Divide the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of a. divide 5a2 + 6a - 9 into 25a4 + 19a2 - a - 78.

We divide by using the long division algorithm as follows:

                         5a^2 - 6a + 20
                       _____________________
5a^2 + 6a - 9 | 25a^4 + 0a^3 + 19a^2 - a - 78
                      | 25a^4 + 30a^3 - 45a^2
                      |___________________
                      |             -30a^3 + 64a^2 - a - 78
                      |             -30a^3 - 36a^2 + 54a
                      |            ____________________
                      |                         100a^2 - 55a - 78
                      |                         100a^2 + 120a - 180
                      |                         __________________
                                                             -175a + 102

Therefore, divided into gives remainder -175a + 102.

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!