1. ## factoring

1.)Factor the expression: $\displaystyle 4y^2-49$
2.)Factor the expression completely: $\displaystyle 2x^2-16xy+32y^2$
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: $\displaystyle x^2+4 (over) x^2+4x$
7.)Simplify: $\displaystyle 3x^3(y-3) (over) 5y^2x^2$
8.) Divide $\displaystyle (15A^3-12A^2-9A)/3A^2$
9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
10.) $\displaystyle f(x)=-2x^2+7x+5$ Find $\displaystyle f (3/2)$

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

3. Originally Posted by jscalalamoboy

1.)Factor the expression: $\displaystyle 4y^2-49$
2.)Factor the expression completely: $\displaystyle 2x^2-16xy+32y^2$
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: $\displaystyle x^2+4 (over) x^2+4x$
7.)Simplify: $\displaystyle 3x^3(y-3) (over) 5y^2x^2$
8.) Divide $\displaystyle (15A^3-12A^2-9A)/3A^2$
9.) Is a function defined by {(-2,3), (0,1), (2,-2), (4,2)}? If so state it's domain.
10.) $\displaystyle f(x)=-2x^2+7x+5$ Find $\displaystyle f (3/2)$
Originally Posted by jscalalamoboy
And the last of it!
1.)Find the equation for the linear function:
$\displaystyle f(4)=-1$ $\displaystyle f(-2)=-4$
2. Sketch the graph of $\displaystyle f(x)=2x+1$
3. Sketch the graph of $\displaystyle f(x)=(2/3)x-3$

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: $\displaystyle 4y^2-49$

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

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

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

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

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

Hint: $\displaystyle 4x^2-2x=0 \Rightarrow 2x(2x-1) = 0$
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.

$\displaystyle l = 25+w$

$\displaystyle Area = 2600$

$\displaystyle lw = 2600$

$\displaystyle (25+w)w = 2600$

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