A board of length (6x4 + 9x2- 21) meters is to be cut into three pieces of the same length. Find the length of each piece.

(2x⁴ + 3x² -7)

Step-by-step explanation:

Length is

It is to be divided by 3.

Note when dividing the polynomial by any value each of the terms is divides by same value:

Each piece is (2x⁴ + 3x² -7) meters long

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