
Dividing Polynomials with Synthetic Division
Authored by FELEICIA COVINGTON
Mathematics
12th Grade
Used 2+ times

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8 questions
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1.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Perform synthetic division to divide (3x^3 + 5x^2 - 2x + 7) by (x - 2).
3x^2 + 11x + 22 + 51/(x - 3)
3x^2 + 11x + 22 + 51/(x + 1)
3x^2 + 11x + 22 + 51/(x - 2)
3x^2 + 11x + 22 + 51/(x + 2)
Answer explanation
The synthetic division process correctly yields 3x^2 + 11x + 22 with a remainder of 51/(x - 2), leading to the correct answer choice.
2.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Divide (4x^4 - 2x^3 + 6x^2 - 8x + 5) by (x + 3) using synthetic division.
4x^3 - 14x^2 + 48x - 152 + 461/(x - 3)
4x^3 - 14x^2 + 48x - 152 + 461/(x + 3)
4x^3 - 14x^2 + 48x - 152 + 461/(x - 5)
4x^3 - 14x^2 + 48x - 152 + 461/(x + 2)
Answer explanation
Choose the correct answer that matches the result of dividing (4x^4 - 2x^3 + 6x^2 - 8x + 5) by (x + 3) using synthetic division.
3.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Find the quotient when (2x^3 - 5x^2 + 3x - 1) is divided by (x + 4) using synthetic division.
2x^2 - 5x + 15
2x^2 - 3x + 15
2x^2 - 3x + 5
2x^2 - 3x + 10
Answer explanation
To find the quotient using synthetic division, the coefficients of the dividend are used. Performing the division, we get 2x^2 - 3x + 15 as the quotient.
4.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Use synthetic division to divide (6x^4 + 3x^3 - 2x^2 + 5x - 1) by (x - 1).
Quotient: 4x^3 + 6x^2 + 5x + 9, Remainder: 7
Quotient: 7x^3 + 8x^2 + 6x + 11, Remainder: 10
Quotient: 5x^3 + 7x^2 + 3x + 10, Remainder: 8
Quotient: 6x^3 + 9x^2 + 7x + 12, Remainder: 11
Answer explanation
Using synthetic division, we find the quotient: 6x^3 + 9x^2 + 7x + 12 and remainder: 11, which matches the correct answer choice.
5.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
What is the result of dividing (5x^3 - 2x^2 + 4x - 7) by (x + 2) using synthetic division?
5x^2 - 12x + 28 - 47/(x + 2)
5x^2 - 12x + 28 - 47/(x - 1)
5x^2 - 12x + 28 - 47/(x - 2)
5x^2 - 12x + 28 - 47/(x + 3)
Answer explanation
The correct answer is 5x^2 - 12x + 28 - 47/(x + 2) obtained by dividing (5x^3 - 2x^2 + 4x - 7) by (x + 2) using synthetic division.
6.
MULTIPLE CHOICE QUESTION
1 min • 1 pt
Divide (8x^5 - 4x^4 + 2x^3 - 6x^2 + 9x - 3) by (x - 3) using synthetic division.
8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 5)
8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 2)
8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 4)
8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 3)
Answer explanation
The correct answer is 8x^4 + 20x^3 + 62x^2 + 180x + 549 + 1650/(x - 3) as obtained by dividing using synthetic division.
7.
MULTIPLE SELECT QUESTION
1 min • 1 pt
Perform synthetic division to divide (7x^4 + 2x^3 - 5x^2 + 3x + 1) by (x + 1).
7x^3 - 5x^2 + 1
7x^3 - 5x^2 + 3
7x^3 - 5x^2 - 3
7x^3 - 5x^2 + 3
Answer explanation
Performing synthetic division, we get the quotient 7x^3 - 5x^2 + 3. Therefore, the correct answer is 7x^3 - 5x^2 + 3.
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