given that -2*k**4 + 0*k**3 + 2*k**2 + n*k**4 - 4*k**3 = 0.
0, 1
Suppose 2*t = 2*v - 0*v - 16, 5*v - t = 28. Suppose 0 = -0*s + v*s - 3*w - 10, 3*w = 0. Factor 0 + 2*f**s - 1/2*f**3 - 2*f.
-f*(f - 2)**2/2
Suppose -7 = -9*c + 11. Let u(y) be the second derivative of 1/80*y**5 + 1/48*y**4 + 0 + 0*y**c + y + 0*y**3. Find x such that u(x) = 0.
-1, 0
Let h(r) be the first derivative of r**9/1512 - r**7/210 + r**5/60 + 2*r**3/3 + 6. Let x(c) be the third derivative of h(c). Determine i, given that x(i) = 0.
-1, 0, 1
Let i(c) be the second derivative of c**7/315 - c**6/60 + c**5/30 - c**4/36 + c**2/2 - 2*c. Let q(v) be the first derivative of i(v). Factor q(a).
2*a*(a - 1)**3/3
Factor 3*i**2 - 3*i**4 + 4*i**3 - 3*i**3 + 2*i**3 - i - 2*i.
-3*i*(i - 1)**2*(i + 1)
Let i = -299/6 + 105/2. What is c in 0 - i*c + 16/3*c**3 - 4*c**4 + 4/3*c**2 = 0?
-2/3, 0, 1
Let p(v) be the third derivative of v**8/112 + v**7/10 + 19*v**6/40 + 5*v**5/4 + 2*v**4 + 2*v**3 + 13*v**2. Solve p(b) = 0 for b.
-2, -1
Let t(d) be the third derivative of d**7/525 + 11*d**6/300 + 4*d**5/25 - 3*d**4/5 + d**2. Suppose t(x) = 0. Calculate x.
-6, 0, 1
Let n = 4/33 + 7/33. Suppose -2/3 - j - n*j**2 = 0. What is j?
-2, -1
Suppose 0 - 1/3*p**4 - 2/3*p**3 + 0*p - 1/3*p**2 = 0. What is p?
-1, 0
Let y(t) be the second derivative of -t**9/6048 + t**7/840 - t**5/240 + 7*t**3/6 + 5*t. Let p(c) be the second derivative of y(c). Find u, given that p(u) = 0.
-1, 0, 1
Let s(y) = 2*y**4 + 6*y**2 + 11*y + 4. Let q(d) = -d**4 - 6*d**2 - 10*d - 4. Let b(k) = -3*q(k) - 2*s(k). Let w(v) be the first derivative of b(v). Factor w(c).
-4*(c - 2)*(c + 1)**2
Let x(f) be the second derivative of f**5/20 - f**4/6 - f**3/6 + f**2 - 2*f. Find b such that x(b) = 0.
-1, 1, 2
Suppose 4 - 1 - 2 - 6*q + 4*q + q**2 = 0. Calculate q.
1
Factor -3*o + 7*o**2 + 3 - 4*o**2 - 3*o.
3*(o - 1)**2
Let g(o) be the third derivative of o**8/2352 - o**7/735 + o**5/210 - o**4/168 - 7*o**2. Factor g(m).
m*(m - 1)**3*(m + 1)/7
Let u be (-13)/(-3) + 4/(-12). Suppose 0*o + 3*o = 4*v - 6, -u = 5*v + 2*o. Suppose v + 2/7*d - 2/7*d**2 = 0. Calculate d.
0, 1
Let q(g) be the second derivative of -g**5/5 - 2*g**4/3 - 2*g**3/3 + 4*g - 6. Factor q(r).
-4*r*(r + 1)**2
Let f(l) be the third derivative of -3*l**2 - 1/40*l**6 - 1/210*l**7 + 0*l**4 + 0 + 0*l**3 + 0*l - 1/30*l**5. Find n, given that f(n) = 0.
-2, -1, 0
Determine r, given that -3/8*r**3 + 0 + 0*r + 3/8*r**2 = 0.
0, 1
Factor 12 + 1/3*x**2 + 4*x.
(x + 6)**2/3
Let p(x) be the third derivative of -x**6/1260 + x**5/210 - x**4/84 + x**3/3 - 3*x**2. Let d(w) be the first derivative of p(w). Suppose d(h) = 0. What is h?
1
Let a = -202/5 + 616/15. Factor 0 + a*g**4 + 2/3*g**3 + 0*g + 0*g**2.
2*g**3*(g + 1)/3
Let q(v) be the first derivative of -1/16*v**4 - 2 + 1/8*v**2 + 0*v**3 + 0*v. What is w in q(w) = 0?
-1, 0, 1
Let u be 12/(4/1) - 2. Let s(h) be the first derivative of -26/3*h**3 + 3*h**4 + u - 2/5*h**5 + 12*h**2 - 8*h. Let s(t) = 0. Calculate t.
1, 2
Let d(r) = 2*r - 13. Let u be d(6). Let s be ((-2)/(-3) + u)*0. Determine b, given that -2/9*b + s + 2/9*b**2 = 0.
0, 1
Let j(c) be the third derivative of -1/12*c**4 + 0*c + 1/60*c**5 + 0 + 0*c**3 + 4*c**2. Determine f, given that j(f) = 0.
0, 2
Let q = -451 - -455. Factor 2*i**2 + 0*i + 0 + 2*i**3 + 1/2*i**q.
i**2*(i + 2)**2/2
Let i(y) = y**2 + 5*y + 6. Suppose 2*f = f - 4. Let g be i(f). Factor 0 - 5*a**g + a**3 - 2 - 2 + a + 7*a.
(a - 2)**2*(a - 1)
Let m be 4/(-6) - (-58)/6. Factor -1 + m*y**2 + 4 - 12*y - 15.
3*(y - 2)*(3*y + 2)
Factor 3/4*d**2 + 3/4*d**3 + 0*d + 0.
3*d**2*(d + 1)/4
Suppose -5*k = 4*y + 2, -2 = 3*y - 0*y + 4*k. Let q(v) be the first derivative of 2/3*v**3 - y + 0*v**2 + 0*v. Factor q(o).
2*o**2
Let y(l) = -42*l**2 - 24*l - 1. Let u(w) = 85*w**2 + 48*w + 2. Let p(c) = 4*u(c) + 7*y(c). Let o(r) = -r**2 - 1. Let z(q) = -2*o(q) + p(q). Factor z(f).
3*(4*f + 1)**2
Suppose 0 - 16 = -4*d. Suppose 16 = d*s - 0*s. Factor -2*c**2 + c**3 - 2*c**s + 4*c**2 - 2*c**3 + c.
-c*(c - 1)*(c + 1)*(2*c + 1)
Let r(j) be the third derivative of 0*j + 0*j**4 + 0 - 1/30*j**5 + 1/3*j**3 - 2*j**2. Let r(l) = 0. What is l?
-1, 1
Let -1/3*p + 1/6*p**2 + 0 = 0. Calculate p.
0, 2
Let u(z) be the third derivative of -z**8/1848 - 2*z**7/1155 - z**6/660 - 13*z**2. Suppose u(q) = 0. What is q?
-1, 0
Factor -2/3 + 4/3*j + 1/6*j**3 - 5/6*j**2.
(j - 2)**2*(j - 1)/6
Let t be ((-6)/4)/(15/20). Let s be 325/104*t/(-5). Find p such that -s*p**4 + 9/4*p**2 - 1 - 2*p**3 + 2*p = 0.
-2, -1, 2/5, 1
Let z(h) be the first derivative of -h**8/480 - h**7/140 - h**6/240 + h**5/120 + h**3/3 + 1. Let i(v) be the third derivative of z(v). Factor i(n).
-n*(n + 1)**2*(7*n - 2)/2
Let s(z) be the second derivative of 0*z**2 - 1/2*z**3 + 1/4*z**4 - 8*z + 0. Let s(x) = 0. Calculate x.
0, 1
Let v(d) be the third derivative of -d**6/260 + d**5/30 - 4*d**4/39 + 4*d**3/39 - 4*d**2. Find u, given that v(u) = 0.
1/3, 2
Let r(f) be the second derivative of f**7/189 + 2*f**6/135 - f**4/27 - f**3/27 + 3*f. Factor r(p).
2*p*(p - 1)*(p + 1)**3/9
Suppose 0*s = -11*s. Let d(y) be the first derivative of -y**4 - 2/3*y**3 + 2*y + s*y**5 + 1/6*y**6 - 1 + 3/2*y**2. Find c such that d(c) = 0.
-1, 1, 2
Suppose 0 = 2*k + k. Let d(p) be the second derivative of 0 - 2*p - 1/24*p**4 + k*p**2 - 1/6*p**3. Find a such that d(a) = 0.
-2, 0
Let p(w) be the second derivative of -5*w**4/42 - w**3/21 + 4*w**2/7 + 6*w + 1. Let p(d) = 0. Calculate d.
-1, 4/5
Let x(c) = -6*c**2 - c - 14. Let v(o) = -o**2 + o - 1. Let k(l) = 5*v(l) - x(l). Solve k(r) = 0 for r.
-3
Let h(d) be the second derivative of d**2 + 0*d**3 + 0 + 1/48*d**4 + 1/120*d**5 + d. Let m(g) be the first derivative of h(g). What is k in m(k) = 0?
-1, 0
Let d(o) be the first derivative of -o**6/18 - o**5/15 + o**4/12 + o**3/9 + 4. Determine b so that d(b) = 0.
-1, 0, 1
Let o(f) be the first derivative of -f**3/2 - 6*f**2 - 24*f + 9. What is t in o(t) = 0?
-4
Suppose k + 1/2*k**2 + 0 = 0. Calculate k.
-2, 0
Let w(a) be the second derivative of 0*a**4 + 0*a**2 + 1/3*a**3 + 3*a + 1/150*a**5 + 0 - 1/900*a**6. Let j(x) be the second derivative of w(x). Factor j(r).
-2*r*(r - 2)/5
Let d(l) = -l**2 - 9*l - 8. Let o be d(-8). Factor o*g**2 + 0*g**2 - g**2 + g**4 + 2*g - 3*g**3 + g**5.
g*(g - 1)**2*(g + 1)*(g + 2)
Let d = 194 + -968/5. Factor -4/5*k**2 + 2/5*k + d.
-2*(k - 1)*(2*k + 1)/5
Let v = 4/7 + -1/14. Find y, given that 1/2*y**2 + v*y**3 - 1/2 - 1/2*y = 0.
-1, 1
Let d = -17 - 8. Let u = d - -51/2. What is o in u*o**2 + 3/2*o**3 + o**4 + 0 + 0*o = 0?
-1, -1/2, 0
Let g = -12 + 11. Let x be ((1 - g)*-2)/(-1). Factor -2/7*m**3 - 2/7*m**x + 0 + 0*m + 2/7*m**5 + 2/7*m**2.
2*m**2*(m - 1)**2*(m + 1)/7
Let l = -460 - -466. Factor 6 - l*t + 3/2*t**2.
3*(t - 2)**2/2
Suppose s - w + 1 = 0, 3*w + w = s + 13. Suppose b + 3 = 0, 4*d - 6*b - 6 = -4*b. Find y such that d*y**2 - 5 + 5*y**2 + s - 3*y**2 = 0.
-1, 1
Let m(c) be the second derivative of 2*c**6/15 + 3*c**5/10 - c**4/6 - c**3 - c**2 + 7*c. Solve m(n) = 0 for n.
-1, -1/2, 1
Suppose -5*y = -15*y. Let n(q) be the third derivative of y*q + 0 + 0*q**5 - 1/140*q**7 + 0*q**4 + 0*q**3 - 1/40*q**6 - 3*q**2. Solve n(z) = 0 for z.
-2, 0
Let x(y) be the second derivative of -1/3*y**4 - 1/5*y**5 + 0*y**2 + 0*y**3 - y + 0. Factor x(c).
-4*c**2*(c + 1)
Let f(y) be the third derivative of y**8/1176 - y**7/147 + y**6/42 - y**5/21 + 5*y**4/84 - y**3/21 - 4*y**2. Find o such that f(o) = 0.
1
Let g(o) be the first derivative of 5 + 1/4*o**2 - o + 1/6*o**3. Let g(t) = 0. Calculate t.
-2, 1
Let w be (-12)/(-40)*24/9. Factor -6/5*m - w*m**2 + 4/5.
-2*(m + 2)*(2*m - 1)/5
Factor 8/17 + 18/17*t**2 - 22/17*t - 2/17*t**4 - 2/17*t**3.
-2*(t - 1)**3*(t + 4)/17
Let o(r) be the third derivative of r**6/720 + r**3/3 - r**2. Let d(u) be the first derivative of o(u). What is v in d(v) = 0?
0
Let c(h) = h**4 + h. Let f(a) = -21*a + 9*a**3 - 15*a**4 - 3*a**2 + 4 + 5 - 3. Let n(d) = -12*c(d) - f(d). Suppose n(r) = 0. What is r?
-1, 1, 2
Let d(n) be the second derivative of -1/10*n**5 + 0*n**3 + 0*n**2 + 1/6*n**4 + 1/21*n**7 - 1/15*n**6 - 7*n + 0. Let d(x) = 0. Calculate x.
-1, 0, 1
Suppose -9*x + 32 = -x. Let z(v) be the second derivative of -v - 1/24*v**x + 1/12*v**3 + 0 + 1/2*v**2. Factor z(p).
-(p - 2)*(p + 1)/2
Factor -10*p**3 - 6*p**4 + 3*