1.) x² + 7x =0 ,,,,,,2.) 6s² + 18s = 0,,,,,,3.) t² + 8t +16 =0 ?????

Question

Hello...can anyone please help me to solve this...the following quadratic equations by Factoring?,,,Thank you in advance~~

Answer 1

Hi,

A factor is a value that multiplies another value.  When factoring, we put the equation into a product of factors.  When any one (or more) of these factors equals 0, the product equals zero.

 

First, we change the equation to make the right side equal to 0.

 

Then, we factor outthe common factors.

 

Any remaining expression may be solved(that is, find the value of x that makes the expression equal to 0, thus making the whole side of the equation equal to zero).

 

Let’s do (1):      x^2 + 7x = 0

    The x is common in the two terms, so    x(x + 7) = 0

    This happens (thus solvingthe equation for x) when    x=0  or  x = -7

 

Now, (2):     6^2 + 18s = 0

     Notice that 6 is a common factorof the two terms, so     6(1 +3s) = 0

     This happens when s = -1/3     (note: 6 will never be 0)

 

O.K. (3):    t^2 + 8t + 16 = 0

     This teaches a special skill (but later, you can use the quadratic formula) -– what two numbers, when multiplied produce 16, but when added, give 8?  (note: there is a method that first finds the prime factorsof each coefficient, then adds combinations to do this quickly).  But, I quickly realized that 4 + 4 = 8  and that 4 * 4 = 16  (later, you will see such numbers in a pyramid, but that’s later).    So,     (t + 4)(t + 4) = 0      (check this using FOIL)

     This happens when  t = -4

 

Cool !  Using a procedure makes this easy.