Using the ac method factor the trimonials.
15x^2 + 31x+2=
15x^2 + 31x + 2
A*C = 15*2 = 30 = 1*30. Sum = 1+30=31=B.
15x^2 + (x+30x) + 2
Form 2 factorable binomials:
(15x^2+x) + (30x+2) =
x(15x+1) + 2(15x+1) =
(15x+1)(x+2).
To factor the trinomial 15x^2 + 31x + 2 using the AC method, follow these steps:
Step 1: Multiply the coefficient of the quadratic term (15) by the constant term (2). In this case, 15 × 2 = 30.
Step 2: Find two numbers that multiply to give the result from Step 1 (30) and add up to the coefficient of the linear term (31x). In this case, the numbers are 30 and 1 since 30 + 1 = 31.
Step 3: Rewrite the middle term (31x) using the numbers found in Step 2. So, the trinomial becomes 15x^2 + 30x + x + 2.
Step 4: Group the terms and factor them by grouping:
(15x^2 + 30x) + (x + 2)
Factor out the greatest common factor from each group:
15x(x + 2) + 1(x + 2)
Now, notice that we have a common factor, (x + 2), in both terms.
Step 5: Factor out the common factor:
(x + 2)(15x + 1)
So, by using the AC method, we have factored the trinomial 15x^2 + 31x + 2 as (x + 2)(15x + 1).