Question

factorise X square + 3 X + 2​

Answer 1

Answer:

$\large{\underline{\boxed{\sf (x+1)(x + 2)}}}$

Step-by-step explanation:

Given that ;

x² + 3x + 2

We can easily factorise it by splitting the middle term. We need two numbers such that their product is 2 and sum is 3.

Such two numbers can be 2 and 1.

$\sf x {}^{2} + 3x + 2 \\ \\ \implies \sf {x}^{2} + (1 + 2)x + 2 \\ \\ \implies \sf {x}^{2} + x + 2x + 2 \\ \\ \implies \sf x(x + 1) + 2(x + 1) \\ \\ \implies \sf (x + 1)(x + 2)$

Further, If you need the value of x,

• (x + 1) = 0 ⇒ x = - 1
• (x + 2) = 0 ⇒ x = - 2

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Hence, the answer is (x + 1)(x + 2).

Answer 2

Answer:

$\huge{\red{\boxed{\boxed{\green{\sf{(x+2)(x+1)}}}}}}$

$\huge{\red{\boxed{\boxed{\green{\sf{x=-1,-2}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}}$

$\: \: \: \: \: \: \:{ \pink {given}}\\ {\green{\boxed{ {x}^{2} + 3x + 2 = 0}}} \\ \\ { \blue{to \: find}} \\{ \red{ \boxed{x = ?}}}$

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${ \orange{\boxed{FIRST \: METHOD}}} \\ \\ {\pink{middle \: term \: spliting}} \\ \to {x}^{2} + 3x + 2 = 0\\ \to {x}^{2} + 2x + x + 2 = 0\\ \to x(x + 2) + 1(x + 2) = 0\\ \to (x + 2)(x + 1) = 0 \\ \\ \to x + 2 = 0 \\ \to x = - 2 - - - - - 1st \: zeroes \\ \\ \to \: x + 1 = 0 \\ \to \: x = - 1 - - - - - 2nd \: zeroes \\ \\ { \orange {\boxed{SECOND \:METHOD}}} \\ \\ {\pink{quadratic \: formula}} \\ {x}^{2} + 3x + 2 = 0 \\ d = {b}^{2} - 4ac \\ d = {3}^{2} - 4 \times 2 \\ d = 9 - 8 \\ d = 1 \\ \\ x = \frac{ - b + - \sqrt{d} }{2a} \\ x = \frac{ - 3 + 1}{2} \\ x = - 1 - - - - - 1st \: zeroes \\ x = \frac{ - 3 - 1}{2} \\ x = \frac{ - 4}{2} \\ x = - 2 - - - - - 2nd \: zeroes$

$\huge{\red{\boxed{\boxed{\green{\sf{(x+2)(x+1)}}}}}}$

$\huge{\red{\boxed{\boxed{\green{\sf{x=-1,-2}}}}}}$

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