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 \(4x^3 + 2x^2\).
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Divide the leading term of the first polynomial by the leading term of the second polynomial: \(\frac{24x^4}{4x^3} = 6x\).
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Multiply \(6x\) by \(4x^3 + 2x^2\) and subtract from the original polynomial.
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Continuing the long division: You'll get \(6x(4x^3 + 2x^2) = 24x^4 + 12x^3\), then subtracting gives \(-36x^3 - 18x^2\).
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Now divide \(-36x^3\) by \(4x^3\) which gives \(-9\).
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Multiply \(-9\) by \(4x^3 + 2x^2\) to get \(-36x^3 - 18x^2\).
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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:
- Divide leading terms: \(11x^3\).
- Multiply and subtract off.
- 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 \(5x - 8\).
- Divide the first term: \(\frac{-30x^6}{5x} = -6x^5\).
- Multiply and subtract.
- Continue with \(6x^5 + \cdots\) to find the next quotient.
- 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.
1 answer