Question

Frds please amswer this​

Answer 1

$\texttt{\textsf{\large{\underline{Question 1}:}}}$

We have to factorize the expression, given that,

= 12x² - 7x + 1

By splitting the middle term, we get,

= 12x² - 4x - 3x +1      [(-4) × (-3) = 12 and (-4) + (-3) = -7]

Take 4x as common from first two terms,

= 4x(3x - 1) - 3x + 1

Take -1 as common from last two terms,

= 4x(3x - 1) - 1(3x - 1)

Take 3x as common from both terms,

= (3x - 1)(4x - 1)

Which is our required answer.

$\texttt{\textsf{\large{\underline{Question 2}:}}}$

Given expression,

= 2x² + 7x + 3

By splitting the middle term, we get,

= 2x² + 6x + x + 3  [6 × 1 = 2 × 3 and 6 + 1 = 7]

Take 2x as common from first two terms,

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

Take 1 as common from last two terms,

= 2x(x + 3) + 1(x + 3)

Take (x + 3) as common from both terms,

= (2x + 1)(x + 3)

Which is our required answer.

$\texttt{\textsf{\large{\underline{Question 3}:}}}$

Given expression,

= 3x² - x - 4

By splitting the middle term,

= 3x² + 3x - 4x - 4  [3 - 4 = -1 and 3 × (-4) = -12]

Take 3x as common from first two terms,

= 3x(x + 1) - 4x - 4

Take -4 as common from last two terms,

= 3x(x + 1) - 4(x + 1)

Take (x + 1) as common from two terms,

= (x + 1)(3x - 4)

Which is our required answer.

$\texttt{\textsf{\large{\underline{Steps To Solve}:}}}$

The general form of a quadratic polynomial is - ax² + bx + c.

We have to split b into two parts (let x and y) whose product is equal to ac, i.e,

→ x + y = b and xy = ac.

Then, we can factorise by grouping method.

Answer 2

Answer:

( ¡ ) 12x^2 - 7x + 1

=> 12x^2 - 4x - 3x + 1

=> 4x ( 3x - 1 ) - 3x + 1

=> 4x ( 3x - 1) - 1 ( 3x - 1 )

=> ( 3x - 1 ) ( 4x - 1 )

(¡¡) 2x^2 + 7x + 3

=> 2x^2 + 6x + x + 3

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

=> 2x ( x + 3 ) + 1 ( x + 3 )

=> ( 2x +1 ) ( x + 3 )

(¡¡¡) 3x^2 - x - 4

=> 3x^2 + 3x - 4x - 4

=> 3x ( x + 1 ) - 4x - 4

=> 3x ( x + 1 ) - 4 ( x - 1 )

=> ( x + 1 ) ( 3x - 4 )

Step-by-step explanation:

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