Polynomials

(x – 1) is a factor of 3x³ + 2x² – 3x – 2

f(x) = (x – 2)(5 x + 4)(3 x + 2) c is a positive integer. The value of f(c) can be written as the product of two prime factors.

Deduce the value of f(c)

(3x – 7) is a factor of 3x³ – 4x² – 13x + 14

Work out the other two linear factors.

(x – 2) is a factor of ax⁴ – 3ax³ + 5x – 22

Work out the value of a.

(2x – 3) is a factor of 6x³ – 25x² + 28x – 6

Give all solutions as exact values.

f(x) = 2x³ + 11x² + 12x – 9

Use the factor theorem to show that (2 x – 1) is a factor of f(x).

Show that f(x) = 0 has exactly two solutions.

f(x) = 200x³ + 100x² – 18x – 9

Use the factor theorem to show that (2 x + 1) is a factor of f(x).

Hence solve f(x) = 0