Question

Find the HCF and LCM of 2x2 – 5x – 3 and x4 – 27x.​

Answer 1

Hello there!

Step-by-step explanation:

✧ First Expression = $\tt{ {2x}^{2} - 5x - 3}$

⇾ $\tt{ {2x}^{2} - (6 - 1)x - 3}$

⇾ $\tt{2 {x}^{2} - 6x + x - 3}$

⇾ $\tt{2x(x - 3) + 1(x - 3)}$

⇾ $\tt{(x - 3)(2x + 1)}$

✧ Second expression : $\tt{ {x}^{4} - 27x}$

⇾ $\tt{x( {x}^{3} - 27})$

⇾ $\tt{x( {x}^{3} - {3}^{3}} )$

⇾ $\tt \: x(x - 3)( {x}^{2} + 3x + 9)$

⇢ H.C.F = $\boxed{ \tt{(x - 3)}}$

⇢ L.C.M = $\boxed{ \tt{x(x - 3)(2x + 1)( {x}^{2} + 3x + 9)}}$

Hope this helps!