2x4 - 9x3 + 13x2 - 15x + 9
= 2x4 - 6x3 - 3x3 + 9x2 + 4x2 - 12x - 3x + 9
= 2x3(x - 3) - 3x2(x - 3) + 4x(x - 3) - 3(x - 3)
= (x - 3)*(2x3 - 3x2 + 4x - 3)
So the quotient is (2x3 - 3x2 + 4x - 3)
and the remainder is 0.
When a polynomial is divided by one of its binomial factors, the quotient is called the "reduced polynomial" or simply the "quotient polynomial." This resulting polynomial represents the original polynomial after removing the factor, and it retains the degree that is one less than the original polynomial.
To find the remainder when a polynomial is divided by (x - 2) using synthetic division, we substitute (2) into the polynomial. The remainder is the value of the polynomial evaluated at (x = 2). If you provide the specific polynomial, I can calculate the remainder for you.
84.5
607.5
0.2667
84.5
607.5
3052.1429
0.2667
The quotient is 47 with a remainder of 1
5.4506
9.875
699.2558
810: quotient 1, remainder 1
26.1538
1.5647
387 divided by 6 is 64 with remainder 3.