alleryStart learning →Factor: 2x + x^2 - 48.
A(x+6)(x-8)
B(x-6)(x+8)
C(x-4)(x+12)
D(x+4)(x-12)
Answer & Solution
Correct answer: B. (x-6)(x+8)
1. Rewrite the expression in decreasing degree order first: x squared + 2x - 48.
2. Find two numbers that multiply to -48 and add to 2.
3. Testing the factor pairs of -48, the pair -6 and 8 multiplies to -48 and adds to 2.
4. Use -6 and 8 as the last terms to get (x - 6)(x + 8), and check: x squared + 8x - 6x - 48 gives back x squared + 2x - 48.
_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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