Answer:
Work Shown:
The rule used is
I've included two questions. Hopefully you can help me with both. Thanks!
1 answer:
Answer:
1. value is 0; x-3 is a factor . . . . . . . . . . . . . .third choice
2. evaluates at x = -1; remainder is -11 . . . . first choice
Step-by-step explanation:
Dividing f(x) by (x -a) gives ...
f(x)/(x -a) = g(x) +r/(x -a) . . . . some quotient and a remainder r
If we multiply this expression by (x -a), we see ...
f(x) = (x -a)g(x) +r
so
f(a) = (a -a)g(a) +r . . . . . evaluate the above equation at x=a
f(a) = 0 +r
f(a) = r . . . . . . . . . a statement of the remainder theorem
If r=0, then x-a is a factor of f(x) = (x-a)g(x).
___
1. We have "a" = 3, and f(3) = 0. Therefore (x-3) is a factor.
__
2. We have "a" = -1, and f(-1) = -11. Therefore the remainder from division by (x+1) is -11.
You might be interested in
Use this property of logarithms:
Your equation transforms into:
Now, you have to apply the definition of a logarithm to express the equation in exponential form:
In case you don't remember, this is the definition of a logarithm:
The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).
Finally, solve the rational equation:
The correct answer is d.
Your equation transforms into:
Now, you have to apply the definition of a logarithm to express the equation in exponential form:
In case you don't remember, this is the definition of a logarithm:
The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).
Finally, solve the rational equation:
The correct answer is d.