if (6r - x) is on factors of 18r^2 + 12ry - 3xr - 2xy, what is the other factor.

Question

a) 2y - 3r
b) 3r + 2y
c) 3r - 2x
d) 3r - 2y

Answer 1

Arrange the polynomial in decreasing power of r:
18r^2 + 12ry - 3xr - 2xy
=18r² + (12y-3x)r -2xy

Do a mental long division,
The first term is:
18r²/(6r) = 3r
The last term is:
-2xy/(-x) = 2y

Therefore the answer is 3r+2y.

Check:
(6r-x)(3r+2y)
=18r² + (12y-3x)r -2xy
The other factor is correct.