Question

middle term break 9x^2-48x-17​

Answer 1

Step-by-step explanation:

9x2-48x-17  

Final result :

 (3x - 17) • (3x + 1)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (32x2 -  48x) -  17

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  9x2-48x-17  

The first term is,  9x2  its coefficient is  9 .

The middle term is,  -48x  its coefficient is  -48 .

The last term, "the constant", is  -17  

Step-1 : Multiply the coefficient of the first term by the constant   9 • -17 = -153  

Step-2 : Find two factors of  -153  whose sum equals the coefficient of the middle term, which is   -48 .

     -153    +    1    =    -152  

     -51    +    3    =    -48    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -51  and  3  

                    9x2 - 51x + 3x - 17

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

                   3x • (3x-17)

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

                    1 • (3x-17)

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

                   (3x+1)  •  (3x-17)

            Which is the desired factorization

Final result :

 (3x - 17) • (3x + 1)

Answer 2

The factors of $9x^{2}-48x-17$ are (3x - 1)(3x + 17).

Step-by-step explanation:

The expression is:

$9x^{2}-48x-17$

Factorize the expression by splitting the middle term as follows:

$9x^{2}-48x-17=9x^{2}-3x+51x-17$

                        $=3x(3x-1)+17(3x-1)\\=(3x-1)(3x+17)$

Thus, the factors of $9x^{2}-48x-17$ are (3x - 1)(3x + 17).

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