I assume you meant x^4 + 5x^2 +10x + 12.
The remainder is 28
Factor the polynomial x2 - 10x + 25. Enter each factor as a polynomial in descending order.
x2+10x-24 = (x-2)(x+12)
(x+1)(x+9)
(x - 5)(x - 5)
Say x^4-5x^2-10x-12 = f(x)(x+2)+c. If we substitute x = -2 something magical happens: (-2)^4-5(-2)^2-10(-2)-12 = f(-2)(-2+2)+c 16-20+20-12 = f(-2)*0+c 4 = c So the remainder must be 4.
Factor the polynomial x2 - 10x + 25. Enter each factor as a polynomial in descending order.
(x+1)(x+9)
x2+10x-24 = (x-2)(x+12)
(x+1)(x+9)
x2+10x+21 = (x+3)(x+7)
(x - 5)(x - 5)
6
Say x^4-5x^2-10x-12 = f(x)(x+2)+c. If we substitute x = -2 something magical happens: (-2)^4-5(-2)^2-10(-2)-12 = f(-2)(-2+2)+c 16-20+20-12 = f(-2)*0+c 4 = c So the remainder must be 4.
45
5x/x-2
10x - 30 10(x - 3) ------------
Factorising, we obtain, x2 + 10x + 21 = (x + 7)(x + 3). Thus, x2 + 10x + 21 / (x + 3) = x + 7. That's usually easier than dividing it out!