Question

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Answer 1

Required answer:-

Question :

• Factorise :

3b² - 13b + 4

Solution :

3b² - 13b + 4

3b² - 12b - 1b + 4

3b ( 1b - 4 ) - 1 ( 1b - 4 )

(1b - 4) (3b - 1)

As, - 12b - 1b

= -13b

and, ( -12 ) × ( -1 )

= 12

Method used:-

• By splitting the middle term

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Know how to solve :

When a trinomial is of the form ax² + bx + c ( or a + bx + cx² ), split b ( the coefficient of x in the middle term ) into two parts such that the sum of these two parts is equal to b and the product of these two parts is equal to the product of a and c.

Then factorise it by the grouping method.

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Answer 2

$\bigstar \:  \:  \:  \boxed{ \pink{ \:  \rm \: Factorize - \: {3b}^{2} - 13b + 4 }}$

Concept Used

Splitting of middle terms :-

• In order to factorize  x² + bx + c we have to find numbers p and q such that p + q = b and pq = c.

• After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

❥ Solution :-

Given

$\rm :  \implies \: {3b}^{2} - 13b + 4$

$\rm :  \implies \: {3b}^{2} - 12b - b + 4$

$\rm :  \implies \:3b(b - 4) - 1(b - 4)$

$\rm :  \implies \:(3b - 1)(b - 4)$

Hence,

$\boxed{ \pink{\rm \implies \: {3b}^{2} - 13b + 4 = (3b - 1)(b - 4)}}$