The DEV ProjectBy Matt

Problem 1

Graph: x³+9x²-64x-576 x³+7x²-50x-336

Given: x=-6

To solve this problem you have to get the numerator and denominator to simplest forms

Since there are four proportional terms we can group the numerator so we start of by factoring out the GCF

After doing that we end up with this because both sides are multiplied by (x+9)

Because of difference of squares we are able to simplify it even more

Since the denominator is not proportional we must long divide using -6(given)

To long divide you must find out what you have to multiply by x to get x³( its x²) then multiply that by the rest of the polynomial then subtract the new from the old and repeat

We come out with this

Reduced to

Now we must get what we need for the graph out of the equations

Factored Standard

Vertical Asymptote: -6,7 in denominator of factor form when we put 0 in for xHorizontal Asymptote: 1 in standard form taking highest power then dividingX int: -9,8 in numerator in factor form when we put 0 in for xY int: 12/7 taking to lowest powers from standard form and dividingHole: -8 in factored form when numerator and denominator are the same

The Graph

Question 2

• Mark has 200 feet of fence he want to make a fence around his garden and use his house as one of the sides to make the garden bigger. What is the maximum area Mark can have?

• Find domain and range when done

We must start of by making 2 equations that show perimeter and area

Since we have 200 feet of fence and we have 3 sides 2 of which are the same the equation is

200=2x+y

We must solve for a now

Start of by solving the Perimeter formula

200-2x=y

Put this equation in for y in the area equationA=x(200-2x)

A= -2x²+200x

To find the maximum value use the formula -b/2a to find the x of the vertex

-200/-4= 50Plug x into the equation to get the maximum

-2(50)²+200(50)=5000D:(-∞,∞)

No number x cannot equalR:(-∞,5000]

No minimum value and already found the maximum

Question 3

Distribute(x+4)(x-4)(x+6)(x-10)(x+2)

Start of by distributing (x+4) to (x-4)Then you should get

Which simplifies to

Distribute (x²-16) to (x+6)

You should get

Distribute (x³+6x²-16x-96) to (x-10)

You should come out with

Simplify to

Distribute (x⁴-4x³-76x²-256x+960) to (x+2)

Comes out to

Simplifies to

Question 4

Factor 10x²+82x+27=x²-2x

Get it Equal to Zero

Subtract x² then add -2xWhich should get you 9x²+84x+27=0

Set it up

(9x+ )( + )You must then find to numbers that multiply to

get 27 but add to get 84x

You should come up with (9x+3)(x+9)

X=3/9X=9