what are the coefficients in the expression 5x^2+2x-6

Question

GPT-4o mini · Answer

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 $-6$.

Monkey balls · Answer

rewrite (5*2x)+4 using the communitive property of Multiplication

GPT-4o mini · Answer

The commutative property of multiplication states that changing the order of the factors does not change the product. In the expression $(5 \cdot 2 x) + 4$ , you can apply the commutative property to rearrange the factors inside the multiplication.

Here's how you can rewrite it:

$(2 x \cdot 5) + 4$

Both representations, $(5 \cdot 2 x) + 4$ and $(2 x \cdot 5) + 4$ , are equivalent due to the commutative property of multiplication.

Monkey balls · Answer

simplify using the distributive property 5(2x-6)

GPT-4o mini · Answer

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 $$ 10x - 30 $$

Monkey balls · Answer

simplify the polynomial and type it in standard form (3x^2-2x-5)+(2x^2+x-10)

GPT-4o mini · Answer

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: $$ 5x^2 - x - 15 $$

Monkey balls · Answer

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

GPT-4o mini · Answer

Let’s examine the steps to identify any potential errors in the subtraction process.

Starting with the two polynomials:

$(3 x^{4} - 8 x^{2} + 4 x) - (9 x - 5 x^{4} + 2 x^{2})$

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:

Step 1: Apply the subtraction: $3 x^{4} - 8 x^{2} + 4 x - 9 x + 5 x^{4} - 2 x^{2}$

In this step, you correctly changed $- (9 x - 5 x^{4} + 2 x^{2})$ to $- 9 x + 5 x^{4} - 2 x^{2}$ .

Step 2: Combine like terms: $3 x^{4} + 5 x^{4} - 8 x^{2} - 2 x^{2} + 4 x - 9 x$
- $3 x^{4} + 5 x^{4} = 8 x^{4}$
- $- 8 x^{2} - 2 x^{2} = - 10 x^{2}$ (this is where the error occurs)
- $4 x - 9 x = - 5 x$
Final answer: Combine the results: $8 x^{4} - 10 x^{2} - 5 x$

So, the final answer should be: $8 x^{4} - 10 x^{2} - 5 x$

The error occurred during Step 2 when combining the $x^{2}$ terms. You computed $- 8 x^{2} + 2 x^{2}$ incorrectly as $- 6 x^{2}$ when it should have been $- 10 x^{2}$ .