Question

Factorise: 2x²+3x-2
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Answer 1

`\sf \sf (x+2)(2x-1)`

Explanation:

In order to factorize the quadratic expression:

`\sf 2x^2 + 3x - 2`

We can use the middle-term factorization method.

We can start by finding two numbers that multiply to the product of the leading coefficient (2) and the constant term (2), which is (2 × 2) = -4, and subtract up to the coefficient of the middle term (3).

The two numbers that fit these criteria are 4 and 1 because:

4 × (1) = 4

4 + (-1) = 3

Now we can use these numbers to factorize the expression:

Replacing the value of 3 as (4-1), we get

`\sf \sf 2x^2 + (4-1)x - 2`

`\sf \sf 2x^2 + 4x -x - 2`

Taking common from each two terms:

`\sf 2x(x+2)-1(x+2)`

Taking common again and keeping remaining in the bracket.

`\sf \sf (x+2)(2x-1)`

Therefore, the factor form is :

`\sf \sf (x+2)(2x-1)`