The expression cannot be factorised.
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This is a quadratic equation question which will have two answers: 2x2+42 = x2+13x 2x2-x2-13x+42 = 0 x2-13x+42 = 0 Factorising the equation gives you: (x-6)(x-7) = 0 Therefore: x = 6 or x = 7
42 + x2 = 13x ∴ x2 - 13x + 42 = 0 ∴ (x - 6)(x - 7) = 0 ∴ x ∈ {6, 7}
(x - 6)(x - 7)
x2 + 13x + 4 = (x + 6½ + √38¼)(x + 6½ - √38¼). To find this, we need to find p and q, where p + q = 13, pq = 4. 4 = 42¼ - 38¼ = (6½ + √38¼)(6½ - √38¼); thus, p = (6½ + √38¼), q = (6½ - √38¼).
x3 + 13x2 + 42x = x(x2 + 13x + 42) = x(x2 + 6x + 7x + 42) = x[x(x + 6) + 7(x + 6)] = x(x + 7)(x + 6)