Question

Factor completely
14a^2 - 68a + 48

Answer 1

5.48 only neglecting the -ve answer

Answer 2

It's easier to consider \(\large 2(7a^2-34a+24)\). Now note that since the middle term is negative and the constant term is positive, the factored form will look something like \(\large (a-b)(c-d)\) (in essence, 24 must be the product of two negative numbers). In this case, we note that the \(\large 7a^2-34a+24\) factors into the form \(\large (7a-\underline{ })(a-\underline{ })\) Note that 24 = (-1)(-24), (-2)(-12), or (-6)(-4). It turns out that the (-6)(-4) pair works the best because -34 = (7)(-4)+(1)(-6). Hence, we see that \(\large 14a^2-68a+48 = 2(7a-6)(a-4)\).

I hope this makes sense (since this is a little hard to explain)!

Answer 3

2 (7a-6) (a-4)