Factor 4x² + 8x + 12
Worked out line by line the way a teacher would write it.
Answer
| Factored form | 4(x² + 2x + 3) |
Step-by-step solution
4 steps-
1 Given4 x^{2} + 8 x + 12
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2 Factor out the greatest common factor 4
4 divides every term, so it can be written once in front of a bracket. This is the distributive property used backwards: ab + ac = a(b + c).
4 \left(x^{2} + 2 x + 3\right)Every term is divisible by 4.
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3 The discriminant -8 is not a perfect square, so the trinomial has no rational factors
A trinomial splits into factors with whole numbers or fractions only when its discriminant b² − 4ac is a perfect square. -8 is not one, so the solutions contain a square root, and the quadratic formula finds them directly.
x^{2} + 2 x + 3 -
4 Fully factored form4 \left(x^{2} + 2 x + 3\right)
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