POLYNOMIALS II (CONT)

Weekend Assignment

(1) Find the remainder when 2x³ – 4x² + x – 3 is divided by x + 3

(a) 84 (b) -86 (c) -64 (d) 76

(2) Factorise x⁴ – 1 completely (a) (x + 2) (x – 3) (b) (x + 1) (x – 1) (x² + 1)

(3) Given that p₁(x) = 2x⁴ + 3x³ – x² + 2x – 3 and p₁(x) = 3x³ + 2x + 2. Find 3p₁(x) – 3p₁(x)

(a) 6x⁴ – 3x² – 15 (b) 5x⁴ – 3x⁴ + 2x² – x + 3 (c) 6x⁴ = 9x³ – 15

(d) 6x⁴ + 18x² + 6x²

(4) Given that p(x) = x³ + 4x² – 3x + 1, find p( ½ )

(a)

(5) Given that p(x) = ax² + bx + 1, p( ½ ) = ½ and p(-2) = 23, determine the values of a and b

(a) a = -3, b = 4 (b) a = 2, b = -3 (c) a = 4, b = -3 (d) a = 3, b = -3

Theory

(1) Find the quotient and remainder when 2x⁴ – 3x³ + x² – 4x + 5 is divided by x² + 3x + 1

(2) If p₁ = 3x³ + 2x² – x + 2, p₂ = 2x² + x – 6 and p₃ = x³ + 3x² + 2x – 4, find

(i) p₃(p₁ + p₂) (ii) p₂ + p₃ – 3p₁ (iii) p₂ x (p₃ + p₁)