Factorization of polynomial

Evaluation

Find the quadratic equation whose roots are (i) 3 & -2 (ii) -1 & 8         (iii) ¾ & ½

General Evaluation

(1) When x² + bx + 2 is divided by x + 3 the remainder is 5. Find the value of b.

(2) If 2x² – (b – 4) x – 4 (b + 2) = 0, has equal roots, find the possible values of b.

(3) Factorise completely x³ + 5x² – 3x + 1

(4) Solve the following pair of equation simultaneously 4x – 3y = 17, 3x² – 2y² + x – 4y = 73

Reading Assignment

Further Maths 1 pages 66 – 69 Exercise 6a Q5, 9 and 10

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)

(c) (x + 1) (x + 2) (x – 3)                    (d) (x² + 1) (x + 1) (x – 2)

(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 )

(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)