Which shows one way to determine the factors of 4x^3+x^2-8x-2

For this case we must factor the following expression:

We group the first two and the last two terms:

We factor the highest common denominator of each group:

We take the common factor

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb