Use the remainder theorem and the factor theorem to determine whether (y-3) is a factor of (y^4 + 2y^2 -4).
A. The remainder is 0 and, therefore, (y-3) is a factor of (y^4 + 2y^2 -4).
B. The remainder is 0 and, therefore, (y-3) isn't a factor of (y^4 + 2y^2 -4).
C. The remainder isn't 0 and, therefore, (y-3) is a factor of (y^4 + 2y^2 -4).
D. The remainder isn't 0 and, therefore, (y-3) isn'tfactor of (y^4 + 2y^2 -4).
Please explain .......THANKS
2007-01-28 15:33:25 · 5 answers · asked by victorbusta5 2 in Science & Mathematics ➔ Mathematics
ok.....thanks .........and.......but if the answer had equal = 0 ........then what would the answer be?......Thank
2007-01-28 15:59:41 · update #1
ok.....thanks .........and.......but if the answer does not equal = 0 ........then what would the answer be?......Thank
2007-01-28 16:00:07 · update #2
If you divide a number (or here, an expression) by a second one and get a remainder of zero, then the second must be a factor of the first. So right off the bat, "B" and "C" don't make any sense. Either the remainder is 0 and thus (y-3) is a factor, or the remainder isn't 0 and thus (y-3) isn't a factor.
The remainder theorem says that when you divide a polynomial by (x-a), the remainder is same value you get when you plug x = a into the polynomial. So plugging y=3 into (y^4 + 2y^2 -4), you get 3^4 + 2(9) - 4 which does not equal zero. Therefore, "D" is the correct choice.
2007-01-28 16:00:35 · answer #1 · answered by Anonymous · 0⤊ 0⤋
When you divide by a potential factor, if it is indeed a factor the remainder is zero. So, just do long division (or synthetic division) of (y^4 + 2y^2 -4) by y-3 and see if there is a remainder.
2007-01-28 15:42:01 · answer #2 · answered by grand_nanny 5 · 0⤊ 0⤋
The answer is D, so therefore there is no way that (y-3) could be a factor.
2007-01-28 15:41:13 · answer #3 · answered by bruinfan 7 · 0⤊ 0⤋
f(y) = y^4 + 2y^2 - 4
f(3) = 3^4 + 2(3^2) - 4 = 95 ≠ 0
The answer is D.
2007-01-28 15:40:09 · answer #4 · answered by sahsjing 7 · 0⤊ 0⤋
on a similar time as I agree alongside with your end, you have trivialized the situation with a fake assumption (extremely, the existence of God implies a million = 0). Mathematical evidence does not artwork all that nicely in issues the place the tip itself is poorly defined. God is, very almost axiomatically, impossible to outline nicely, so i choose to propose a rigorous argument extremely than mathematical evidence. Sorry to burst your bubble.
2016-12-17 04:48:33 · answer #5 · answered by ? 3 · 0⤊ 0⤋