Hey guys, I need help w/ these 8 problems. I have to use factoring to solve.....?

Question

(x - 2)(2x - 5) = 0

x2 + 6x - 27 = 0

x2 + 6 = -5x

5x2 = 2x - 7x2

3x2 + 6x = 2x2 - 9

5x2 - 11x + 2 = 0

x2 - 9 = 0

The area of a rectangle is 24 square meters. Find the length and width of the rectangle if its length is 2 meters greater than its width. Use an equation and the formula ® area of a rectangle = (width)(length).

Answer 1

(1) (x - 2)(2x - 5) = 0
This one is easy because it is already factored. If the product is zero, it means that one of the terms is zero, so there is one answer for each:

x - 2 = 0
x = 2

or

2x - 5 = 0
2x = 5
x = 5/2

x = 2 and x = 5/2 are the solutions.

(2) x^2 + 6x - 27 = 0

That factors to (x + 9)(x - 3), so the solutions are x = -9 and x = 3.

(3) x2 + 6 = -5x
x^2 + 5x + 6 = 0
(x + 2)(x + 3) = 0

X = -2 and x = -3 are the two solutions.

(4) 5x^2 = 2x - 7x^2
12x^2 - 2x = 0
2x(6x - 1) = 0

x = 0 or x = 1/6

(5) 3x^2 + 6x = 2x^2 - 9
x^2 + 6x + 9 = 0
(x + 3)(x + 3) = 0

x = -3. This one has only one solution, because x = -3 causes both terms in the product to be zero.

(6) 5x^2 - 11x + 2 = 0
(5x - 1)(x - 2) = 0

x = 1/5 and x = 2 are the solutions.

(7) x^2 - 9 = 0
(x + 3)(x - 3) = 0

x = 3 and x = -3 are the two solutions.

(8) L = W + 2
A = WL

Use the second equation, and substitute the first (change "L" to "W+2") and also the known value for area:

A = W * L
24 = W * (W + 2)
W^2 + 2W - 24 = 0
(W + 6)(W - 4) = 0

The solutions are W=-6 and W=4, but we can ignore the negative solution. So we know that the width is 4. This means tha the the length, which is two more than the width, is 6.

Answer 2

I'm not sure what you are asking for the first problem. It is already in factored form. To expand it, just use the foil method (fancy talk for multiplying between the two) by starting with just the values in one part and mulitply them number by number by the values in the other part taking care to remember sign values. So it would be 2x*x+2x*(-2)+(-5)*x+(-5)*(-2). Solve these easy products and that is the expanded form. I hope it's what you want.

The trick to solving the next one is to just figure what numbers added together can make the middle term and when the same numbers are multiplied can make the last term. Sometimes you will need to combine a negative and a positive number to get the right set. +9 and -3 work well here.
9 + (-3) = 6
9 * (-3) = -27
So these would be the numbers in the factored parts.
(x+9)(x-3)=0

The next three problems are solved basically the same way but before you start you will need to move the value on the other side of the equal sign to the side with the rest of the numbers. From there just find the numbers that match the sum and product as before.

For the third problem

2 + 3 = 5
2 * 3 = 6

For the fourth move all values to one side again (remember proper signs!!)

This one is a little tricky because there is no end term. So you start with 12x^2-2x. There is no end term but both of the terms that you do have, have x in them. Factor out as much as you can (but it has to be a value you can take from both terms) and that is the simplified factored form. The largest value you can take out is a 2x from both terms leaving
2x(6x-1). A quick expansion will show that this is the same as the original equation.

For the fifth problem, move all terms to one side again. Then it should be of the form x^2 +6x +9=0
3+3=6
3*3=9

In the sixth problem you have a number in front of the x^2, don't worry it doesn't mess things up too much, but it does change the way you calculate because now that 5 can affect the middle term.

so what you start with is 5x^2-11x+2=0

The factored from is going to look like this: (x+_)(5x+_)
The 5 is going to be used to solve for the -11 because it has an x included. But you will still have to add the other unknown term to get the -11 too.

5 * (-2)+(-1) = -11
(-2) * (-1) = 2 (this part doesn't have an x so you just use the 2 and 1)

The seventh problem is missing the middle term. What this means is that the middle term was cancelled out. So you want to find the numbers that make a -9 when multiplied but a 0 when added.

the obvious choice being

3 + (-3) =0
3 * (-3) = -9

The last problem is only difficult until you write out what it gives you. You have a distance (let's call it x) that is 2 meters longer than another side. This means that for x meters they are the same size and then one side is just 2 meters longer.

Length = 2+x
Width = x

A= L*W

The area is given so just solve for x.

(2+x) * x = 24

maybe using the expanded form is useful here. After moving the 24 to the other side and multiplying the x through the (2+x) your equation should look like this

x^2+2x-24=0 This is old hat now. Just find the two values that sum to 2 and multiply to -24.

(x+_)(x+_)=0

6 + (-4) =2
6 * (-4) = -24

when dealing with area and distance the numbers are always positive. So your answer is just 6 and 4.

I didn't show all of the steps for these problems, you will still have to write the solutions in proper form as well. Practice writing out every step and spend time manipulating the values from one side to another and just plugging in numbers and you will get a feel for how factoring, foil multiplication and expansion work. This is a good website for math instruction;

http://tutorial.math.lamar.edu/

You can google Paul's Online Math Notes to find the page also. I think if you go to the class notes on algebra you will see some more factoring problems worked out.

Answer 3

Well, the first one is easy. It is zero when either of the two factors are zero.

So x - 2 = 0 or 2x - 5 = 0.

x = 2 or 2x = 5 (which means that x = 2.5)



(x^2 + 6x - 27) = 0

Look at 27. One of the ways to get 27 is 9 x 3.

(x ? 9)(x ? 3) = 0

The equation says NEGATIVE 27, so one of the question marks is a minus sign and the other is a plus.

If it was -9 and +3, then when we multiplied we'd get -9x + 3x for the middle term, or -6x. Instead, the middle term is 6x. So it's the other way: 9 and -3

(x + 9)(x - 3) = 0.
x = -9 or x = 3



x^2 + 6 = -5x.

Get all the terms onto one side.
x^2 + 5x + 6 = 0

6 = 6 * 1 or 2 * 3.

Because 6 is positive, either I'm going to get two (x - some number) or two (x + some number). Because 5 is positive, it has to be two (x + some number). I can't add 6 + 1 and get 5. 2 + 3, however = 5

(x + 2)(x + 3) = 0
x = -2 or x = -3



For the next one, when you move all terms to the left.


5x^2 - 11x + 2 = 0

Two is positive, but 11 is negative, so we are going to get something like
( - )( - )

2 is prime and can only be factored 2 and 1.
( - 2)( - 1)

5 is also prime and can only be factored 2 and 1.
You will have 5x and x. Which one goes with the 2 and which with the 1?



(x^2 - y^2) always factors as (x + y)(x - y). If y^2, what is y?



L x W = 24
L = W + 2
(W + 2) * W = 24
W^2 + 2W = 24
W^2 + 2W - 24 = 0

24 = 24 * 1 or 12 * 2 or 6 * 4 or 4 * 3. Which adds or subtracts to make 2?

24 is negative, so you have one of each sign.

(x - something)(x + something).

Since the middle term is positive, add the larger and subtract the smaller.

E-mail me if you'd like more help.

Answer 4

Haha you can't solve it, however you can simplify it. The only way you'd be able to solve it is if it equalled something. Okay so first you take everything in the parenthesis to the third power. This will give you: w^3 - 125 + 8 Now you will want to add (-125) and 8 which gives you (-117). Since you can't simplify any longer, your final solution is: w^3-117 If it really did say to SOLVE the problem, and you realized that you forgot to add the equals sign, then post it up and I'll be happy to help you!

Answer 5

first one is already factored.. x=2, x=5/2

factor the second to (x+9)(x-3), so x=-9, x=3

rearrange the third to 0 = 2x - 12x^2. same as -12x^2 + 2x =0
same as -12x^2 = -2x. divide both side by -12x. x=0, x=1/6

last one x^2-9 = (x+3)(x-3) so x=3, x=-3

Answer 6

1)x-2=0
x=2

2x-5=0
2x=5
x=5/2

2)x^2+6x-27=0
(x-3)(x+9)=0
x=3
x=-9

3)x^2+5x+6=0
(x+3)(x+2)=0
x=-3
x=-2

4)12x^2-2x=0
2x(6x-1)=0
2x=0
x=0

6x-1=0
6x=1
x=1/6

5)x^2+6x+9=0
(x+3)(x+3)=0
x=-3

6)(5x-1)(x-2)=0
5x-1=0
5x=1
x=1/5

x-2=0
x=2

7)(x-3)(x+3)=0
x=3
x=-3

8)L=2+w
wL=24.
w(2+w)=24
w^2+2w-24=0
(w-4)(w+6)=0
w =4 (because w couldnt be -6)

SO, width=4
Length=24/4=6.