factorising cubics (example 1) factorise x 3 + 7x 2 + 7x 15 given that (x + 3) is a factor x 3 + 7x...

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Factorising Cubics (Example 1) orise x 3 + 7x 2 + 7x 15 given that (x + 3) is a fact 3 + 7x 2 + 7x 15 = (x + 3)(x 2 + ax 5) + 7x 2 + 7x 15 = x 3 + ax 2 5x + 3x 2 + 3ax 15 Equate coefficients of x 2 7 = a + 3 a = 4 x 3 + 7x 2 + 7x 15 = (x + 3)(x 2 + 4x 5) Expand the brackets = (x + 3)(x + 5)(x 1)

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Factorising Cubics (Example 1) Factorise x 3 + 7x 2 + 7x 15 given that (x + 3) is a factor x 3 + 7x 2 + 7x 15 = (x + 3)(x 2 + ax 5) x 3 + 7x 2 + 7x 15 = x 3 + ax 2 5x + 3x 2 + 3ax 15 Equate coefficients of x 2 7 = a + 3 a = 4 x 3 + 7x 2 + 7x 15 = (x + 3)(x 2 + 4x 5) Expand the brackets = (x + 3)(x + 5)(x 1)
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Factorising Cubics (Example 2) Factorise 6x 3 + 7x 2 9x + 2 given that (2x 1) is a factor 6x 3 + 7x 2 9x + 2 = (2x 1)(3x 2 + ax 2) 7x 2 = 2ax 2 3x 2 Equate coefficients of x 2 7 = 2a 3 2a = 10 6x 3 + 7x 2 9x + 2 = (2x 1)(3x 2 + 5x 2) Expand the brackets for the x 2 term a = 5 =(2x 1)(3x 1)(x + 2)

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