Create your own factorable trinomial. Explain, in complete sentences, how the trinomial is factored and the process used to check the factors for accuracy

Question

anonymous · Answer

$$x^{2} + 3x + 2$$

First, the factors of the third term, 2, are listed.
-2, -1, 1, 2
Second, pairs of factors of the third term are manipulated using addition to form a equation is is equal to the coefficient of the second term.
1 + 2 = 3 (Valid)
2 + 1 = 3 (Valid)
1 + (-2) = -1 (Invalid)
2 + (-1) = 1 (Invalid)
Third, two terms are multiplied such that each term is the sum of x and one of the terms in a valid equation (from step 2).
(x + 1)(x+2) = $$x^{2} + 3x + 2$$

To check this, simply expand the factored side of the equation using the distributive property and verify that both sides of the equation or equivalent.
$$x^{2} + 2x + x + 2$$ = $$x^{2} + 3x + 2$$