Question

Question 1
A)Simplify 4x2−12x+24. Write your answer in standard form.(1 point)
4x
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Question 2
A)Simplify x2+5x+6. Write your answer in standard form.(1 point)
x+2
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Question 3
A)Use long division to divide the polynomial 24x4−24x3−18x2 by 4x3+2x2. Write your answer in standard form.(1 point)

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Question 4
A)Use long division to divide the polynomial 33x5+22x4−50x3−26x2+13x by 3x2+2x−1. Write your answer in standard form.(1 point)

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Question 5
A)Use long division to divide the polynomial −30x6+48x5+50x−80 by 5x−8. Write your answer in standard form.(1 point)

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answer the blank spots with the answer.

Answer 1

Let's go through each question one by one.

### Question 1
A) Simplify \(4x^2 - 12x + 24\).

To factor out the common factor of 4:
\[
4(x^2 - 3x + 6)
\]

Thus, the answer is:
```
4(x^2 - 3x + 6)
```

### Question 2
A) Simplify \(x^2 + 5x + 6\).

Factoring the quadratic:
\[
(x + 2)(x + 3)
\]

Thus, the answer is:
```
(x + 2)(x + 3)
```

### Question 3
A) Use long division to divide the polynomial \(24x^4 - 24x^3 - 18x^2\) by \(4x^3 + 2x^2\).

1. Divide the leading term of the first polynomial by the leading term of the second polynomial:
\(\frac{24x^4}{4x^3} = 6x\).

2. Multiply \(6x\) by \(4x^3 + 2x^2\) and subtract from the original polynomial.

3. Continuing the long division:
You'll get \(6x(4x^3 + 2x^2) = 24x^4 + 12x^3\),
then subtracting gives \(-36x^3 - 18x^2\).

4. Now divide \(-36x^3\) by \(4x^3\) which gives \(-9\).

5. Multiply \(-9\) by \(4x^3 + 2x^2\) to get \(-36x^3 - 18x^2\).

6. Subtract and you will have a remainder of 0.

So, the final quotient is:
```
6x - 9
```

### Question 4
A) Use long division to divide the polynomial \(33x^5 + 22x^4 - 50x^3 - 26x^2 + 13x\) by \(3x^2 + 2x - 1\).

Doing the long division step by step, we arrive at:
1. Divide leading terms: \(11x^3\).
2. Multiply and subtract off.
3. Continue dividing, applying the same method.

After carrying out the division completely, we end up with:
```
11x^3 + 4x^2 - 2x - 4
```

### Question 5
A) Use long division to divide the polynomial \(-30x^6 + 48x^5 + 50x - 80\) by \(5x - 8\).

1. Divide the first term: \(\frac{-30x^6}{5x} = -6x^5\).
2. Multiply and subtract.
3. Continue with \(6x^5 + \cdots\) to find the next quotient.
4. After performing all steps, we arrive at the final quotient:

Thus, the answer is:
```
-6x^5 + 18x^4 + 10x^2 + 16
```

Please write down or fill the blanks with the answers provided.