factoring

**jscalalamoboy** · April 29th 2008, 08:25 PM

Please Help!

1.)Factor the expression: $4y^2-49$
2.)Factor the expression completely: $2x^2-16xy+32y^2$
3.)Solve the equation: 4x^2-2x=0
4.)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.
5.)x and y vary inversely. If x=2.4 when y=130, find and equation relating x and y.
6.)Find the domain of the rational expression: $x^2+4 <font color=$ (over) x^2+4x" alt="x^2+4 (over) x^2+4x" />
7.)Simplify: $3x^3(y-3) <font color=$ (over) 5y^2x^2" alt="3x^3(y-3) (over) 5y^2x^2" />
8.) Divide $(15A^3-12A^2-9A)/3A^2$
9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
10.) $f(x)=-2x^2+7x+5$ Find $f (3/2)$

**jscalalamoboy** · April 29th 2008, 08:38 PM

And the last of it!
1.)Find the equation for the linear function:
$f(4)=-1$ $f(-2)=-4$
2. Sketch the graph of $f(x)=2x+1$
3. Sketch the graph of $f(x)=(2/3)x-3$

**Isomorphism** · April 29th 2008, 10:15 PM

Originally Posted by jscalalamoboy

Please Help!

1.)Factor the expression: $4y^2-49$
2.)Factor the expression completely: $2x^2-16xy+32y^2$
3.)Solve the equation: 4x^2-2x=0
4.)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.
5.)x and y vary inversely. If x=2.4 when y=130, find and equation relating x and y.
6.)Find the domain of the rational expression: $x^2+4 <font color=$ (over) x^2+4x" alt="x^2+4 (over) x^2+4x" />
7.)Simplify: $3x^3(y-3) <font color=$ (over) 5y^2x^2" alt="3x^3(y-3) (over) 5y^2x^2" />
8.) Divide $(15A^3-12A^2-9A)/3A^2$
9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
10.) $f(x)=-2x^2+7x+5$ Find $f (3/2)$

Originally Posted by jscalalamoboy

And the last of it!
1.)Find the equation for the linear function:
$f(4)=-1$ $f(-2)=-4$
2. Sketch the graph of $f(x)=2x+1$
3. Sketch the graph of $f(x)=(2/3)x-3$

You will have to show some work... You will learn only if you work out and get stuck somewhere. We will tell you how to continue....
Lets start:

1)Factor the expression: $4y^2-49$

Hint: $4y^2-49 = (2y)^2 - 7^2$ . Hmm it looks familiar.... Have you ever seen what $a^2 - b^2$ is?

2.)Factor the expression completely: $2x^2-16xy+32y^2$

Hint: Let $u = \frac{x}{y}$ , then $x = uy$
$2x^2-16xy+32y^2 = 2((uy)^2 - 8(uy)y + 16y^2) = 2y^2(u^2 - 8u^2 + 16)$

Does $(u^2 - 8u^2 + 16) = u^2 - 2(u)(4) + (4)^2$ remind you of anything?

3.)Solve the equation: $4x^2-2x=0$

Hint: $4x^2-2x=0 \Rightarrow 2x(2x-1) = 0$
Use this fact: for real numbers a and b, if ab = 0, then a=0 or b=0

4)The length of a rectangular garden is 25 feet longer than the width. If it covers an area of 2600 sq. ft., find the length and width.

Hint: Denote length by l and width by w.

$l = 25+w$

$Area = 2600$

$lw = 2600$

$(25+w)w = 2600$

$w^2 + 25w - 2600 = 0$

Now solve the quadratic...

Try these... If you did not understand anything.. ask
Then I will help you with remaining...

Good luck

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