P(x) is a polynomial of order 4 and you are dividing by a polynomial of order 1 so the quotient will be of order 4 - 1 = 3
So suppose the quotient is Ax3 + Bx2 + Cx + D
Then p(x)/(x + 2) = Ax3 + Bx2 + Cx + D with remainder R.
To find R, simply evaluate p(x) at x = -2.
p(2) = -24
Cross-multiply:
p(x) = (x + 2)*(Ax3 + Bx2 + Cx + D) - 24
= Ax4 + 2Ax3 + Bx3 + 2Bx2 + Cx2 + 2Cx + Dx + 2D - 24
Comparing coefficients of:
x4: 1 = A
x3: 2 = 2A +B = 2 + B => B = 0
x2: 1 = 2B + C = 0 + C => C = 1
x : 8 = 2C + D = 2 + D => D = 6
and, as a check,
x0 : -12 = 2D + R = 12 + R => R = -24
x3 -3x2 -x - 1 divided by x+2 equals x2-5x+9 remainder -19 It's difficult to show how to work it out on this computer but division with algebra has a lot in common with doing long division with integers.
No, it equals 4y2
X squared = x+6 6+x=x squared X=6
if x= 3 or -3
5.
No. 11 is the Quotient and 3 is the remainder.
35.6818
44.3333
6.5
245.3333
289/3 = 96 remainder 1 Therefore, x = 3.
Dividend divided by divisor equals quotient
Dividend divided by divisor equals quotient.
1155 divided by 55 equals 21 which is the quotient
5
Dividend divided by divisor equals quotient.
6.25