Thread: Polynomial

Question>> the polynomial x^4+5x+a is denoted by p(x). It is given that x^2-x+3 is a factor of p(x).
part (1) Find the value of a in p(x).

Can somebody please reply to this quickly. Thank you

so [tex] we get which means a_2 = 1. So and since . So now you got and since so again so a = -6.

Code:

................. x^2  +  x  - 2
.................-----------------------------
x^2 - x + 3 | x^4 + 0x^3 + 0x^2 + 5x + a
............  x^4 -  x^3  + 3x^2
..............-----------------------------
....................x^3  - 3x^2 + 5x + a
....................x^3  -  x^2 + 3x
....................---------------------
........................- 2x^2 + 2x + a
........................- 2x^2 + 2x - 6
........................----------------
......................................a+6

remainder, a+6 = 0

a = -6

thanks jakncoke. Thankyou skeeter, i was also using the same method but my remainder included the variable 'x' so i thought it was wrong. Found my mistake though, thanks once again.