d(l) be the second derivative of -l**8/6720 + l**6/1440 - l**3/3 + 2*l. Let u(a) be the second derivative of d(a). Let u(c) = 0. What is c?
-1, 0, 1
Suppose -4*g + 4 + 20 = 0. Let h be (0 + 2)/(4/g). Factor -1/3*j**2 + 1/3 - 1/3*j**h + 1/3*j.
-(j - 1)*(j + 1)**2/3
Let m = -7 + 7. Let s be (2 + -2 + 0)/(-3). Let -2/5*o**5 + m*o + 2/5*o**3 + 0 + 0*o**2 + s*o**4 = 0. What is o?
-1, 0, 1
Let v(j) = 4 - 3*j - 3*j**2 + 2*j + 3. Let s(u) = 2*u**2 + u - 4. Let z = -2 + -1. Let x(d) = z*v(d) - 5*s(d). Solve x(m) = 0.
-1
Let i(y) be the third derivative of y**6/30 - y**5/5 + y**4/2 - 2*y**3/3 + 15*y**2. Suppose i(c) = 0. What is c?
1
Let u(z) be the first derivative of -4/7*z + 1/7*z**2 + 2/3*z**3 + 11 - 2/35*z**5 + 2/21*z**6 - 1/2*z**4. Determine a, given that u(a) = 0.
-2, -1/2, 1
Suppose 0 = q - 0*q - 6. Factor -1 - 2*w**2 + q + 2*w + 0*w - 1.
-2*(w - 2)*(w + 1)
Suppose 0 = -3*p + 2*p + 2. Let i = 1/20 + 1/5. Suppose 2*a + i*a**3 - 5/4*a**p - 1 = 0. Calculate a.
1, 2
Suppose -5*w + 10 + 15 = 0. Suppose -8*d = -w*d. Factor -3/4*n**2 - 1/4*n + d - 3/4*n**3 - 1/4*n**4.
-n*(n + 1)**3/4
Let m(h) be the third derivative of 1/12*h**4 - 2/3*h**3 + h**2 + 1/10*h**5 + 0 + 0*h. Factor m(l).
2*(l + 1)*(3*l - 2)
Let m = 1/316 + 311/1580. Find t such that -3/5 + 2/5*t + m*t**2 = 0.
-3, 1
Find k such that -10*k**3 + 0 + 0*k + 25/2*k**2 - 5/2*k**4 = 0.
-5, 0, 1
Let v(s) be the third derivative of s**7/210 + s**6/120 - s**5/60 - s**4/24 - s**2. Factor v(y).
y*(y - 1)*(y + 1)**2
Let n(p) = 6*p**2 - 3*p - 4. Let y(o) = -o**3 - 4*o**2 + 4*o - 1. Let i be y(-5). Let z(c) = 5*c**2 - 2*c - 3. Let a(v) = i*n(v) - 5*z(v). Factor a(d).
-(d + 1)**2
Let t be ((-16)/(-10))/(3/15). Suppose 0 = -t*a + 4*a. What is i in 3 - 5*i**2 - 7*i + a - 5 = 0?
-1, -2/5
Let j(w) be the third derivative of w**4/6 - w**3/6 - w**2. Let o be j(1). Suppose 0 + 1/3*z**o + 1/3*z + 2/3*z**2 = 0. Calculate z.
-1, 0
Let m = 41 + -37. Find h, given that -1/2*h**m + 1/2 - h + 0*h**2 + h**3 = 0.
-1, 1
Let t(k) be the first derivative of -k**4/12 - 2*k**3/9 + 13. What is b in t(b) = 0?
-2, 0
Let i be (-4)/((0 - -2)/(-1)). Let c(a) be the third derivative of 1/210*a**6 + 0 - 1/42*a**4 + i*a**2 + 1/21*a**3 - 1/735*a**7 + 0*a + 0*a**5. Factor c(b).
-2*(b - 1)**3*(b + 1)/7
Let s(a) be the third derivative of 0*a**4 + 0 + 0*a**5 + a**2 + 0*a**3 + 1/240*a**6 + 0*a. Determine c so that s(c) = 0.
0
Factor -35 + 0*i - 80*i**2 - 10 - 120*i.
-5*(4*i + 3)**2
Let l(x) be the second derivative of 2/3*x**2 + 0 - 2/9*x**3 - x + 1/36*x**4. Factor l(z).
(z - 2)**2/3
Suppose 4*c - 20 - 112 = 0. Let s = c + -31. Factor 2/5*z**s - 4/5*z + 2/5.
2*(z - 1)**2/5
Let f = 0 - -2. Let x(g) = -g + 8. Let a be x(5). Factor -7*r**4 - 4*r + a*r**2 + f*r + 0*r + 3*r**3 + 3*r**5.
r*(r - 1)**3*(3*r + 2)
Let q be (-1)/((-6)/(-8) - 1). Let k(j) be the first derivative of -1 + 24/5*j**5 + 1/3*j**3 + 0*j - 9/4*j**q + 0*j**2 - 8/3*j**6. Find a such that k(a) = 0.
0, 1/4, 1
Let x(v) be the third derivative of -v**7/2520 + v**6/360 - v**4/24 - 3*v**2. Let q(p) be the second derivative of x(p). Suppose q(l) = 0. What is l?
0, 2
Suppose -2*p = 3*m - 16, 0 = 5*m - p - 0 - 5. What is c in -2*c + 42/11*c**m - 34/11*c**3 + 10/11*c**4 + 4/11 = 0?
2/5, 1
Suppose -3*k - 5*k = 0. Factor 16 + 3*i + k*i + i**2 + 5*i.
(i + 4)**2
Let x = -3 + 5. Factor -3 + 7 + 3*v**x - 1 - 6*v.
3*(v - 1)**2
Let b(d) be the second derivative of 6*d - 4/15*d**4 + 6/25*d**6 + 0 + 0*d**3 + 1/21*d**7 + 6/25*d**5 + 0*d**2. Determine u, given that b(u) = 0.
-2, 0, 2/5
Factor 0 + 1/2*q**3 - q**2 + 0*q.
q**2*(q - 2)/2
Let j(n) = -3*n**3 - 15*n**2 - 4*n - 4. Let g(f) = 3*f**3 + 15*f**2 + 5*f + 5. Let c(h) = 4*g(h) + 5*j(h). Find q, given that c(q) = 0.
-5, 0
Let w(f) = -66*f**3 + 117*f**2 - 51*f - 27. Let d(b) = -5*b**3 + 9*b**2 - 4*b - 2. Let q(a) = 27*d(a) - 2*w(a). Solve q(j) = 0 for j.
0, 1, 2
Factor -3*j**4 - 25*j**3 - 3*j**4 - 15*j - 11*j**2 + j**4 - 24*j**2.
-5*j*(j + 1)**2*(j + 3)
Factor 6/7 + 2/7*m**2 - 8/7*m.
2*(m - 3)*(m - 1)/7
Let h(f) be the second derivative of 0*f**3 - 1/10*f**5 + 0*f**2 - 5*f + 1/6*f**4 - 1/15*f**6 + 1/21*f**7 + 0. Factor h(n).
2*n**2*(n - 1)**2*(n + 1)
Suppose 1059*q**3 - 1049*q**3 + 8*q + 2*q - 25*q**2 = 0. What is q?
0, 1/2, 2
Let 53 - 2*q**3 + 3*q**2 - 57 + q**3 = 0. Calculate q.
-1, 2
Let c = 59/11 + 3/22. Factor 2*g + 6*g**2 + 25/2*g**5 - 15*g**4 + 0 - c*g**3.
g*(g - 1)**2*(5*g + 2)**2/2
Let z(p) be the second derivative of -p**7/420 + p**6/90 - p**5/60 - 2*p**3/3 + 2*p. Let m(s) be the second derivative of z(s). Factor m(j).
-2*j*(j - 1)**2
Let z(t) be the first derivative of 42*t**5/85 + 29*t**4/34 + 8*t**3/51 - 4*t**2/17 - 34. Find l, given that z(l) = 0.
-1, -2/3, 0, 2/7
Find z such that -18 + 12*z + 6*z**2 + 14*z**3 - 17*z**3 - 6 = 0.
-2, 2
Let a be (7 + (-19)/2)/((-10)/8). Determine h so that 7/3*h**3 - 4*h**a + h + 2/3 = 0.
-2/7, 1
Let m(v) be the first derivative of 3*v**5/5 - 6*v**3 + 12*v**2 - 9*v - 4. Find q such that m(q) = 0.
-3, 1
Let s be (8/3)/(-4)*-2. Let u be 1 + 3 - 4/(-6). Determine n so that -s - 2*n**2 - 14/3*n**3 + 10/3*n**4 + u*n = 0.
-1, 2/5, 1
Solve 11*p**3 - 57*p**2 + p**4 - 8*p - 3*p**3 + 12 + 3*p**4 + 41*p**2 = 0 for p.
-3, -1, 1
Let c(f) = f**3 + 2*f**2 - f - 2. Let x be c(2). Factor -w**2 - w**3 - x*w + 6*w + 7*w + w**4.
w*(w - 1)**2*(w + 1)
Let i(d) be the first derivative of d**4/4 + d**3/3 + 11. Factor i(m).
m**2*(m + 1)
Let p be 18/(-6)*25/(-90). Factor -2/3*l + 0 + p*l**3 + 2/3*l**2 - 1/2*l**4.
-l*(l - 2)*(l + 1)*(3*l - 2)/6
Let n(r) be the second derivative of -r**7/840 - r**6/120 - r**5/40 - r**4/24 + 2*r**3/3 - 9*r. Let u(b) be the second derivative of n(b). Solve u(p) = 0.
-1
Let j be ((-1)/(-2))/(2/16). Let q(p) be the first derivative of 1 - 1/16*p**j + 0*p - 1/20*p**5 + 0*p**2 + 0*p**3. Factor q(w).
-w**3*(w + 1)/4
Let i be ((-2)/(-10)*1)/(0 + 1). Let b be -3 - (7/(-5) - 2). Determine v so that i*v**2 - 1/5*v - b = 0.
-1, 2
Let m = 4 + 1. Suppose 1 = -2*q + m. Determine n, given that 2*n + n**3 + n**4 - n**q + 0*n**3 - 3*n**3 = 0.
-1, 0, 1, 2
Determine p, given that 2/7*p - 2/7*p**2 - 2/7*p**3 + 2/7 = 0.
-1, 1
Let t(i) be the third derivative of -i**6/1980 - i**5/660 + i**4/66 - i**3/6 - 6*i**2. Let s(n) be the first derivative of t(n). Suppose s(r) = 0. Calculate r.
-2, 1
Let m(a) = a**3 + 5*a**2 + a + 5. Let q be m(-5). Let j = 2 - q. Factor 2/5*r + 0 + 2/5*r**j.
2*r*(r + 1)/5
Let f(r) be the third derivative of 0*r - 1/30*r**5 + 2*r**2 - 1/30*r**6 + 0 + 0*r**4 - 1/105*r**7 + 0*r**3. Solve f(o) = 0 for o.
-1, 0
Let g = -255/4 - -127. Let r = g - 63. Factor -t**2 - 1/2 - r*t**3 - 5/4*t.
-(t + 1)**2*(t + 2)/4
Let y = 38 + -24. Let f = y + -12. What is m in 0*m + 0 + 1/4*m**f = 0?
0
Let i(x) = -x**2 + 11*x + 17. Let r be i(12). Let g(z) be the first derivative of -2/25*z**r - 2 + 0*z**3 + 0*z**2 + 0*z - 1/10*z**4. What is t in g(t) = 0?
-1, 0
Let g be (3 + 18/(-4))*-2. Let n(z) be the second derivative of 0*z**g + 1/24*z**4 - 1/20*z**5 + 1/60*z**6 + 0*z**2 + z + 0. Factor n(x).
x**2*(x - 1)**2/2
Let l = -103 + 928/9. Let t(n) be the third derivative of -5/36*n**4 - 1/18*n**6 - 1/504*n**8 + 0 + 1/63*n**7 + l*n**3 + 1/9*n**5 + 0*n - 3*n**2. Factor t(o).
-2*(o - 1)**5/3
What is d in 2/9*d**3 - 2/9*d + 0*d**2 + 0 = 0?
-1, 0, 1
Let m(d) = 8*d**3 + 14*d**2 + 11. Let l(s) = 3*s**3 + 5*s**2 + 4. Let t(i) = -11*l(i) + 4*m(i). Suppose t(w) = 0. What is w?
0, 1
Let f(k) = 3*k**5 - 6*k**4 + 9*k**3 + 6. Let l(v) = -2*v**5 + 5*v**4 - 9*v**3 + v**2 - 5. Let z(i) = 5*f(i) + 6*l(i). Factor z(o).
3*o**2*(o - 1)**2*(o + 2)
Let c(w) = -8*w**4 - 8*w**3 + 19*w**2 + 45*w + 16. Let n(u) = -12*u**4 - 12*u**3 + 29*u**2 + 67*u + 24. Let y(k) = 7*c(k) - 5*n(k). Suppose y(g) = 0. What is g?
-1, 2
Let f(g) = -3*g**2 - 3*g + 9. Let l(d) = -3*d**2 - 3*d + 8. Let p be 6/(-45)*3*-5. Let j(c) = p*f(c) - 3*l(c). Factor j(x).
3*(x - 1)*(x + 2)
Let q(a) be the second derivative of -a**7/42 - a**6/30 + a**5/10 + a**4/6 - a**3/6 - a**2/2 - 3*a. Solve q(z) = 0.
-1, 1
Factor -11/4*y + 7/4*y**2 - 1/4*y**3 + 5/4.
-(y - 5)*(y - 1)**2/4
Let m be ((-825)/(-35))/(-5) - -5. Determine a so that 4/7*a**2 - 2/7*a - 2/7*a**4 - 2/7*a**5 + 4/7*a**3 - m = 0.
-1, 1
Let z(r) = r**3 - 8*r**2 - 9*r + 6. Let n be z(9). Factor -2*c**3 - c + n*c**2 + 10*c + 4 - 2*c