Question

Factorise x^4 + 2x^3 - 13x^2 - 14x + 20

Answer 1

Answer:

x^4 - 2x³ - 13x² + 14x + 24 = 0

x^4 - 2x³ - 15x² + 2x² + 14x + 24 = 0

x²(x²-2x-15) + 2(x²+7x+12) = 0

x²(x-5)(x+3) + 2(x+4)(x+3) = 0

(x+3)[x²(x-5) + 2(x+4)] = 0

(x+3)[x³-5x²+2x+8] = 0

(x+3)[x³-4x²+4x-x²-2x+8] = 0

(x+3)[x(x²-4x+4) - (x²+2x-8)] = 0

(x+3)[x(x-2)(x-2) - (x+4)(x-2)] = 0

(x+3)(x-2)[x(x-2)-(x+4)] = 0

(x+3)(x-2)[x²-2x-x-4] = 0

(x+3)(x-2)[x²-3x-4] = 0

(x+3)(x-2)(x-4)(x+1) = 0

x = -3, -1, 2, 4