We have to determine the complete factored form of the given polynomial
.
Let x= -1 in the given polynomial.
So, 
So, by factor theorem
(x+1) is a factor of the given polynomial.
So, dividing the given polynomial by (x+1), we get quotient as 
.
So, 
= (x+1).
= 
=![(x+1)[ 2x(3x-5)-3(3x-5)]](https://tex.z-dn.net/?f=%28x%2B1%29%5B%202x%283x-5%29-3%283x-5%29%5D)
= 
is the completely factored form of the given polynomial.
Option D is the correct answer.
Answer:
k = 13
Step-by-step explanation:
substitute x = x + 5 into f(x) , that is
f(x + 5) = (x + 5)² + 3(x + 5) - 10 ← expand squared factor using FOIL
= x² + 10x + 25 + 3x + 15 - 10
= x² + 13x + 30
compare this with f(x + 5) = x² + kx + 30
for the 2 expressions to be equal , then k = 13
The GCF is 2
Merry Christmas
Let’s say, hypothetically speaking, you chose the second marble without replacing the first marble so, events are hypothetically dependent. Events are dependent if the occurrence of one hypothetical event hypothetically does affect the likelihood that the other events occur. The probably of two or more dependent events A and B is the probability of A times the probability of B after A hypothetically occurs
P(A and B) = P(A) x P(B after A)
Choose the first marble
The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.
P(red)=1/4
Choose the second marble
Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.
P(green) = 1/3
The probability of choosing red and then, hypothetically, green is:
P(red and green) = P(red) x P(green)
=1/4 x 1/3
= 1/12
P(red and green) is hypothetically equal to 1/12 on a hypothetical account.
Final hypothetical answer: 1/12
