How do I factor these completely?

Question

1) 4x^3-4x

2) 8x^2+2x-15

3) 49-25x^2

4) x^2 +15x=56

It's been a while since I last took math class, and I can't remember how to solve these problems, can you please help show me how to figure them out?

Answer 1

use the quadratic formula if you can't factor nicely in this case.

http://www.purplemath.com/modules/quadfo...

Answer 2

1./ 4x^3 - 4x

     4x(x^2 - 1)

     4x(x-1)(x+1)

2./ 8x^2 + 2x - 15

     (4x - 5)(2x + 3)

3./ 49 - 25x^2

     (7 - 5x)(7 + 5x)

4./ x^2 + 15x = 56

     x^2 + 15x - 56 = 0

     Stopped here

if it's x^2 + 15x = -56 then

        x^2 + 15x + 56 = 0

        (x + 7)(x + 8) = 0

Answer 3

1)4x(x^2 -1)

  4x(x+1)(x-1)

2)(4x-5)(2x+3)

3)(-5x+7)(5x+7)

4)(x+8)(x+7)=0

Answer 4

1)

4x^3 - 4x

= 4(x^3 - x)

= 4x(x^2 - 1)

= 4x(x + 1)(x - 1)

2)

8x^2 + 2x - 15

= 8x^2 + 12x - 10x - 15

= (8x^2 + 12x) - (10x + 15)

= 4x(2x + 3) - 5(2x + 3)

= (2x + 3)(4x - 5)

3)

a^2 - b^2 = (a + b)(a - b)

49 - 25x^2 = (7 + 5x)(7 - 5x)

4)

x^2 + 15x = 56

x^2 + 15x - 56 = 0

x = [-b ±√(b^2 - 4ac)]/2a

a = 1

b = 15

c = -56

x = [-15 ±√(225 + 224)]/2

x = [-15 ±√449]/2

x ≈ [-15 ±21.18]/2



x ≈ [-15 + 21.18]/2

x ≈ 6.18/2

x ≈ 3.09

x ≈ [-15 - 21.18]/2

x ≈ -36.18/2

x ≈ -18.09

∴ x ≈ -18.09 , 3.09

Answer 5

are you familiar with the tic tac toe method?

I really cant explain it over the internet unless we were in an IM but i could tell you the answers if youd like?

Answer 6

2)  (4x-5)(2x+3)

Answer 7

1) 4x(x^2-1)

4x(x+1)(x-1)

2) (4x-5)(2x+3)

3) (7+5x^2)(7-5x^2)

4) actually cant factor this one. can do quadform though.

x^2+15x-56=0

x=(-b+-sqrt(b^2-4ac))/(2a)

a=1 b=15 c=-56

x=(-15+-sqrt(449))/2

x=3.09, x=-18.09

make it a good day

Answer 8

1) 4x^3--4x = 4x(x^2--1) = 4x(x+1)(x--1)

2) 8x^2+2x--15

= 8x^2+12x--10x--15 = 4x(2x+3)--5(2x+3) = (2x+3)(4x--5)

3) 49--25x^2 = (7)^2--(5x)^2 = (7+5x)(7--5x)

4) x^2+15x+56 = x^2+8x+7x+56 = x(x+8)+7(x+8) = (x+8)(x+7)

Answer 9

1) 4x^3-4x

First look to see if you can "pull out" a common factor ... you might be tempted to take just the 4, but you can actually factor out a 4x.

4x (x^2 - 1)

Next, look to see if what's in the parentheses can be factored. (x^2 - 1 ) can be factored ... keep the 4x

4x (x+1)(x-1)    ANSWER

**(whenever you see a missing middle term followed by a minus sign, try factoring with your x +/- your constant. If you had tried (x+1)^2 or (x-1)^2 you would have had a middle term (2x)

2) 8x^2+2x-15

This polynomial has to be factored using the FOIL method

The last sign is negative so your signs will be opposite. Start with factors of 8 and remember that the last constant (-15) is the product of your constants.

(2x + 3 )(4x - 5) ---> 8x^2 -10x+12x -15 = 8x^2 + 2x - 15

3) 49-25x^2

Both factors are squares, the middle term is missing, and there is a minus sign ...

  ( 7 - 5x)(7 + 5x)

Check: 49 +35x - 35x - 25x^2 = 49 - 25x^2

4) x^2 +15x=56

Same as #2 ... except that you have to move the 56 to get the polynomial into the form that you areused to seeing.

x^2 +15x=56

I just worked the problem out that way and you can't have a +15x and a -56 ... probably your = sign is a "typo" and was supposed to be a + sign ... in that case,

(x + 7)(x + 8) = x^2 + 8x + 7x + 56 = x^2 + 15x + 56

You will occasionally run into a polynomial that has the constant on one side of the equal sign and must be  "moved" so that the equation can be set equal to zero. Afterwards you will find what values of x will give you a product = 0.

Hope I helped. Good luck!