Question

Find the HCF and LCM of the following: f(x)=40(2x³-5x²-3x) and g(x)=35(x⁴-27x)

Answer 1

$f(x) = 40x(2 {x}^{2} - 5x - 3) \\ \: \: \: \: \: \: = 40x(2 {x}^{2} - 6x + x - 3) \\ = 40x(2x(x - 3) + 1(x - 3)) \\ = 40x(2x + 1)(x - 3) \\ = 2 \times 2 \times 2 \times 5x(2x + 1)(x - 3) \\ \\ g(x) = 35 ({x}^{4} - 27x) \\ = 35x( {x}^{3 } - 27) \\ = 35x( {x}^{3} - {3}^{3} ) \\ = 35x(x - 3)( {x}^{2} - 3x + 9) \\ = 5 \times 7 \times x(x - 3)( {x}^{2} - 3x + 9) \\ \\ so \: hcf \: is \: = 5x(x - 3) \\ lcm = {2}^{3} \times 5 \times 7 \times x \\ (2x + 1)(x - 3)( {x}^{2} - 3x + 9) \\ = 280x(2x + 1)(x - 3)( {x}^{2} - 3x + 9)$