Which of the following is a facator of 4by-3bz+8dy-6dz?
a)4by-3bz
b)b+d
c)4y-3z
d)4b+3d
4 b y - 3 b z + 8 d y - 6 d z =
y ( 4 b + 8 d ) + z ( - 3 b - 6 d ) =
y [ ( 4 ( b + 2 d ) ] + z [ ( - 3 ) ( b + 2 d ) ] =
4 y ( b + 2 d ) - 3 z ( b + 2 d) =
( b + 2 d ) ( 4 y - 3 z )
Answer c)
To find out which of the options is a factor of the given expression 4by - 3bz + 8dy - 6dz, we need to see if any of the options can be divided into the expression evenly, resulting in no remainder.
Let's test each option one by one:
a) 4by - 3bz
To check if this is a factor, we can divide the given expression by 4by - 3bz:
(4by - 3bz + 8dy - 6dz) ÷ (4by - 3bz)
Dividing the expression, we get:
= 1 + 2dy - 6dz ÷ (4by - 3bz)
Since there is a remainder after division, option a) is not a factor of the expression.
b) b + d
Dividing the expression by b + d:
(4by - 3bz + 8dy - 6dz) ÷ (b + d)
Dividing the expression, we get:
= 4y - 3z + (8dy - 6dz) ÷ (b + d)
Again, there is a remainder after division, so option b) is not a factor.
c) 4y - 3z
Dividing the expression by 4y - 3z:
(4by - 3bz + 8dy - 6dz) ÷ (4y - 3z)
Dividing the expression, we get:
= b + 8d - 6dz ÷ (4y - 3z)
Once again, there is a remainder after division, so option c) is not a factor.
d) 4b + 3d
Finally, let's divide the expression by 4b + 3d:
(4by - 3bz + 8dy - 6dz) ÷ (4b + 3d)
Dividing the expression, we get:
= y - bz - 6dz ÷ (4b + 3d)
Here, we can see that there is no remainder, meaning that option d) is a factor of the given expression.
Therefore, the correct answer is d) 4b + 3d.