Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x)/D(x) in the form
P(x)
D(x)
= Q(x) +
R(x)
D(x)
.
P(x) = 10x3 + x2 − 21x + 9, D(x) = 5x − 7
P(x)
D(x)
=
2x2+3x
Incorrect: Your answer is incorrect.
Also how is this incorrect? what is the right answer that is throwing me off?
the quotient is indeed 2x^2 + 3x
There is a remainder of 9.
So,
P(x) = (5x-7)(2x^2+3x) + 9
Not sure why your answer is marked incorrect, since you have the quotient right. Maybe you had to supply both Q and R.
P(x)/(5x-7) = 2x^2+3x + 9/(5x-7)
To divide the polynomial P(x) = 10x^3 + x^2 − 21x + 9 by D(x) = 5x − 7 using synthetic division, follow these steps:
1. Set up the division problem by writing the coefficients of P(x) in descending order:
10 1 -21 9
---------------------
2. Since D(x) has a degree of 1, we only need one division line.
5x - 7 | 10 1 -21 9
10
3. Multiply the number outside the division line (10) by the divisor (5x − 7) and write the result under the next coefficient:
5x - 7 | 10 1 -21 9
10 ... ...
50x - 70
4. Add the row above to the next row:
5x - 7 | 10 1 -21 9
10 ... ...
-------------
0
5. Write the values in descending order from the row formed:
5x - 7 | 10 1 -21 9
10 20 -21
-------------
0 21
The quotient part (Q(x)) comes from the coefficients in the second row without the remainder. The remainder part (R(x)) comes from the last value, which is 21 in this case.
Therefore, the correct answer is:
P(x) / D(x) = Q(x) + R(x)/D(x)
= 10x^2 + 20x - 21 + 21/(5x - 7)
= 10x^2 + 20x - 21 + 21/(5x - 7)