Algebra — practice questions with answers
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If x + 1/x = 5, then the value of x² + 1/x² is:If x − 1/x = 3, then the value of x³ − 1/x³ is:If a + b + c = 0 and abc = 5, then a³ + b³ + c³ equals:If a + b + c = 12 and ab + bc + ca = 47, then a² + b² + c² equals:If x + y = 10 and xy = 21, then x³ + y³ equals:Given that x − 1/x = 2, what does x⁴ + 1/x⁴ equal?If x = 2 + √3, then the value of x + 1/x is:The expression (x² − 9)/(x² + 6x + 9), where x ≠ −3, simplifies to:The sum 1/(x − 1) + 1/(x + 1) simplifies to:The complete factorisation of x³ − 6x² + 11x − 6 is:The expression x⁴ + x² + 1 factorises as:The expression x² − y² − 4x + 4 factorises as:If (x − 1) is a factor of x³ + kx² − 2x + 6, then k equals:The remainder when x⁵⁰ + 1 is divided by (x + 1) is:The degree of the polynomial (x² + 1)³ (x − 2)² is:If α and β are the zeros of the polynomial x² − 7x + 10, then 1/α + 1/β equals:The sum of the zeros of the cubic polynomial 2x³ − 5x² + 3x − 1 is:The pair of equations 2x + 3y = 5 and 4x + ky = 10 has infinitely many solutions when k equals:For which value of k does the pair kx + 3y = k − 3 and 12x + ky = k have no solution?The pair of equations x − 2y = 8 and 5x − 10y = 10 is:The sum of the digits of a two-digit number is 9. When 27 is added to the number, its digits are…Five years ago a father was three times as old as his son. Ten years from now he will be twice as…A fraction becomes 1/3 when 1 is subtracted from its numerator, and it becomes 1/4 when 8 is added…The nature of the roots of the equation 2x² − 4x + 3 = 0 is:If α and β are the roots of 2x² − 5x + 3 = 0, then α² + β² equals:
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