Question

The factors of \[2{x^2} - 3x - 2\] are
A.\[\left( {2x - 1} \right)\left( {x + 2} \right)\]
B.\[\left( {2x + 1} \right)\left( {x - 2} \right)\]
C.\[\left( {x + 1} \right)\left( {x - 2} \right)\]
D.\[\left( {x - 1} \right)\left( {x + 2} \right)\]

Answer 1

Hint: Split the middle term of the given polynomial and after splitting the middle term take the terms common from first and second term and third and fourth term. And after taking common action our required answer will be obtained.

Complete step-by-step answer:
\[2{x^2} - 3x - 2\]
The given polynomial can be written as
\[ = 2{x^2} - 4x + x - 2\] …(1)
Now, take the terms common from (1)
\[ = 2x\left( {x - 2} \right) + \left( {x - 2} \right)\]
\[ = \left( {2x + 1} \right)\left( {x - 2} \right)\]
Option (b) is the correct answer.

Note: Split the middle term properly without any mistake. Collect common terms without any mistake. Keep in mind use while taking common take sign convention properly.
Quadratic factorization using splitting of the middle term: In this method splitting of the middle term into two factors. In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to first and last term.