Final answer:
To factor the trinomial m^2 + 19m + 21, find factors of the constant term 21 that add up to the coefficient of the middle term 19. The factors are 1 and 21, so the factored form is (m + 1)(m + 21).
Step-by-step explanation:
To factor the trinomial m^2 + 19m + 21, we need to find two binomials whose product equals the given trinomial. The binomials will have the form (m + a) and (m + b), where a and b are numbers. We need to find a and b such that (m + a)(m + b) equals the given trinomial. To do this, we can look for factors of the constant term 21 that add up to the coefficient of the middle term 19. The factors of 21 are 1, 3, 7, and 21, and the pairs of factors that add up to 19 are 1 and 21. Therefore, the factored form of the trinomial is (m + 1)(m + 21).
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