Factor x3 – 4x2 + 7x – 28 by grouping. what is the resulting expression?
(x2 – 4)(x + 7)
(x2 + 4)(x – 7)
(x2 – 7)(x + 4)
(x2 + 7)(x – 4)

Consider polynomial You can group first two terms and last two terms:

In first brackets the common factor is and in second brackets the common factor is 7, then

the correct answer is D.

hello from mrbilldoesmath!

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

discussion:

in general, the factorization of a^3 + b^3 is

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

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

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

you,

mrb

(a + b) (a^2 - a b + b^2)