9709 · topic questions
Algebra
12 past-paper questions on Algebra
The polynomial 4x³ + ax² +5x+b, where a and b are constants, is denoted by p(x). It is given that (2x+1) is a factor of p(x).…
Express 6x²-9x-16 / 2x²-5x-12 in partial fractions.
Express (6x²-2x+2)/((x-1)(2x+1)) in partial fractions.
Let f(x) = (5x² +8x+5)/((1+2x)(2+x²)). Express f(x) in partial fractions.
Hence find the coefficient of x³ in the expansion of f(x).
Solve the inequality |5x+7|>|2x-3|.
(b) Hence factorise p(x) completely. [3]
(b) Solve the inequality |3x+8|<9. [3]
Hence find the coefficient of x³ in the expansion of (3+ax)⁶(1−2x).
The polynomial p(x) is defined by p(x) = 9x³ + 6x² +12x+k, where k is a constant. Find the quotient when p(x) is divided by…
Find the quotient and remainder when x⁴ + 16 is divided by x² +4.
Find the equation of C₁ in the form y = a/(bx+c) + dx + e, where a, b, c, d and e are integers.
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