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ALGEBRA - Factorising Quadratics

Factorise the quadratics first, and then solve the equations:
  1. x2+ 3x — 10 = 0
  2. x2— 5x + 6 = 0
  3. x2 — 2x + 1 = 0
  4. x2 — 4x + 3 =0
  5. X2 - X - 20 = 0
  6. x2— 4x — 5 = 0
  7. x2+ 6x — 7 = 0
  8. x2 + 14x + 49 = 0 / x2 — 2x — 15 = 0.
Rearrange into the form "x2 + bx + c = 0", then solve by factorising: a) x2+ 6x = 16 f) x2-21 = 4x k) x + 4 — .,1 =0 x b) x2 + 5x = 36 g) x2— 300 = 20x 1) x(x — 3) = 10 e) x2 + 4x = 45 h) x2 + 48 = 26x m)x2— 3(x + 6) = 0 d) x2 = 5x i) x2+ 36 = 13x n) x — = x 2 14 _ 0 = _12 e) x2= 11x j) x±5 o) x + 1 x x Solve x2— 1 = 0 4 The area of a rectangular swimming pool is 28 m2. The width is x m. The difference between the length and width is 3 m. Find the value of x. A rug has length x m. The width is exactly 1 m less than the length. x rn a) Write down an expression for the area of the rug. b) If the area of the rug is 6 m2, find the value of x. A triangle has height (x + 1) cm and a base of 2x cm. a) Write an expression for the area of the triangle and simplify it. b) If the area of the triangle is 12 cm2, find the value of x. 2X CM A square room has a floor of sides x metres. The height of the walls is 3 m. Write down an expression for: a) the floor area b) the area of all four walls. c) If the total area of the floor and the four walls is 64 m2, form a quadratic equation and solve it to find x.




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