials is important because it helps us to factorize them into the product of two binomials.

Examples of Trinomials

Here are some examples of trinomials:

• $2x^2 + 3x - 4$
• $x + 2y^2 - 7$
• $3x^2 - 2x + 1$

Why is it Important to Identify Trinomials?

Identifying trinomials is important because it helps us to factorize them into the product of two binomials. This can be useful in solving quadratic equations and other mathematical problems.

How to Factorize Trinomials

To factorize a trinomial, you need to find two binomials whose product is equal to the trinomial. This can be done by using the factoring method, which involves finding the greatest common factor (GCF) of the terms and then factoring out the GCF.

Conclusion

In conclusion, a trinomial is a type of polynomial that consists of three terms. It can be written in the form of $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $x$ is the variable. Identifying trinomials is important because it helps us to factorize them into the product of two binomials, which can be useful in solving quadratic equations and other mathematical problems.