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