Question

show that ( x-2) is a factor of the polynomial f(x)= 2x³-3x²-17x+30 and hence factorize f(x).

Answer 1

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Answer 2

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Now,

f(x)

$2 {x}^{3} - 3 {x}^{2} - 17x + 30 \\ \\ = 2 {x}^{3} - 4 {x}^{2} + {x}^{2} - 2x - 15x + 30\\ \\ =2 {x}^{2} (x - 2) + x(x - 2) - 15(x - 2) \\ \\ = (x - 2)(2 {x}^{2} + x - 15) \\ \\ = (x - 2)(2 {x}^{2} + 6x - 5x - 15) \\ \\ = (x - 2)(2x(x + 3) - 5(x + 3)) \\ \\ = (x - 2)(x + 3)(2x - 5)$


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