Question

Factorise : 3x2 + 7x + 2​

Answer 1

Question:-

Factorise : 3x² + 7x + 2

Answer:-

• Value of x is –1/3 or –2.

To find:-

• Value of x

Solution:-

According to question,

$\large{ \tt : \implies \: \: \: \: \: 3 {x}^{2} + 7x + 2 = 0}$

Splitting the middle term:-

$\large{ \tt : \implies \: \: \: \: \: 3 {x}^{2} + 6x + x + 2 = 0}$

$\large{ \tt : \implies \: \: \: \: \: 3x(x + 2) + 1(x + 2) = 0}$

$\large{ \tt : \implies \: \: \: \: \: (x + 2)(3x + 1) = 0}$

$\large{ \tt : \implies \: \: \: \: \: x + 2 = 0 \: \: \: \: \: \boxed{or} \: \: 3x + 1 = 0}$

Either,

$\large{ \tt : \implies \: \: \: \: \: x + 2 = 0}$

$\large{ \tt : \implies \: \: \: \: \: x = - 2}$

Or,

$\large{ \tt : \implies \: \: \: \: \: 3x + 1 = 0}$

$\large{ \tt : \implies \: \: \: \: \: 3x = - 1}$

$\large{ \tt : \implies \: \: \: \: \: x = \frac{ - 1}{3} }$

Hence,

Value of x is –1/3 or –2.

Answer 2

Given

• 3x² + 7x + 2

⠀

Solution

• We will split the middle term.

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {3x^2 + 6x + x + 2}$

⠀

★ Taking common out of the bracket

$\tt:\implies\: \: \: \: \: \: \: \: {3x(x + 2) + 1(x + 2)}$

⠀

$\tt:\implies\: \: \: \: \: \: \: \: {(3x + 1) (x + 2)}$

⠀

★ Put the factors = 0

$\tt\longrightarrow{3x + 1 = 0}$

$\tt\longrightarrow{3x = -1}$

⠀

$\orange{\boxed{\implies{\sf{\purple{x = \dfrac{-1}{3}}}}}}$

⠀

★ Similarly

$\tt\longrightarrow{x + 2 = 0}$

$\orange{\boxed{\implies{\sf{\purple{x = -2}}}}}$

⠀

Hence,

$\tt\longmapsto{x = \dfrac{-1}{3}}$

⠀

$\tt\longmapsto{x = -2}$

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