Help I'm stuck
I need to factor a trinomial expression using the AC method
15x^2 + 31x + 2
ac=30
factors must add to 31
30+1 = 31
(x+2)(15x+1)
or, regrouping a bit
15x^2 + 30x + x + 2
15x(x+2) + 15x+2
(15x+1)(x+2)
thank you
15x(x+2) + 1(x+2)
No problem! I can help you factor the trinomial expression using the AC method step by step.
The AC method, also known as the "splitting the middle term" method, is a technique used to factor trinomials of the form ax^2 + bx + c.
Step 1: Multiply the coefficient of the x^2 term (a) by the constant term (c). In this case, a = 15 and c = 2, so ac = 15 * 2 = 30.
Step 2: Find two numbers that multiply to give ac (30) and add up to the coefficient of the x term (b). In this case, b = 31. So, we need to find two numbers that multiply to give 30 and add up to 31.
The two numbers that fit this criteria are 30 and 1.
Step 3: Rewrite the middle term (31x) using the two numbers found in Step 2 (30 and 1). This is done by splitting the middle term into two terms and replacing them with the numbers found.
So, 31x can be written as 30x + 1x.
Now, your trinomial expression becomes:
15x^2 + 30x + 1x + 2.
Step 4: Group the terms in pairs and factor out the greatest common factor from each group.
In the first group, we can factor out 15x. So, we get:
15x(x + 2).
In the second group, we can factor out 1. So, we get:
1(x + 2).
Step 5: Notice that both groups have a factor of (x + 2) in common. Factor out this common factor.
So, your factored expression becomes:
(15x + 1)(x + 2).
And that's the final factored form of the trinomial expression 15x^2 + 31x + 2 using the AC method!