Question

X² + 3x +2= 0 solve by factorization

Answer 1

• x = -1 or -2

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Explanation:

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Let us first split the middle term 3x as 2x + 1x [because (2x) × (1x) = 2x² = x² × 2]

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`\dashrightarrow \sf \: \: \: x^2 + 3x + 2 = 0 \\ \\`

`\dashrightarrow \sf \: \: \: x^2 + 2x + 1x + 2 \\ \\`

`\dashrightarrow \sf \: \: \: x(x + 2) +1 (x + 2) \\ \\`

`\dashrightarrow \sf \: \: \: (x + 1)(x + 2) \\ \\`

• x² + 3x +2= 0 can be rewritten as (x + 1)(x + 2) = 0

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• So, the values of x for which x² + 3x +2= 0 are the same for which (x + 1)(x + 2)

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i.e., either x + 1 = 0 or x + 2 = 0.

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Now,

`\dashrightarrow \sf \: \: \: x + 1 = 0 \\ \\`

`\dashrightarrow \sf \: \: \:</p><p>x = -1 \\ \\`

`\dashrightarrow \sf \: \: \: x + 2 = 0 \\ \\`

`\dashrightarrow \sf \: \: \: x = -2.</p><p> \\ \\`

Hence,

`\dashrightarrow \sf \: \: \: x = -1 \: or \: -2 \\ \\`