Degrees, zeroes, remainder & factor theorem, algebraic identities, polynomial division.
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Q1 · Polynomials · EASY
If p(x) = 2x³ - 5x² + 3x - 7, what is the degree of the polynomial?
Q2 · Polynomials · MEDIUM
When the polynomial p(x) = x³ - 4x² + x + 6 is divided by (x - 2), what is the remainder?
Q3 · Polynomials · MEDIUM
If (x - 3) is a factor of the polynomial x³ - 6x² + kx - 12, then what is the value of k?
Q4 · Polynomials · HARD
The zeroes of the quadratic polynomial x² - 5x + 6 are α and β. What is the value of α² + β²?
Q5 · Polynomials · MEDIUM
If p(x) = x³ - 6x² + 11x - 6, and one of its zeros is 1, then what is the product of the other two zeros?