I need help trying to put the correct vocabulary words when solving this problem such as grouping, factor, prime factor, GCF, and perfect square, and please check and see if I am doing this correctly.

15x^2+31x+2

In my last problem I will be using the “ac method”

A*C = 15*2 = 30 = 1*30. Sum = 1+30=31=B.

Ac=30

Factors must add to 31

30+1 = 31

(x+2)(15x+1)

15x^2 + (x+30x) + 2

(15x^2+x) + (30x+2) =

X (15x+1) + 2(15x+1) =

15x^2 + 30x + x + 2

1 answer

(15x+1)(x+2) is correct
to check using FOIL
First 15 x^2
Outer 30 x
Inner 1 x
Last 1 * 2 = 2
so 15 x^2 + 31 x + 2
to check using distributive property of multiplication
15 x ( x+2) = 15 x^2 + 30 x
+1 (x+2) = x + 2
sum = 15 x^2 + 31 x + 2