Answer:
1. C. 2c
2. [tex]3d^2(2d^2+3d-4)[/tex]
Step-by-step explanation:
A. We have been given an expression and we are asked to find the GCF of our given expression.
[tex]8c^3+12c^2+10c[/tex]
Let us find factors of each of our given terms.
Factors of [tex]c^3[/tex] are [tex]c*c*c[/tex],
Factors of [tex]c^2[/tex] are [tex]c*c[/tex],
We can see that c is the greatest common factor of [tex]c^3[/tex], [tex]c^2[/tex] and [tex]c[/tex].
Factors of 8 are: 1, 2, 4, 8.
Factors of 12 are: 1, 2, 3, 4, 6, 12.
Factors of 10 are: 1, 2, 5, 10.
The greatest common factor of 8,12 and 10 is 2.
So let us factor out 2c from our expression.
[tex]2c(4c^2+6c+5)[/tex]
Therefore, the greatest common factor of our given expression is 2c and option C is the correct choice.
2. We have been given a polynomial and we are asked to factor our given polynomial.
[tex]6d^4+9d^3-12d^2[/tex]
We will pull out the greatest common factor of the terms of our given polynomial.
We can see that GCF of [tex]d^4[/tex], [tex]d^3[/tex] and [tex]d^2[/tex] is [tex]d^2[/tex].
The GCF of 6, 9 and 12 is 3.
So let us factor out [tex]3d^2[/tex] from our polynomial.
[tex]3d^2(2d^2+3d-4)[/tex]
Therefore, the factored form of our given polynomial is [tex]3d^2(2d^2+3d-4)[/tex].