Asked by x
Simplify 4x^2−12x+24/4x
. Write your answer in standard form.(1 point)
. Write your answer in standard form.(1 point)
Answers
Answered by
x
Simplify 15x^5−3x^3+9x^2/3x
. Write your answer in standard form.(1 point)
. Write your answer in standard form.(1 point)
Answered by
x
What is the quotient of 14x^2−21/7
?(1 point)
?(1 point)
Answered by
x
What is the quotient of the following?
68x^8/4x^3
(1 point)
68x^8/4x^3
(1 point)
Answered by
x
What is the quotient of the following?
35x^5−20x^4+45x^3/5x^2
(1 point)
35x^5−20x^4+45x^3/5x^2
(1 point)
Answered by
x
Incorrect
Divide the monomial into each term of the polynomial in the numerator. Divide the coefficients and subtract the exponents of the variables.
Divide the monomial into each term of the polynomial in the numerator. Divide the coefficients and subtract the exponents of the variables.
Answered by
GPT-4o mini
To simplify the expression \(\frac{4x^2 - 12x + 24}{4x}\), we first factor out the numerator:
1. Factor out the common factor of 4 from the numerator:
\[
4x^2 - 12x + 24 = 4(x^2 - 3x + 6).
\]
So the expression becomes:
\[
\frac{4(x^2 - 3x + 6)}{4x}.
\]
2. Now, we can cancel the common factor of 4:
\[
= \frac{x^2 - 3x + 6}{x}.
\]
3. Next, we can break this fraction into two parts:
\[
= \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}.
\]
4. Simplifying each term gives us:
\[
= x - 3 + \frac{6}{x}.
\]
Thus, the simplified expression in standard form is:
\[
x - 3 + \frac{6}{x}.
\]
1. Factor out the common factor of 4 from the numerator:
\[
4x^2 - 12x + 24 = 4(x^2 - 3x + 6).
\]
So the expression becomes:
\[
\frac{4(x^2 - 3x + 6)}{4x}.
\]
2. Now, we can cancel the common factor of 4:
\[
= \frac{x^2 - 3x + 6}{x}.
\]
3. Next, we can break this fraction into two parts:
\[
= \frac{x^2}{x} - \frac{3x}{x} + \frac{6}{x}.
\]
4. Simplifying each term gives us:
\[
= x - 3 + \frac{6}{x}.
\]
Thus, the simplified expression in standard form is:
\[
x - 3 + \frac{6}{x}.
\]
Answered by
GPT-4o mini
To simplify the expression \(\frac{15x^5 - 3x^3 + 9x^2}{3x}\), we can follow these steps:
1. **Separate the terms in the numerator**:
\[
\frac{15x^5}{3x} - \frac{3x^3}{3x} + \frac{9x^2}{3x}
\]
2. **Simplify each term**:
- For \(\frac{15x^5}{3x}\):
\[
= \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4
\]
- For \(\frac{3x^3}{3x}\):
\[
= \frac{3}{3} \cdot \frac{x^3}{x} = 1 \cdot x^{3-1} = x^2
\]
- For \(\frac{9x^2}{3x}\):
\[
= \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x
\]
3. **Combine the simplified terms**:
\[
5x^4 - x^2 + 3x
\]
Now we arrange the expression in standard form, which is typically from the highest degree to the lowest degree:
The final simplified expression is:
\[
5x^4 + 3x - x^2
\]
When arranged in standard form, it is:
\[
5x^4 - x^2 + 3x
\]
1. **Separate the terms in the numerator**:
\[
\frac{15x^5}{3x} - \frac{3x^3}{3x} + \frac{9x^2}{3x}
\]
2. **Simplify each term**:
- For \(\frac{15x^5}{3x}\):
\[
= \frac{15}{3} \cdot \frac{x^5}{x} = 5x^{5-1} = 5x^4
\]
- For \(\frac{3x^3}{3x}\):
\[
= \frac{3}{3} \cdot \frac{x^3}{x} = 1 \cdot x^{3-1} = x^2
\]
- For \(\frac{9x^2}{3x}\):
\[
= \frac{9}{3} \cdot \frac{x^2}{x} = 3 \cdot x^{2-1} = 3x
\]
3. **Combine the simplified terms**:
\[
5x^4 - x^2 + 3x
\]
Now we arrange the expression in standard form, which is typically from the highest degree to the lowest degree:
The final simplified expression is:
\[
5x^4 + 3x - x^2
\]
When arranged in standard form, it is:
\[
5x^4 - x^2 + 3x
\]
Answered by
GPT-4o mini
To find the quotient of \(\frac{14x^2 - 21}{7}\), we can simplify each term in the numerator by dividing by 7:
1. **Separate the terms in the numerator**:
\[
\frac{14x^2}{7} - \frac{21}{7}
\]
2. **Simplify each term**:
- For \(\frac{14x^2}{7}\):
\[
= 2x^2
\]
- For \(\frac{21}{7}\):
\[
= 3
\]
3. **Combine the results**:
\[
2x^2 - 3
\]
Thus, the final quotient is:
\[
2x^2 - 3
\]
1. **Separate the terms in the numerator**:
\[
\frac{14x^2}{7} - \frac{21}{7}
\]
2. **Simplify each term**:
- For \(\frac{14x^2}{7}\):
\[
= 2x^2
\]
- For \(\frac{21}{7}\):
\[
= 3
\]
3. **Combine the results**:
\[
2x^2 - 3
\]
Thus, the final quotient is:
\[
2x^2 - 3
\]
Answered by
GPT-4o mini
To find the quotient of \(\frac{68x^8}{4x^3}\), we can simplify it by performing the division as follows:
1. **Divide the coefficients**:
\[
\frac{68}{4} = 17
\]
2. **Apply the quotient rule for exponents**:
\[
\frac{x^8}{x^3} = x^{8-3} = x^5
\]
3. **Combine the results**:
\[
17x^5
\]
Thus, the final quotient is:
\[
17x^5
\]
1. **Divide the coefficients**:
\[
\frac{68}{4} = 17
\]
2. **Apply the quotient rule for exponents**:
\[
\frac{x^8}{x^3} = x^{8-3} = x^5
\]
3. **Combine the results**:
\[
17x^5
\]
Thus, the final quotient is:
\[
17x^5
\]
Answered by
GPT-4o mini
To find the quotient of \(\frac{35x^5 - 20x^4 + 45x^3}{5x^2}\), we can simplify it by dividing each term in the numerator by \(5x^2\):
1. **Separate the terms in the numerator**:
\[
\frac{35x^5}{5x^2} - \frac{20x^4}{5x^2} + \frac{45x^3}{5x^2}
\]
2. **Simplify each term**:
- For \(\frac{35x^5}{5x^2}\):
\[
= \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3
\]
- For \(\frac{20x^4}{5x^2}\):
\[
= \frac{20}{5} \cdot \frac{x^4}{x^2} = 4x^{4-2} = 4x^2
\]
- For \(\frac{45x^3}{5x^2}\):
\[
= \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x
\]
3. **Combine the results**:
\[
7x^3 - 4x^2 + 9x
\]
Thus, the final quotient is:
\[
7x^3 - 4x^2 + 9x
\]
1. **Separate the terms in the numerator**:
\[
\frac{35x^5}{5x^2} - \frac{20x^4}{5x^2} + \frac{45x^3}{5x^2}
\]
2. **Simplify each term**:
- For \(\frac{35x^5}{5x^2}\):
\[
= \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3
\]
- For \(\frac{20x^4}{5x^2}\):
\[
= \frac{20}{5} \cdot \frac{x^4}{x^2} = 4x^{4-2} = 4x^2
\]
- For \(\frac{45x^3}{5x^2}\):
\[
= \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x
\]
3. **Combine the results**:
\[
7x^3 - 4x^2 + 9x
\]
Thus, the final quotient is:
\[
7x^3 - 4x^2 + 9x
\]
Answered by
GPT-4o mini
I apologize for any confusion in my previous response; let's carefully go through the process step by step, focusing on dividing the monomial into each term of the polynomial correctly.
We want to simplify:
\[
\frac{35x^5 - 20x^4 + 45x^3}{5x^2}
\]
We will divide each term of the polynomial in the numerator by the monomial \(5x^2\).
1. **Divide the first term**:
\[
\frac{35x^5}{5x^2} = \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3
\]
2. **Divide the second term**:
\[
\frac{-20x^4}{5x^2} = \frac{-20}{5} \cdot \frac{x^4}{x^2} = -4x^{4-2} = -4x^2
\]
3. **Divide the third term**:
\[
\frac{45x^3}{5x^2} = \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x
\]
Now, we combine the simplified terms:
\[
7x^3 - 4x^2 + 9x
\]
Thus, the correct final answer for the quotient is:
\[
7x^3 - 4x^2 + 9x
\]
Thank you for your patience, and I hope this clarification helps!
We want to simplify:
\[
\frac{35x^5 - 20x^4 + 45x^3}{5x^2}
\]
We will divide each term of the polynomial in the numerator by the monomial \(5x^2\).
1. **Divide the first term**:
\[
\frac{35x^5}{5x^2} = \frac{35}{5} \cdot \frac{x^5}{x^2} = 7x^{5-2} = 7x^3
\]
2. **Divide the second term**:
\[
\frac{-20x^4}{5x^2} = \frac{-20}{5} \cdot \frac{x^4}{x^2} = -4x^{4-2} = -4x^2
\]
3. **Divide the third term**:
\[
\frac{45x^3}{5x^2} = \frac{45}{5} \cdot \frac{x^3}{x^2} = 9x^{3-2} = 9x
\]
Now, we combine the simplified terms:
\[
7x^3 - 4x^2 + 9x
\]
Thus, the correct final answer for the quotient is:
\[
7x^3 - 4x^2 + 9x
\]
Thank you for your patience, and I hope this clarification helps!