Asked by x
Simplify x^2+5x+6/x+2
. Write your answer in standard form.(1 point)
. Write your answer in standard form.(1 point)
Answers
Answered by
x
Simplify 2x^2−7x−4/x−4
. Write your answer in standard form.(1 point)
. Write your answer in standard form.(1 point)
Answered by
x
What is the quotient of 35x^2−15/−5
?(1 point)
?(1 point)
Answered by
x
What is the quotient of the following?
52x^8/13x^2
(1 point)
Responses
4x^6
4 x to the 6th power
4x^4
4 x to the 4th power
39x^4
39 x to the 4th power
39x^6
52x^8/13x^2
(1 point)
Responses
4x^6
4 x to the 6th power
4x^4
4 x to the 4th power
39x^4
39 x to the 4th power
39x^6
Answered by
x
What is the quotient of the following?
24x^6−30x^4/6x^2
(1 point)
Responses
4x^4−5x^2
4 x to the 4th power minus 5 x squared
18x$4−24x^2
18 x to the 4th power minus 24 x squared
4x^3−5x^2
4 x cubed minus 5 x squared
18x^3−24x^2
24x^6−30x^4/6x^2
(1 point)
Responses
4x^4−5x^2
4 x to the 4th power minus 5 x squared
18x$4−24x^2
18 x to the 4th power minus 24 x squared
4x^3−5x^2
4 x cubed minus 5 x squared
18x^3−24x^2
Answered by
GPT-4o mini
To simplify the expression \(\frac{x^2 + 5x + 6}{x + 2}\), we can factor the numerator.
The numerator \(x^2 + 5x + 6\) can be factored as follows:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now we can rewrite the original expression:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
Assuming \(x + 2 \neq 0\) (i.e., \(x \neq -2\)), we can cancel the \(x + 2\) terms:
\[
= x + 3
\]
Thus, the simplified form of the expression in standard form is:
\[
\boxed{x + 3}
\]
The numerator \(x^2 + 5x + 6\) can be factored as follows:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now we can rewrite the original expression:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
Assuming \(x + 2 \neq 0\) (i.e., \(x \neq -2\)), we can cancel the \(x + 2\) terms:
\[
= x + 3
\]
Thus, the simplified form of the expression in standard form is:
\[
\boxed{x + 3}
\]
Answered by
GPT-4o mini
To simplify the expression \(\frac{2x^2 - 7x - 4}{x - 4}\), we first need to factor the numerator \(2x^2 - 7x - 4\).
To factor \(2x^2 - 7x - 4\), we will look for two numbers that multiply to \((2 \times -4) = -8\) and add up to \(-7\). The numbers that satisfy this are \(-8\) and \(1\).
We can split the middle term using these numbers:
\[
2x^2 - 8x + x - 4
\]
Now, we can factor by grouping:
\[
= 2x(x - 4) + 1(x - 4)
\]
Now, we can factor out the common factor \((x - 4)\):
\[
= (2x + 1)(x - 4)
\]
Now we can rewrite the original expression:
\[
\frac{2x^2 - 7x - 4}{x - 4} = \frac{(2x + 1)(x - 4)}{x - 4}
\]
Assuming \(x - 4 \neq 0\) (i.e., \(x \neq 4\)), we can cancel the \((x - 4)\) terms:
\[
= 2x + 1
\]
Thus, the simplified form of the expression in standard form is:
\[
\boxed{2x + 1}
\]
To factor \(2x^2 - 7x - 4\), we will look for two numbers that multiply to \((2 \times -4) = -8\) and add up to \(-7\). The numbers that satisfy this are \(-8\) and \(1\).
We can split the middle term using these numbers:
\[
2x^2 - 8x + x - 4
\]
Now, we can factor by grouping:
\[
= 2x(x - 4) + 1(x - 4)
\]
Now, we can factor out the common factor \((x - 4)\):
\[
= (2x + 1)(x - 4)
\]
Now we can rewrite the original expression:
\[
\frac{2x^2 - 7x - 4}{x - 4} = \frac{(2x + 1)(x - 4)}{x - 4}
\]
Assuming \(x - 4 \neq 0\) (i.e., \(x \neq 4\)), we can cancel the \((x - 4)\) terms:
\[
= 2x + 1
\]
Thus, the simplified form of the expression in standard form is:
\[
\boxed{2x + 1}
\]
Answered by
GPT-4o mini
To find the quotient of the expression \(\frac{35x^2 - 15}{-5}\), we can simplify it by dividing each term in the numerator by \(-5\).
1. Divide \(35x^2\) by \(-5\):
\[
\frac{35x^2}{-5} = -7x^2
\]
2. Divide \(-15\) by \(-5\):
\[
\frac{-15}{-5} = 3
\]
Now, we can combine these results:
\[
\frac{35x^2 - 15}{-5} = -7x^2 + 3
\]
So, the quotient is:
\[
\boxed{-7x^2 + 3}
\]
1. Divide \(35x^2\) by \(-5\):
\[
\frac{35x^2}{-5} = -7x^2
\]
2. Divide \(-15\) by \(-5\):
\[
\frac{-15}{-5} = 3
\]
Now, we can combine these results:
\[
\frac{35x^2 - 15}{-5} = -7x^2 + 3
\]
So, the quotient is:
\[
\boxed{-7x^2 + 3}
\]
Answered by
GPT-4o mini
To find the quotient of the expression \(\frac{52x^8}{13x^2}\), we can divide the coefficients and subtract the exponents of \(x\).
1. Divide the coefficients:
\[
\frac{52}{13} = 4
\]
2. Subtract the exponents of \(x\):
\[
x^{8-2} = x^6
\]
Now we combine these results:
\[
\frac{52x^8}{13x^2} = 4x^6
\]
Thus, the correct response is:
\[
\boxed{4x^6}
\]
1. Divide the coefficients:
\[
\frac{52}{13} = 4
\]
2. Subtract the exponents of \(x\):
\[
x^{8-2} = x^6
\]
Now we combine these results:
\[
\frac{52x^8}{13x^2} = 4x^6
\]
Thus, the correct response is:
\[
\boxed{4x^6}
\]
Answered by
GPT-4o mini
To find the quotient of the expression \(\frac{24x^6 - 30x^4}{6x^2}\), we can divide each term in the numerator by \(6x^2\).
1. For the first term \(24x^6\):
\[
\frac{24x^6}{6x^2} = 4x^{6-2} = 4x^4
\]
2. For the second term \(-30x^4\):
\[
\frac{-30x^4}{6x^2} = -5x^{4-2} = -5x^2
\]
Now, we combine these results:
\[
\frac{24x^6 - 30x^4}{6x^2} = 4x^4 - 5x^2
\]
Thus, the correct response is:
\[
\boxed{4x^4 - 5x^2}
\]
1. For the first term \(24x^6\):
\[
\frac{24x^6}{6x^2} = 4x^{6-2} = 4x^4
\]
2. For the second term \(-30x^4\):
\[
\frac{-30x^4}{6x^2} = -5x^{4-2} = -5x^2
\]
Now, we combine these results:
\[
\frac{24x^6 - 30x^4}{6x^2} = 4x^4 - 5x^2
\]
Thus, the correct response is:
\[
\boxed{4x^4 - 5x^2}
\]