Factor x² − 15x + 56
Worked out line by line the way a teacher would write it.
Answer
| Factored form | (x − 8)(x − 7) |
Step-by-step solution
3 steps-
1 Givenx^{2} - 15 x + 56
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2 Find two numbers whose product is c = 56 and whose sum is b = -15
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 = 56 and add up to b = -15.
List the pairs of numbers whose product is 56, with their signs, and pick the pair whose sum is -15.
(-8) \cdot (-7) = 56,\qquad (-8) + (-7) = -15 -
3 Factored form\left(x - 8\right) \left(x - 7\right)
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