Question

Factorise 2x^2+3x-2​

Answer 1

(x+2)(2x-1)

Explanation:

I used a little guess and check for this so bear with me :P

The final answer would always have to be two brackets with x and the relevant variables.

2x²: You know the possible factors that can be multiplied together would be 2x and x. Each factor would have to be in different brackets, so we get (x + smth else)(2x +smth else)

When factorising quadratic expressions, you need to find the correct pair of factors, that when multiplied together, becomes (-2). They also need to become 3x when they are multiplied with the term in the bracket (either x or 2x) and then added together.

Possible factors:

1. 1 × (-2) = (-2)

2. -1 × 2 = (-2)

Assume (x+1)(2x-2) = 2x² -2x +2x -2

= 2x² +0 - 2 (Wrong)

Assume (x-2)(2x+1) = 2x² +x -4x -2

= 2x² -3x -2 (Wrong)

Assume (x-1)(2x+2) = 2x² +2x -2x -2

= 2x² +0 - 2 (Wrong)

Assume (x+2)(2x-1) = 2x² -x +4x -2

= 2x² +3x -2 (Correct!)

Thus, (x+2)(2x-1) is the answer.

Answer 2

QUESTION:

Factorise 2x^2+3x-2

ANSWER:

`\green{{(x + 2) × (2x - 1)}}`

STEP-BY-STEP EXPLANATION:

Write
`{3x}` as a diffrence

2x² +
`\red{{3x}}` - 2

2x² +
`\red{{4x - x}}` - 2

Factor out
`{2x}` from the expression

`\red{{2x² + 4x}}` - x - 2

`\red{{2x×(x + 2)}}` - x - 2

Factor out the negative sign from the expression

2x² + 4x -
`\red{{x - 2}}`

2x × (x + 2) -
`\red{{(x + 4)}}`

Factor out
`{x + 2}` from the expression

`\red{{2x× (x + 2) - (x + 2}}`

`\green{\boxed{(x + 2) × (2x - 1)}}`

hope it's helps