Asked by Monkey balls

what are the coefficients in the expression 5x^2+2x-6
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
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 \(-6\).
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.
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

\[
10x - 30
\]
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:

\[
5x^2 - x - 15
\]
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 \(-10x^2\).