The expression \(3x^2 + 14x + 8\) can be written in the form\((3x + A)(x + B)\) where \(A\) and \(B\) are integers. What is the value of \(A - B\)?

Guest May 20, 2022

#2**0 **

The expression can be factored by using the X method or the multiplying method,

which is (3x+4)(x+2). A and B are 4 and 2, so A - B = 2. btw the multiplying method is where you multiply 8 by 3 and get 24, and 12*2=24 12+2=14,

3*4=12, so (3x+4) comes together. then the 2 is prime, so it goes on the other side. ( it's a little confusing at first but it gets better )

hipie May 20, 2022

#3**0 **

Wait.. I got a different answer.

To factor the equation \(3x^2 + 14x + 8\), we need to find a pair of numbers that sum to 14 (middle number, coefficient of x) and multiply to 24 (product of 3 and 8, x^2 coefficient)

The 2 numbers that satisfy this pair are 2 and 12. Now, we rewrite the equation as: \(3x^2 + 12x +2x+ 8\)

Now, we can factor the first 2 terms and last 2 terms seperatelty. This gives us: \(3x(x+4) + 2(x+4)\).

However, because both have an \((x+4)\) term in them, we can add them, giving us:\((3x+2)(x+4)\).

This means that \(A = 2\) and \(B = 4\), meaning \(A - B = 2 - 4 = \color{brown}\boxed{-2}\)

BuilderBoi May 20, 2022