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Find two integers r and s that multiply to -12 and sum to 1.

Mathematics

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−3 and 4-3 \text{ and } 4

Here is the completed table, assuming the goal is to find two integers rr and ss that multiply to −12-12 and sum to 1 (as is common for factoring x2+x−12x^2 + x - 12):

Factors of -12Product of the two factorsSum of the two factorsResult
1 and -121×(−12)=−121 \times (-12) = -121+(−12)=−111 + (-12) = -11Product = -12 but sum ≠\neq 1
-1 and 12(−1)×12=−12(-1) \times 12 = -12(−1)+12=11(-1) + 12 = 11Product = -12 but sum ≠\neq 1
2 and -62×(−6)=−122 \times (-6) = -122+(−6)=−42 + (-6) = -4Product = -12 but sum ≠\neq 1
-2 and 6(−2)×6=−12(-2) \times 6 = -12(−2)+6=4(-2) + 6 = 4Product = -12 but sum ≠\neq 1
3 and -43×(−4)=−123 \times (-4) = -123+(−4)=−13 + (-4) = -1Product = -12 but sum ≠\neq 1
-3 and 4(−3)×4=−12(-3) \times 4 = -12(−3)+4=1(-3) + 4 = 1Product = -12 and sum = 1

Based on the table, the two integers, rr and ss, that multiply to −12-12 and sum to 1 are −3 and 4\boxed{-3 \text{ and } 4}.

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