Asked by Monkey balls
what are the coefficients in the expression 5x^2+2x-6
Answers
Answered by
Monkey balls
rewrite (5*2x)+4 using the communitive property of Multiplication
Answered by
Monkey balls
simplify using the distributive property 5(2x-6)
Answered by
Monkey balls
simplify the polynomial and type it in standard form (3x^2-2x-5)+(2x^2+x-10)
Answered by
Monkey balls
what is the error made while subtracting these two polynomials
(3x^4-8x_2+4x)-(9x-5x^4+2x^2)
Step 1: 3x^4-8x^2+4x-9x+5x^4+2x^2
Step 2: 3x^4+5x^4-8x^2+2x^2+4x-9x
Step 3: 8x^4-6x^2-5x
Final answer: 8x^4-6x^2-5x
(3x^4-8x_2+4x)-(9x-5x^4+2x^2)
Step 1: 3x^4-8x^2+4x-9x+5x^4+2x^2
Step 2: 3x^4+5x^4-8x^2+2x^2+4x-9x
Step 3: 8x^4-6x^2-5x
Final answer: 8x^4-6x^2-5x
Answered by
GPT-4o mini
In the expression \(5x^2 + 2x - 6\), the coefficients are the numbers that multiply the variable terms. They are as follows:
- The coefficient of \(x^2\) is \(5\).
- The coefficient of \(x\) is \(2\).
- The constant term, which does not have a variable, can be thought of as having a coefficient of \(-6\) (although it's not directly associated with a variable).
So, the coefficients are \(5\), \(2\), and \(-6\).
- The coefficient of \(x^2\) is \(5\).
- The coefficient of \(x\) is \(2\).
- The constant term, which does not have a variable, can be thought of as having a coefficient of \(-6\) (although it's not directly associated with a variable).
So, the coefficients are \(5\), \(2\), and \(-6\).
Answered by
GPT-4o mini
The commutative property of multiplication states that changing the order of the factors does not change the product. In the expression \( (5 \cdot 2x) + 4 \), you can apply the commutative property to rearrange the factors inside the multiplication.
Here's how you can rewrite it:
\[
(2x \cdot 5) + 4
\]
Both representations, \( (5 \cdot 2x) + 4 \) and \( (2x \cdot 5) + 4 \), are equivalent due to the commutative property of multiplication.
Here's how you can rewrite it:
\[
(2x \cdot 5) + 4
\]
Both representations, \( (5 \cdot 2x) + 4 \) and \( (2x \cdot 5) + 4 \), are equivalent due to the commutative property of multiplication.
Answered by
GPT-4o mini
To simplify the expression \( 5(2x - 6) \) using the distributive property, you multiply \( 5 \) by each term inside the parentheses:
\[
5(2x) + 5(-6)
\]
Calculating each term:
1. \( 5(2x) = 10x \)
2. \( 5(-6) = -30 \)
Now, combine the results:
\[
10x - 30
\]
So, the simplified expression is
\[
10x - 30
\]
\[
5(2x) + 5(-6)
\]
Calculating each term:
1. \( 5(2x) = 10x \)
2. \( 5(-6) = -30 \)
Now, combine the results:
\[
10x - 30
\]
So, the simplified expression is
\[
10x - 30
\]
Answered by
GPT-4o mini
To simplify the polynomial \((3x^2 - 2x - 5) + (2x^2 + x - 10)\), we will combine like terms.
1. **Combine the \(x^2\) terms:**
\[
3x^2 + 2x^2 = 5x^2
\]
2. **Combine the \(x\) terms:**
\[
-2x + x = -x
\]
3. **Combine the constant terms:**
\[
-5 - 10 = -15
\]
Now we can write the combined polynomial:
\[
5x^2 - x - 15
\]
This expression is already in standard form, which is typically written as \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants.
So the final simplified polynomial in standard form is:
\[
5x^2 - x - 15
\]
1. **Combine the \(x^2\) terms:**
\[
3x^2 + 2x^2 = 5x^2
\]
2. **Combine the \(x\) terms:**
\[
-2x + x = -x
\]
3. **Combine the constant terms:**
\[
-5 - 10 = -15
\]
Now we can write the combined polynomial:
\[
5x^2 - x - 15
\]
This expression is already in standard form, which is typically written as \(ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants.
So the final simplified polynomial in standard form is:
\[
5x^2 - x - 15
\]
Answered by
GPT-4o mini
Let’s examine the steps to identify any potential errors in the subtraction process.
Starting with the two polynomials:
\[
(3x^4 - 8x^2 + 4x) - (9x - 5x^4 + 2x^2)
\]
When subtracting the second polynomial, it's important to distribute the negative sign correctly across all terms in the second polynomial. Here's how it should go:
1. **Step 1: Apply the subtraction**:
\[
3x^4 - 8x^2 + 4x - 9x + 5x^4 - 2x^2
\]
In this step, you correctly changed \( - (9x - 5x^4 + 2x^2) \) to \( -9x + 5x^4 - 2x^2 \).
2. **Step 2: Combine like terms**:
\[
3x^4 + 5x^4 - 8x^2 - 2x^2 + 4x - 9x
\]
- \( 3x^4 + 5x^4 = 8x^4\)
- \( -8x^2 - 2x^2 = -10x^2\) (this is where the error occurs)
- \( 4x - 9x = -5x\)
3. **Final answer**: Combine the results:
\[
8x^4 - 10x^2 - 5x
\]
So, the final answer should be:
\[
8x^4 - 10x^2 - 5x
\]
The error occurred during Step 2 when combining the \(x^2\) terms. You computed \(-8x^2 + 2x^2\) incorrectly as \(-6x^2\) when it should have been \(-10x^2\).
Starting with the two polynomials:
\[
(3x^4 - 8x^2 + 4x) - (9x - 5x^4 + 2x^2)
\]
When subtracting the second polynomial, it's important to distribute the negative sign correctly across all terms in the second polynomial. Here's how it should go:
1. **Step 1: Apply the subtraction**:
\[
3x^4 - 8x^2 + 4x - 9x + 5x^4 - 2x^2
\]
In this step, you correctly changed \( - (9x - 5x^4 + 2x^2) \) to \( -9x + 5x^4 - 2x^2 \).
2. **Step 2: Combine like terms**:
\[
3x^4 + 5x^4 - 8x^2 - 2x^2 + 4x - 9x
\]
- \( 3x^4 + 5x^4 = 8x^4\)
- \( -8x^2 - 2x^2 = -10x^2\) (this is where the error occurs)
- \( 4x - 9x = -5x\)
3. **Final answer**: Combine the results:
\[
8x^4 - 10x^2 - 5x
\]
So, the final answer should be:
\[
8x^4 - 10x^2 - 5x
\]
The error occurred during Step 2 when combining the \(x^2\) terms. You computed \(-8x^2 + 2x^2\) incorrectly as \(-6x^2\) when it should have been \(-10x^2\).