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1. what is the GCF of the terms of 8c^3+12c^2+10c?

A.2
B.4
C.2c
D.4c


2. How can the polynomial 6d^4+9d^3-12d^2 be factored l?

Sagot :

ShawnaMarieXDidn
If you pay attention 2 goes into 8, 10, & 12 and it looks like they all have one C. So what do you think it is lol?(:

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].

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