Without doing the long division, find the remainder when 3x^4 - 5x^2 + 4 is divided by x^2 + 2.
2006-12-26 01:35:44 · 5 answers · asked by iqnabeel 1 in Science & Mathematics ➔ Mathematics
see other post...don't repost be just a LITTLE patient sheesh
2006-12-26 02:04:38 · answer #1 · answered by a_math_guy 5 · 0⤊ 0⤋
Begin with the change of variable u = x^2. Then, the question becomes:
"Without doing long division, find the remainder when 3u^2 -5u+4 is divided by u + 2". Since you are now dividing by a linear factor, you can just evaluate the first polynomial in u at u = -2, to get the answer, which is 26.
2006-12-26 11:06:11 · answer #2 · answered by Asking&Receiving 3 · 0⤊ 0⤋
if x^2+2 is the divisor the remainder will be
f(rt2i)=3(rt2i)^4-5(rt2i)^2+4
=3(4)+10+4=26
f(-rt2i)=2(-rt2i)^4-5(-rt2i)^2+4
=26
so the raminderis 26
2006-12-26 10:04:29 · answer #3 · answered by raj 7 · 0⤊ 0⤋
( 3x^4 - 5x^2 + 4)/(x^2+2)
sorry
2006-12-26 10:27:39 · answer #4 · answered by Ankit B 4 · 0⤊ 1⤋
x^2 + 2 | 3x^4 - 5x^2 + 4 | 3x^2 + 1
..............3x^4 + 6x^2
..............------------------
........................... x^2 + 4
........................... x^2 + 2
...........................-----------------
................................... 2
Q : 3x^2+1
R : 2
2006-12-26 10:15:54 · answer #5 · answered by Anonymous · 0⤊ 1⤋