Completely factor the expression 16t3 − 50t2 + 36t. A. 2t(8t − 9)(t − 2)

B. Prime
C. 2t(8t + 9)(t + 2)

D. 2t(8t − 25t + 18)
  Completely factor the expression 48u4v4 − 18u2v2 − 3u8v5.

A. Nonfactorable
B. 3u2v2(16u2v2 − 6 − u6v3) C. 3(16u4v4 −6u2v2 − u8v5) D. u2v2(48u2v2 − 18 −3u6v3)

Completely factor the expression y2+ 12y + 35. A. (y + 7)(y − 5)
B. (y − 7)(y − 5)
C. (y + 7)(y + 5)

D. Prime

Please help me i am stuck

1. 16t^3 - 50t^2 + 36t =

2t(8t^2 - 25t + 18)
A*C = 8*18 = 144 = -9*(-16). Sum = -25 =
B.

2t((8t^2-16t) - (9t-18))
2t(8t(t-2) - 9(t-2)) =
2t(8t-9)(t-2)

4. y^2 + 12y + 35
35 = 7*5, Sum = 7 + 5 = 12 = B.
(y+7)(y+5)

To factor these expressions, we'll need to look for common factors and then use different factoring techniques depending on the structure of the expressions.

1. For the expression 16t^3 - 50t^2 + 36t, we notice that each term has a common factor of 2t. Factoring out this common factor gives us:
16t^3 - 50t^2 + 36t = 2t(8t^2 - 25t + 18)

Now, we need to factor the quadratic expression inside the parentheses. We're looking for two numbers whose product is (8 * 18 =) 144 and whose sum is -25. The numbers that satisfy these conditions are -9 and -16. So, we rewrite the quadratic as:
8t^2 - 25t + 18 = (8t - 9)(t - 2)

Finally, combining both factors, we get the completely factored form as:
16t^3 - 50t^2 + 36t = 2t(8t - 9)(t - 2)

Therefore, the correct answer is A: 2t(8t - 9)(t - 2).

2. For the expression 48u^4v^4 - 18u^2v^2 - 3u^8v^5, we can factor out a common factor of 3u^2v^2:
48u^4v^4 - 18u^2v^2 - 3u^8v^5 = 3u^2v^2(16u^2v^2 - 6 - u^6v^3)

Now, we need to factor the quadratic expression inside the parentheses. We're looking for two numbers whose product is (16 * -6 =) -96 and whose sum is 0 (since there is no middle term). Since no such numbers exist, the quadratic expression cannot be factored any further.

Therefore, the correct answer is B: 3u^2v^2(16u^2v^2 - 6 - u^6v^3).

3. For the expression y^2 + 12y + 35, we're looking for two numbers whose product is (1 * 35 =) 35 and whose sum is 12. The numbers that satisfy these conditions are 7 and 5. So, we can rewrite the expression as:
y^2 + 12y + 35 = (y + 7)(y + 5)

Therefore, the correct answer is A: (y + 7)(y - 5).

I hope this helps! Let me know if you have any other questions.