Respuesta :

Question 6

x² - 16 = 0
x² = 16
√x² = √16
x = 4 or -4

Question 7

x²  + 3x - 54 = 0
Factorizing

Find two numbers that add to make 3x and multiply to make 54
Write out the factor of -54 in pairs
1, -54
-1, 54
2, -27
-2, 27
3, -18
-3, 18
4, -16
-4, 16
6, -9
-6, 9
Then find the pair that, when added = +3 (in bold)
-6 + 9 = 3

x² + 9 - 6x - 54 = 0
x(x + 9)      -6(x + 9)

Use the (x + 9) and the coefficient of these brackets to make double brackets.
(x+9)(x-6) = 0

If the product of two terms =0, at least one must equal 0

x + 9 = 0
x = -9

x - 6 = 0
x = 6

x = -9 or 6


Question 8

2x² -11x - 6 = 0

First, multiply the coefficient of x² by the value of c (the number on its own)2 x -6 = 12

This time, find factors of -12 that equal -11
1, -12
-1, 12
2, -6
-2, 6
3, -4
-3, 4
The pair is in bold
1 + -12 = -11

2x² -12x + x - 6
Split down the middle and factorise in singe brackets
2x(x - 6)        1(x - 6)
Now use the brackets pre-made (x - 6) and put together what is in front of them (2x +1)
(2x + 1)(x - 6)

 If the product of two or more terms = 0, at least 1 must equal 0
2x + 1 = 0
2x = -1
2x/2 = x       -1/2 = -0.5

x - 6 = 0
x = 6

x = -0.5 or 6
AL2006

Question #6:
They expect you to remember that the difference
of two squares can be factored as 

   (the sum of the squared numbers) times (their difference).

So   [ x² - 16 = 0 ]  can be written as  (x + 4) (x - 4) = 0 .

Now, a rule that you've used hundreds of times before
and you'll use thousands of times again: 
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.

So ...  
(x+4) = 0 gives you one solution,
and (x-4)=0 gives you the other solution.
__________________________________

Question #7:

Factor the left side of the equation.

       (x + 9) (x - 6) = 0 .

Now, use a rule that you heard somewhere VERY recently:
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.

So ...
(x + 9) = 0 gives you one solution, and
(x - 6) gives you the other one.
_______________________________________

Question #8:

Factor the left side of the equation:

           (2x + 1) (x - 6) = 0

Now use the golden rule that you've memorized by now:
If the equation says that the product of two things is zero,
then the equation is true if EITHER of them is zero.

So ...
(2x + 1) = 0 gives you one solution,
and (x - 6) = 0 gives you the other one.



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