Question

factorize: 2x^2-x-6​

Answer 1

Answer:

2x²-x-6

Using the AC method

2x²-4x+3x-6

=2x(x-2)+3(x-2)

=(x-2)(2x+3)

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Answer 2

$\huge\underline\mathcal\purple{Answer:}$

(2x + 3) (x - 2)

$\huge\underline\mathcal\purple{Explaination:}$

2x² - x - 6

By using middle term splitting

1) Find the product of 1st and last term

=> 2 × - 6 = - 12

2) Find the factors of 12 in such way that addition or subtraction of that factors is the middle term ( here middle term is - 1x)

=> -4 × 3 = - 12

=> -4 + 3 = - 1

3) Write the center term using the sum of the two new factors, including the proper signs.

=> 2x² - 4x + 3x - 6

4)Group the terms to form pairs - the first two terms and the last two terms. Factor each pair by finding common factors.

=> 2x (x - 2) + 3 (x - 2)

5)Factor out the shared (common) binomial parenthesis.

=> (2x + 3) (x - 2)

About middle term splitting :

Splitting the middle term is a method for factoring quadratic equations.