Question 1

Question

A)Simplify 4x2−12x+244x. Write your answer in standard form.(1 point)
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Question 2
A)Simplify x2+5x+6x+2. Write your answer in standard form.(1 point)
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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

Sure! Here are the solutions for each of the questions:

Question 1
Simplifying \(4x^2 - 12x + 24x\):
Combine like terms:
\(4x^2 + (24x - 12x) = 4x^2 + 12x\)

So the answer in standard form is:
4x² + 12x

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Question 2
Simplifying \(x^2 + 5x + 6x + 2\):
Combine like terms:
\(x^2 + (5x + 6x) + 2 = x^2 + 11x + 2\)

So the answer in standard form is:
x² + 11x + 2

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Question 3
Using long division to divide \(24x^4 - 24x^3 - 18x^2\) by \(4x^3 + 2x^2\):

1. Divide the leading term: \(\frac{24x^4}{4x^3} = 6x\)
2. Multiply and subtract:
   \(24x^4 - 24x^3 - 18x^2 - (6x)(4x^3 + 2x^2)\)
   \(= 24x^4 - 24x^3 - 18x^2 - (24x^4 + 12x^3)\)
   \(= -24x^3 - 18x^2 + 12x^3 = -12x^3 - 18x^2\)
3. Divide again: \(\frac{-12x^3}{4x^3} = -3\)
4. Multiply and subtract:
   \(-12x^3 - 18x^2 - (-3)(4x^3 + 2x^2)\)
   \(-12x^3 - 18x^2 + 12x^3 + 6x^2 = -12x^2\)

So the quotient is:
6x - 3
And the remainder is:
-12x²
Thus final answer in full form:
6x - 3 - (12x²)/(4x³ + 2x²)

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Question 4
Using long division to divide \(33x^5 + 22x^4 - 50x^3 - 26x^2 + 13x\) by \(3x^2 + 2x - 1\):

1. Divide the leading term: \(\frac{33x^5}{3x^2} = 11x^3\)
2. Multiply and subtract:
   \(33x^5 + 22x^4 - 50x^3 - 26x^2 + 13x - (11x^3)(3x^2 + 2x - 1)\)
   \(= 33x^5 + 22x^4 - 50x^3 - 26x^2 + 13x - (33x^5 + 22x^4 - 11x^3)\)
   \(= -39x^3 - 26x^2 + 13x\)
3. Divide the leading term: \(\frac{-39x^3}{3x^2} = -13x\)
4. Multiply and subtract:
   \(-39x^3 - 26x^2 + 13x - (-13x)(3x^2 + 2x - 1)\)
   \(-39x^3 - 26x^2 + 13x + (39x^3 + 26x^2 - 13x)\)
   \(= 0\)

So the quotient is:
11x^3 - 13x
And the remainder is
0

Thus the answer is:
11x³ - 13x

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Question 5
Using long division to divide \(-30x^6 + 48x^5 + 50x - 80\) by \(5x - 8\):

1. Divide the leading term: \(\frac{-30x^6}{5x} = -6x^5\)
2. Multiply and subtract:
   \(-30x^6 + 48x^5 + 50x - 80 - (-6x^5)(5x - 8)\)
   \(-30x^6 + 48x^5 + 50x - 80 + (30x^6 - 48x^5)\)
   \(= 0 + 50x - 80\)

Next Steps:

1. Divide leading term: \(\frac{50x}{5x} = 10\)
2. Multiply and subtract:
   \(50x - 80 - (10)(5x - 8) = 50x - 80 - (50x - 80)\)
   \(= 0\)

So the quotient is:
-6x^5 + 10
And the remainder is:
0

Thus the final answer is:
-6x^5 + 10

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