Question

Need help on few math question?

for this perform indicated operations and simplify.

v-4/v-7 - v+1/v+7 + v-49/v^2-49

for this one factor the following

r^2+4r+4

this one subtract polynomials

(-9a^2+9a+4)(9a^2+4)

this one find the vertex, line symmetry, and the maxamum or maximum of f(x)

f(x)-1/2 (x+3)to the sec power +2

Answers

For the first one, you must simply make common denominators:

v - 4 v + 7 v + 1 v - 7 v - 49

___ * ____ - ____ * ____ + __________

v - 7 v + 7 v + 7 v - 7 (v + 7) (v - 7)

Simplify this to get:

v^2 + 3v - 28 v^2 - 6v - 7 v - 49

__________ - __________ + __________

(v + 7) (v - 7) (v + 7) (v - 7) (v + 7) (v - 7)

Add it all up to get this:

9v - 80

__________

(v + 7) (v - 7)

To factor r^2 + 4r + 4, you can use a neat method:

For a standard polynomial x^2 + bx + c, you can find two factors of c that add up to become b. We will call these two factors g and h. If these factors add up to become b, then the factored result will be (x + g) (x + h).

So, to factor this polynomial (r^2 + 4r + 4), we must find two factors of 4 that add up to four. 2 * 2 = 4 and 2 + 2 = 4, therefore, the new polynomial is (x + 2) (x + 2). What you could also have done is used the square polynomial pattern: (a + b) (a + b) = a^2 + 2ab + b^2. If we plug-in a = x and b = 2, we would get this: x^2 + 2x*2 + 2^2, which is x^2 + 4x + 4. Some people recognize this right off the bat and go to factoring.

Subtracting polynomials is simple, you must add like terms, that's all:

-9a^2 + 9a + 4 - (9a^2 + 4) = -9a^2 + 9a + 4 - 9a^2 - 4 (distribute the -1)

-18a^2 + 9a

And, if you want, you can factor this:

-9a(2a - 1)

To find the vertex, you must first find the axis of symmetry. First, let us simplify this equation:

f(x) = -(1/2)(x + 3)^2 + 2

(x + 3)^2 = x^2 + 6x + 9 (remember the pattern: a^2 + 2ab + b^2)

f(x) = -(1/2)(x^2 + 6x + 9) + 2

f(x) = -0.5x^2 - 3x - 4.5 + 2

f(x) = -0.5x^2 - 3x - 2.5

Right now, we can tell that this function has a maximum, and not a minimum, because a < 0.

To find the axis of symmetry, recall that the formula for this is -b/(2a). Applying this formula, we get 3/(-1) = -3. To find the vertex, you simply must input -3 for x:

-0.5(-3)^2 - 3(-3) - 2.5 = -9/2 + 9 - 2.5 = 2

The maximum for this function is 2, and the vertex is located at (-3, 2).

#1

23 - 87-7= ......

#2