Question

Factorize the following.

1.
$2x {}^{2} + 13x + 6$
​

Answer 1

Question:

Factorize:

$2{x}^{2} + 13x + 6$

Solution:

Factorising any polynomial means breaking a polynomial into simpler factors.

To factorize p(x)

By splitting the middle term,

$p(x) = 2{x}^{2} + 13x + 6 \\ p(x)= 2{x}^{2} + 12x + x + 6 \\ p(x) = 2x(x+6) +1(x+6) \\ p(x) = (2x+1)(x+6)$

Factors of $p(x) =2{x}^{2} + 13x + 6$ are (2x+1)(x+6)

Answer 2

So, we are given a polynomial 2x² + 13x + 6.

And we have to factorize it.

So, we can use two methods for solving this question, or we can say solving any polynomial.

• Splitting the middle term
• Completing the square

But we'll solve this question using splitting the middle term, that's because in the question we haven't been mentioned about completing the square.

So , let's start solving the question; :)

2x² + 13x + 6

For solving it further we'll need to multiply the coefficient of x² with the constant term, but we'll never use that in the polynomial as we are just supposing it.

*So, over equation looks like 2x² + 13x + 12, Note- We are just supposing it*

Now we have to find the factors of 12 such that when they are added, it is the same that of the coefficient of x, and the product is equal to the number itself.

So, as we go through the factors of 12, we get 12 × 1, 12 and 1 when added it become 13, i.e., the coefficient of x and when multiplied it remains 12.

So now let's put these 2 numbers with the coefficient x in place of 13x.

So, our equation look like;

2x² + 12x + 1x + 6

Now, let's simplify the above equation;

2x (x + 6) + 1 (x + 6)

Let's take (x + 6) as common;

(x + 6) (2x + 1)

Hence we factorized that equation 2x² + 13x + 6 to (x + 6) (2x + 1).