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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 ___?
A shortcut method of dividing a polynomial by a linear polynomial by using only the coefficients of the terms of the polynomial is called ___?
- Polynomial division
- Synthetic division (correct)
- Factorization
- Long division
What is the result of (3x³ + 5x² - 14x - 18) ÷ (x - 2)?
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)?
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)?
What is the quotient when dividing (5x³ + 3x² + 8x - 2) by (2)?
What is the result of (5x³ + 3x² + 8x - 2) ÷ (-3)?
What is the result of (5x³ + 3x² + 8x - 2) ÷ (-3)?
What is the result of (x² - 5x + 2) ÷ (x - 3)?
What is the result of (x² - 5x + 2) ÷ (x - 3)?
What is the result of (2x² - 3x - 5) ÷ (x + 1)?
What is the result of (2x² - 3x - 5) ÷ (x + 1)?
What is the quotient of (3x³ + 17x² + 26x + 24) ÷ (x + 4)?
What is the quotient of (3x³ + 17x² + 26x + 24) ÷ (x + 4)?
What is the equation of (2x³ + x² - 11 + 2) ÷ (x - 2)?
What is the equation of (2x³ + x² - 11 + 2) ÷ (x - 2)?
What is the correct graph of y = |x - 1| + 2?
What is the correct graph of y = |x - 1| + 2?
What is the product of the matrices [1 2] and [-2 3 -1; 5 0]?
What is the product of the matrices [1 2] and [-2 3 -1; 5 0]?
Which is the equation of an ellipse?
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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