Factor using the x method

( please do not answer without showing work )

Step-by-step explanation:

We are factoring

So:

((2•5^2x^2) +  485x) -  150

Pull like factors :

50x^2 + 485x - 150  =   5 • (10x^2 + 97x - 30)

Factor

 10x^2 + 97x - 30

Step-1: Multiply the coefficient of the first term by the constant   10 • -30 = -300

Step-2: Find two factors of  -300  whose sum equals the coefficient of the middle term, which is 97.

-300    +    1    =    -299

     -150    +    2    =    -148

     -100    +    3    =    -97

     -75    +    4    =    -71

     -60    +    5    =    -55

     -50    +    6    =    -44

     -30    +    10    =    -20

     -25    +    12    =    -13

     -20    +    15    =    -5

     -15    +    20    =    5

     -12    +    25    =    13

     -10    +    30    =    20

     -6    +    50    =    44

     -5    +    60    =    55

     -4    +    75    =    71

     -3    +    100    =    97

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  100

                    10x^2 - 3x + 100x - 30

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

                   x • (10x-3)

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

                   10 • (10x-3)

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

                   (x+10)  •  (10x-3)

            Which is the desired factorization

Thus your answer is

Step-by-step explanation:

we would like to factor out the following expression:

notice that, in every term there's a common factor of 5 thus factor it out:

now we have to rewrite the middle term as sum or substraction of two different terms in that case 100x-3x can be considered:

factor out 10x:

factor out -3:

group:

and we are done!

hence,

our answer is B)

When the function is asked to be shifted to 1 unit to the left, we replace x with x + 1. Hence, f(x) = x3 + 2x2 - 2x + 1;  f(x + 1) = (x + 1)^3 + (x + 1)^2 - 2(x + 1) - 5 
= (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2(x + 1) + 1 = x^3 + 3x^2 + x^2 + 3x + 2x - 2x + 1 + 1 - 2  + 1 = x^3 + 4x^2 + 3x + 1 

The final equation is  x^3 + 4x^2 + 3x + 1