Question

What two numbers multiply into -42 but add into 19

Answer 1

21 and -2
-2 x 21 = -42
21 + (-2) = 19

Answer 2

Answer:

  -2 and 21

Step-by-step explanation:

You can generally answer questions of this type by considering factor pairs of the product. When the product is negative, the numbers in each pair will have opposite signs. You can save some effort by paying attention to which number needs to be largest in magnitude.

  42 = (-1)(42 = (-2)(21) = (-3)(14) = (-6)(7)

Sums of the factor pairs are, respectively, 41, 19, 11, 1. The factor pair that has a sum of 19 is -2 and 21.

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Additional comment

You only need to consider a number of pairs equal to half the number of divisors.

The prime factorization of 42 is 42 = 2·3·7. Each of these primes has an exponent of 1. The number of divisors is the product of these exponents, each increased by 1: (1+1)(1+1)(1+1) = 8. So, we only need to consider 4 factor pairs. Above, we have listed all of them that will have a positive sum for the product -42.