Factoring
Factor completely over the real numbers:
16x4-81
(4x2+9)(2x+3)(2x-3)
Find the vertex of the parabola 3x2-12x+21
(2,9)
If 2+5i is a root of f(x), name another root of f(x)
2-5i
Describe the end behavior of
f(x)=(4x^4+3x^3+2x^2+x-1)/(-2x^4+10x^3-15x^2+35)
f(x) approaches -2 as x approach positive or negative infinity
Factor into two quadratics: x4+x2+25
(x2+3x+5)(x2-3x+5)
Find the equation of a parabola with a root at 5 and a y-intercept of 80.
4x2-36x+80
The roots of ax3+bx2-6x+c are 1,-1, and -2. Find a,b, and c.
a=6, b=12, c=-12
Compute
(2x^5+x^4-3x^3+5x^2-21x+8)/(x^2+2x-1)
2x3-3x2+5x-8
Factor completely: x3+17x2+59x-77
(x-1)(x+7)(x+11)
A parabola has vertex at (-3,-2) and y-intercept at 16. Find its roots.
-2 and -4
One of the roots of 2x3-20x2+bx+c is 3-4i. Find the other two roots.
3+4i and 4
Find all pairs of positive integers whose squares differ by 21
(10,11) and (2,5)
Factor the following completely into (x-a)(x-b)(x-c)(x-d) where a,b,c, and d are real or complex numbers:
x4-6x6-16
Hint: complete the square
(x+2\sqrt2)(x-2\sqrt2)(x+sqrt2i)(x-sqrt2i)
The parabolas 2x2+bx+c and x2+x+1 intersect when x=2 and when x=6. Find b and c.
b=-7 and c=13
Suppose that f(x)=ax3+bx2+cx+d and that two of its roots are u+vi and r where u,v, and r are real numbers. If the y-intercept of f(x) is u2+v2, find a in terms of u,v, and r.
a=-1/r
The roots of 4x4-48x3-36x2+992x+1680 are -2,a,b, and c. If a+b=c, find c.
7