Questions and Answers
A shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called ___?
What is the result of (3x³ + 5x² - 14x - 18) ÷ (x - 2)?
3x² + 11x + 8 - 2/(x - 2)
What is the result of (2x³ + 7x² + 13x + 14) ÷ (x + 2)?
2x² + 3x + 7
What is the quotient when dividing (5x³ + 3x² + 8x - 2) by (2)?
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What is the result of (5x³ + 3x² + 8x - 2) ÷ (-3)?
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What is the result of (x² - 5x + 2) ÷ (x - 3)?
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What is the result of (2x² - 3x - 5) ÷ (x + 1)?
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What is the quotient of (3x³ + 17x² + 26x + 24) ÷ (x + 4)?
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What is the equation of (2x³ + x² - 11 + 2) ÷ (x - 2)?
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What is the correct graph of y = |x - 1| + 2?
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What is the product of the matrices [1 2] and [-2 3 -1; 5 0]?
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Which is the equation of an ellipse?
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Study Notes
Synthetic Division
- Synthetic division simplifies polynomial division by only using coefficients.
- Commonly used for dividing a polynomial by a linear polynomial.
Division Problem Examples
- For dividing (3x³ + 5x² - 14x - 18) by (x - 2), the result is 3x² + 11x + 8 with a remainder of -2.
- Dividing (2x³ + 7x² + 13x + 14) by (x + 2) yields 2x² + 3x + 7.
Quotients from Division Problems
- Dividing 2 | 5 3 8 -2 results in a quotient of 5x² + 13x + 34 with a remainder of 66.
- For -3 | 5 3 8 -2, the quotient is 2x² - 5x + 10 with a remainder of -28.
Additional Division Examples
- Dividing (x² - 5x + 2) by (x - 3) results in x - 2 with a remainder of -4.
- (2x² - 3x - 5) divided by (x + 1) gives a quotient of 2x - 5.
Advanced Polynomial Division
- (3x³ + 17x² + 26x + 24) divided by (x + 4) results in the quotient 3x² + 5x + 6.
- Dividing (2x³ + x² - 11 + 2) by (x - 2) results in a quotient of 2x² + 5x - 1.
Graph Characteristics
- The graph of y = |x - 1| + 2 has a V-shape opening upwards.
Matrix Multiplication
- Finding the product of matrices [1 2], [-2 3 -1], [5 0] results in [-2 -4], [-6 2], [-10 0].
Ellipse Equation
- The equation of an ellipse is represented as ((x - 5)^2/16 + (y + 2)^2/9 = 1).
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Description
This quiz covers the concept of synthetic division, focusing on simplifying polynomial division using coefficients. You will learn how to divide polynomials by linear polynomials and analyze various division problem examples, including the calculation of quotients and remainders.
