Question

Factor using the x method ( please do not answer without showing work )

Answer 1

Answer:

$5(x + 10)(10x - 3)$

Step-by-step explanation:

We are factoring

$50x^{2} + 485x - 150$

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

$5(x + 10)(10x - 3)$

Answer 2

Answer:

$\displaystyle \rm 5({x}^{} + 10)( 10x - 3)$

Step-by-step explanation:

we would like to factor out the following expression:

$\displaystyle {50x}^{2} + 485x - 150$

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

$\displaystyle 5( {10x}^{2} + 97x - 30)$

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

$\displaystyle 5( {10x}^{2} + 100 - 3x - 30)$

factor out 10x:

$\displaystyle 5( 10({x}^{2} + 10)- 3x - 30)$

factor out -3:

$\displaystyle \rm 5( 10x({x}^{} + 10)- 3(x + 10))$

group:

$\displaystyle \rm 5({x}^{} + 10)( 10x - 3)$

and we are done!

hence,

our answer is B)