Factor 3x² + 12x + 9
Worked out line by line the way a teacher would write it.
Answer
| Factored form | 3(x + 1)(x + 3) |
Step-by-step solution
5 steps-
1 Given3 x^{2} + 12 x + 9
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2 Factor out the greatest common factor 3
3 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).
3 \left(x^{2} + 4 x + 3\right)Every term is divisible by 3.
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3 Find two numbers whose product is c = 3 and whose sum is b = 4
The goal is to write x² + bx + c as (x + p)(x + q). Multiplying that out gives x² + (p + q)x + p·q, so p and q must multiply to c = 3 and add up to b = 4.
List the pairs of numbers whose product is 3, with their signs, and pick the pair whose sum is 4.
1 \cdot 3 = 3,\qquad 1 + 3 = 4 -
4 Factored form\left(x + 1\right) \left(x + 3\right)
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5 Fully factored form3 \left(x + 1\right) \left(x + 3\right)
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