Question

I have no idea what im doing someone help pls! due soon

Answer 1

4x2-28x+49  

Final result :

 (2x - 7)2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (22x2 -  28x) +  49

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  4x2-28x+49  

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -28x  its coefficient is  -28 .

The last term, "the constant", is  +49  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 49 = 196  

Step-2 : Find two factors of  196  whose sum equals the coefficient of the middle term, which is   -28 .

     -196    +    -1    =    -197  

     -98    +    -2    =    -100  

     -49    +    -4    =    -53  

     -28    +    -7    =    -35  

     -14    +    -14    =    -28    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  -14  

                    4x2 - 14x - 14x - 49

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

                   2x • (2x-7)

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

                   7 • (2x-7)

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

                   (2x-7)  •  (2x-7)

            Which is the desired factorization

Multiplying Exponential Expressions :

2.2    Multiply  (2x-7)  by  (2x-7)  

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (2x-7)  and the exponents are :

         1 , as  (2x-7)  is the same number as  (2x-7)1  

and   1 , as  (2x-7)  is the same number as  (2x-7)1  

The product is therefore,  (2x-7)(1+1) = (2x-7)2  

Final result :

 (2x - 7)2

Answer 2

ok so we know that 49 stays the same.

_(x + _)^2+ 49

So 4 and 28 both have a factor of 4 right? If we take out the 4 we get....

4(x^2 + 7x) + 49

Hmm.... Oh wait we can take out an x!!

4x(x + 7) + 49

That's your answer!