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What is the lesser of two consecutive positive integers whose product is 90?
Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for multiplication, the equation is x(x + 1) = 90. Multiply by using the distributive property on the left side of the equation: x2 + x = 90. Put the equation in standard form and set it equal to zero: x2 + x - 90 = 0. Factor the trinomial: (x - 9)(x + 10) = 0. Set every factor equal to zero and solve: x - 9 = 0 or x + 10 = 0; x = 9 or x = -10. Since you are looking for a positive integer, reject the x-value of -10. Thus, the lesser positive integer would be 9.
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