Question

Factorise
$36x^{2} + 13x + 1$
​

Answer 1

Solution :-

36x² + 13x + 1

Split the middle term to get its factors ;

-> 36x² + 9x + 4x + 1

-> 9x (4x + 1) + 1 (4x + 1)

-> (9x + 1) (4x + 1)

Hence, the answer is :-

(9x + 1) (4x + 1).

Middle Term Splitting Method :-

Middle term splitting method is used to Factorise a polynomial. In this method, we have to split the middle term in such a case, its sum should be equal to the middle term and its product should be equal to the product of 1st & 3rd term.

In this question, we have splitted the middle term "13x" as "9x + 4x". "9x + 4x" is equal to "13x" i.e. the middle term and its product "9x × 4x" is equal to 36x² which is the product of 1st & 3rd term.

Answer 2

Answer :

(4x+1) (9x+1)

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Step-by-step explanation :

Given :

$36x^2+13x+1$

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We have to factorise

$36x^2+13x+1$

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We have to find 2 integer

whose product is 36 and

sum or difference is 13.

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Here we use hit and

trial method.

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Let us try to find 2 integer

whose product is 36 and

sum or difference is 13.

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1.    36 ⇒ 1 × 36 = 36 , Sum ⇒ 36 + 1 = 37 and  Difference ⇒ 36 - 1 = 35

2.   36 ⇒ 2 × 18 =36,   Sum ⇒ 18 + 2 = 20 and Difference ⇒ 18 - 2 = 16

3.   36 ⇒ 3 × 12 = 36,  Sum ⇒ 12 + 3 = 15 and  Difference ⇒ 12 - 3 = 10

4.   36 ⇒ 4 × 9 = 36,  Sum ⇒ 9 + 4  = 13 (✔️) and Difference ⇒ 9 - 4 = 5

5. 36 ⇒ 6 × 6 = 36,    Sum ⇒ 6 + 6  = 12 and Difference = 6 - 6 = 0.

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From above observation

we get perfect integer

whose product is 36

and sum is 13.

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Let us solve our question,

$\implies36x^2+13x+1\\\\\\=36x^2+9x+4x+1\\\\\\=9x(4x+1)+1(4x+1)\\\\\\=(4x+1)\:(9x+1)$