We appreciate your visit to Factor tex 80x 5 70x 2 60x 7 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Find the greatest common factor (GCF) of the coefficients, which is 10.
- Identify the smallest exponent of the variable x, which is 2.
- Factor out $10x^2$ from the expression: $80x^5 - 70x^2 - 60x^7 = 10x^2(-6x^5 + 8x^3 - 7)$.
- The factored form is $\boxed{10x^2(-6x^5 + 8x^3 - 7)}$.
### Explanation
1. Understanding the Problem
We are asked to factor the polynomial $80x^5 - 70x^2 - 60x^7$. Factoring involves finding common factors in each term and extracting them to simplify the expression.
2. Finding the GCF of Coefficients
First, let's identify the greatest common factor (GCF) of the coefficients: 80, -70, and -60. The GCF is the largest number that divides all three coefficients. We found that the GCF of 80, 70, and 60 is 10.
3. Finding the Common Variable Factor
Next, we look at the variable $x$ in each term: $x^5$, $x^2$, and $x^7$. The smallest exponent of $x$ is 2, so $x^2$ is a common factor.
4. Factoring out the GCF
Now, we factor out $10x^2$ from the entire expression: $$80x^5 - 70x^2 - 60x^7 = 10x^2(8x^3 - 7 - 6x^5)$$.
5. Rearranging the terms
Rearranging the terms inside the parenthesis in descending order of the exponent of x, we get: $$10x^2(-6x^5 + 8x^3 - 7)$$.
6. Final Answer
Thus, the factored form of the given expression is $10x^2(-6x^5 + 8x^3 - 7)$.
### Examples
Factoring polynomials is useful in many areas of mathematics and engineering. For example, in structural engineering, factoring can help simplify equations that describe the forces acting on a bridge, making it easier to analyze the bridge's stability. Similarly, in economics, factoring can be used to analyze supply and demand curves to find equilibrium points more efficiently.
- Identify the smallest exponent of the variable x, which is 2.
- Factor out $10x^2$ from the expression: $80x^5 - 70x^2 - 60x^7 = 10x^2(-6x^5 + 8x^3 - 7)$.
- The factored form is $\boxed{10x^2(-6x^5 + 8x^3 - 7)}$.
### Explanation
1. Understanding the Problem
We are asked to factor the polynomial $80x^5 - 70x^2 - 60x^7$. Factoring involves finding common factors in each term and extracting them to simplify the expression.
2. Finding the GCF of Coefficients
First, let's identify the greatest common factor (GCF) of the coefficients: 80, -70, and -60. The GCF is the largest number that divides all three coefficients. We found that the GCF of 80, 70, and 60 is 10.
3. Finding the Common Variable Factor
Next, we look at the variable $x$ in each term: $x^5$, $x^2$, and $x^7$. The smallest exponent of $x$ is 2, so $x^2$ is a common factor.
4. Factoring out the GCF
Now, we factor out $10x^2$ from the entire expression: $$80x^5 - 70x^2 - 60x^7 = 10x^2(8x^3 - 7 - 6x^5)$$.
5. Rearranging the terms
Rearranging the terms inside the parenthesis in descending order of the exponent of x, we get: $$10x^2(-6x^5 + 8x^3 - 7)$$.
6. Final Answer
Thus, the factored form of the given expression is $10x^2(-6x^5 + 8x^3 - 7)$.
### Examples
Factoring polynomials is useful in many areas of mathematics and engineering. For example, in structural engineering, factoring can help simplify equations that describe the forces acting on a bridge, making it easier to analyze the bridge's stability. Similarly, in economics, factoring can be used to analyze supply and demand curves to find equilibrium points more efficiently.
Thanks for taking the time to read Factor tex 80x 5 70x 2 60x 7 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
