alleryStart learning →Factor: x^2 + 7x + 12.
A(x+3)(x+4)
B(x+2)(x+6)
C(x+1)(x+12)
D(x-3)(x-4)
Answer & Solution
Correct answer: A. (x+3)(x+4)
1. Write the factors as two binomials with first terms x: (x )(x ).
2. Find two numbers that multiply to 12 and add to 7.
3. The numbers 3 and 4 multiply to 12 and add to 7.
4. Use 3 and 4 as the last terms of the binomials to get (x + 3)(x + 4), and check by multiplying: x squared + 4x + 3x + 12 gives back x squared + 7x + 12.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.2 Factor Quadratic Trinomials with Leading Coefficient 1_
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