Question

Which of the following is a solution of the equation x^2-6x+5=0?

Answer 1

Answer:

Factoring  x2-6x+5  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +5  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 5 = 5  

Step-2 : Find two factors of  5  whose sum equals the coefficient of the middle term, which is   -6 .

     -5    +    -1    =    -6    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  -1  

                    x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x-1)  •  (x-5)

            Which is the desired factorization (x - 1) • (x - 5)  = 0 2.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well. 2.2      Solve  :    x-1 = 0  

Add  1  to both sides of the equation :  

                     x = 12.3      Solve  :    x-5 = 0 Add  5  to both sides of the equation :  

                     x = 5

Explanation:

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Answer 2

${x}^{2} - 6x + 5 \\ by \: splitting \: middle \: terms \\ {x}^{2} - x - 5x + 5 \\ x(x - 1) + 5(x - 1) \\ = (x - 1)(x - 5)$

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