Factoring and variables?

Question

could use a little help here please

Thanks

Factoring first

24x - 3x(^2) - 36

and

a(^2) - 5a - 24

variables

x + x - 2

-- ---- = 3

3 5

and

n - 2n

--- --- = 5

2 9

I tried to make them as understandable as possible

if you could please explain how to do these be cause these are pretty much examples

Thanks so much

Answer 1

Factor them by solving quadratic equations:

24x - 3x^2 - 36 = 0 // Let's first rearrange the equation

-3x^2 + 24x - 36 = 0 // divide by -3

x^2 - 8x + 12 = 0

I can see that -2 - 6 = -8 and (-2)*(-6) = 12, thus

x^2 - 6x - 2x + 12 = 0

or

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

x(x - 6) - 2(x - 6) = 0

(x - 2)(x - 6) = 0

But, (x - 2)(x - 6) = x^2 - 8x - 12, Let's multiply by -3

-3(x - 2)(x - 6) = 24x - 3x^2 - 36

====================================

a^2 - 5a - 24 = 0 // -5 = -8 + 3 and -24 = (-8)*3, thus

a^2 - 8a + 3a  - 8 * 3 = 0

a(a - 8) + 3(a - 8) = 0

(a + 3)(a - 8) = 0

a^2 - 5a - 24 = (a + 3)(a - 8)

========================

Did you mean (x/3) + (x - 2)/5 = 3 ?

Let's multiply both sides by 3 * 5 = 15:

5x + 3(x - 2) = 45

5x + 3x - 6 = 45

8x - 6 = 45 // add 6

8x = 51

x = 6 + 3/8

===================

(n / 2) - (2n / 9) = 5  // Multiply by 2*9

9n - 2*2n = 90

9n - 4n = 90

5n = 90

n = 18

Answer 2

Factorizations:

1) The expression =

-3(x^2-8x+12)=

-3(x-6)(x-2)

2) The expression=

(a-8)(a+3)

This method is usually called the method of inspection or the

cross-method:

take a^2-5a-24 as an example,

24= 1*24 or 2*12 or 3*8 or 4*6, then you examine which pair

of the factors can give 5 after addition of substraction. In this

example, we select 3,8. Next, we choose the sign for 3 & 8

respectively such that 3*8 will give -24 and 3+8 will give -5.

Here we choose -8 and +3. So, we write (a-8)(a+3) as the

answer.

I don't know what "variables" means here, but I guess you want

to solve these 2 equations. If so, my answers are as follows:

3) (x+x-2)/35=3=>

2x-2=105=>

2x=107=>

x=53.5

4) (n-2n)/29=5=>

-n=145=>

n=-145

Should you have any question, ask your teacher.

Answer 3

1)

24x - 3x^2 - 36

= -3x^2 + 24x - 36

= -3(x^2 - 8x + 12)

= -3(x^2 - 2x - 6x + 12)

= -3(x - 2)(x - 6)

(answer a)

2)

a^2 - 5a - 24

= a^2 + 3a - 8a - 24

= (a^2 + 3a) - (8a + 24)

= a(a + 3) - 8(a + 3)

= (a + 3)(a - 8)

(answer a)

3)

x/3 + (x - 2)/5 = 3

15[x/3 + (x - 2)/5] = 15[3]

5x + 3(x - 2) = 45

5x + 3x - 6 = 45

8x = 45 + 6

8x = 51

x = 51/8

(answer a)

4)

n/2 - 2n/9 = 5

18(n/2 - 2n/9) = 18(5)

9n - 4n = 90

5n = 90

n = 90/5

n = 18

(answer a)

Answer 4

then if its -36 then you should do this:

3x^2-24x-36.

3(x^2-8-12)

Factor out the GCF of 3 from

are you sure it's -36? if its +36 then it goes like this:

first arrange it according to its degree.

=> 3x^2 - 24 x + 36

get the factors of 3: 3 and 1 so (3x-___)(x-___)

get the factors of 36: 6 and 6

(3x-6)(x-6)

<i used negative bcoz if you multiply this it will give you positive.

use foil method to check:

3x^2-18x-6x+36

3x^2 - 24x + 36

same with no. 2

a^2 - 5a - 24

a has only one factor so it is 1: (a + ____)(a-_____)

again get the factors of 24. now the factors should sum up to 5.

24: 8 and 3

(a+8)(a-3)

you do the checking.

i can't clearly understand the last part :D