Question

If the polynomial 6x47x3-44x² + 83x - 30 is divided by another polynomial 6x² - 13x + 5, the quotient and remainder were (ax² + bx - c) and d respectively, then the value (a + b + c + d) is​

Answer 1

Answer:

Step-by-step explanation:

The first term is,  6x2  its coefficient is  6 .

The middle term is,  -13x  its coefficient is  -13 .

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

Step-1 : Multiply the coefficient of the first term by the constant   6 • -5 = -30  

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -13 .

    -30    +    1    =    -29  

    -15    +    2    =    -13    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  2  

                   6x2 - 15x + 2x - 5

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

                  3x • (2x-5)

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

                   1 • (2x-5)

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

                  (3x+1)  •  (2x-5)

           Which is the desired factorization