PLS HELP ME!!

I really need the answers to these few questions I need toturn them in ASAP.

Factor out the GCF (Greatest Common Factor)
Hint: What can you divide every term by?
14. 3b^4-9b^2+6b

15. 4g^2+8g

16. 45c^5-63c^3+27

Factor each polynomial.
HINT: Change from x^2+bx+c to (x+p)(x+q) where p and q are the factors of c that add to b.
17. x^2+8x+12 = (x+2)(x+6)

18. t^2-5t-14

You did fine on 17. What is happening with the other problems?

14. 3b
15. 4g
16. If 27 does not have some value of c, 9
18. -7, 2

14. 3b^4 - 9b^2 + 6b = 3b(b^3 - 3b + 2).

16. 45c^5 -63c^3 + 27. = 9(5c^5 - 7c^3 + 3).

Sure! I'd be happy to help you with these questions. Let's go through them one by one.

14. To factor out the greatest common factor (GCF) of the given expression 3b^4 - 9b^2 + 6b, we need to find the common factor that can be divided from each term. In this case, the common factor is 3b.

So, we can divide each term by 3b, which gives us:

3b^4 / (3b) - (9b^2) / (3b) + 6b / (3b)

Simplifying this further, we get:

b^3 - 3b + 2

Therefore, the factored expression is b^3 - 3b + 2.

15. Similarly, to factor out the GCF in 4g^2 + 8g, we find that the common factor is 4g. Dividing each term by 4g, we get:

4g^2 / (4g) + 8g / (4g)

Simplifying this gives us:

g + 2

So, the factored expression is g + 2.

16. For the expression 45c^5 - 63c^3 + 27, we can factor out the GCF by finding the common factor between the terms. In this case, the common factor is 9c^3. Dividing each term by 9c^3, we have:

45c^5 / (9c^3) - 63c^3 / (9c^3) + 27 / (9c^3)

Simplifying this further gives us:

5c^2 - 7 + 3 / (c^3)

Therefore, the factored expression is 5c^2 - 7 + 3 / (c^3).

17. Moving on to factoring the polynomial x^2 + 8x + 12, we can use the hint provided. We need to find two factors of 12 that add up to 8, which are 2 and 6.

So, we rewrite the polynomial as:

(x + 2)(x + 6)

Therefore, the factored expression is (x + 2)(x + 6).

18. Finally, let's factor the polynomial t^2 - 5t - 14. Using the hint given, we need to find two factors of -14 that add up to -5. The factors are -7 and 2.

Rewriting the polynomial using these factors, we have:

(t - 7)(t + 2)

Therefore, the factored expression is (t - 7)(t + 2).

I hope this helps you in turning in your assignment. Remember, understanding the process of factoring will help you solve similar problems in the future!