Question

Factorise 6x2 - x - 2

Answer 1

`\boxed{(2x + 1)(3x - 2)}`

Explanation:

`\mathsf{ {6x}^(2) - x - 2}`

Write -x as a difference

`\mathsf{6 {x}^(2) + 3x - 4x - 2}`

Factor out 3x from the expression

`\mathsf{3x(2x + 1) - 4x - 2}`

Factor out -2 from the expression

`\mathsf{3x(2x + 1) - 2(2x + 1)}`

Factor out 2x + 1 from the expression

`\mathsf{(2x + 1)(3x - 2)}`

`\mathcal{Hope \: I \: helped!}`

`\mathcal{Best \: regards!}`

Answer 2

`\boxed{\sf (3x - 2)(2x + 1)}`

Explanation:

`\sf Factor \: the \: following: \\ \sf \implies 6 {x}^(2) - x - 2 \\ \\ \sf The \: coefficient \: of \: {x}^(2) \: is \: 6 \: and \: the \: constant \\ \sf term \: is \: - 2. \: The \: product \: of \: 6 \: and \: - 2 \\ \sf is \: - 12. \\ \sf The \: factors \: of \: - 12 \: which \: sum \: to \\ \sf - 1 \: are \: 3 \: and \: - 4. \\ \\ \sf So, \\ \sf \implies 6 {x}^(2) - 4x + 3x - 2 \\ \\ \sf \implies 2x(3x - 2) + 1(3x - 2) \\ \\ \sf \implies (3x - 2)(2x + 1)`