Solving Polynomial Equations
This worksheet focuses on solving polynomial equations using various algebraic techniques appropriate for Grade 12 mathematics.
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Solving Polynomial Equations
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Read each question carefully and solve the polynomial equations using the most appropriate method. Show all your work for full credit.
1. Solve the polynomial equation by factoring: x³ - 4x² - 5x = 0
2. Find all real roots of the equation: 2x³ + 7x² + 6x = 0
3. Which of the following is a possible rational root of the polynomial P(x) = 3x³ - 2x² + 5x - 6?
-1/2
2/3
5/3
6
4. If (x - 2) is a factor of P(x) = x³ - 3x² + kx - 2, then the value of k is .
5. Use synthetic division to find the quotient and remainder when (x⁴ - 5x² + 4) is divided by (x + 2). The quotient is and the remainder is .
6. Find all complex roots of the equation: x³ + 8 = 0
7. Given that 2 is a root of x⁴ - 2x³ - 7x² + 8x + 12 = 0, find all other roots.
8. A polynomial of degree 'n' always has 'n' real roots.
True
False