5, 0, 2
Let m(d) be the first derivative of d**7/2520 - d**6/540 - d**5/360 + d**4/36 - 4*d**3/3 + 3. Let q(t) be the third derivative of m(t). What is v in q(v) = 0?
-1, 1, 2
Let y be (-37)/(-3) + 30/45. Suppose -y = -k - 11. Factor 6/5*p**k + 4/5 - 2*p.
2*(p - 1)*(3*p - 2)/5
Let x(o) be the second derivative of o**5/120 + o**4/12 + o**3/4 + o**2/2 - 2*o. Let p(s) be the first derivative of x(s). What is t in p(t) = 0?
-3, -1
Let f be -2*(-39)/(-6)*-1. Determine h so that f*h**4 - 3*h**2 + 8*h**5 - 2*h + 12*h**3 + 2*h**2 - 3*h**5 - 3*h**3 = 0.
-1, 0, 2/5
Let o(i) be the third derivative of 1/96*i**4 + 0*i**3 - 1/840*i**7 - i**2 + 1/240*i**5 + 0*i - 1/480*i**6 + 0. Factor o(n).
-n*(n - 1)*(n + 1)**2/4
Let g be -1 - ((-72)/32)/(6/4). Solve g + 0*v - 1/2*v**2 = 0 for v.
-1, 1
Let p(n) be the first derivative of -1/5*n**3 + 6 + 1/10*n**6 + 0*n + 0*n**2 + 9/20*n**4 - 9/25*n**5. Suppose p(u) = 0. Calculate u.
0, 1
Let -4*u**3 - 132*u - 2*u**2 + 36 + 120*u - 18*u**2 = 0. What is u?
-3, 1
Let q(w) be the first derivative of w**7/420 + w**6/30 + w**5/5 + 2*w**4/3 - w**3 - 2. Let f(l) be the third derivative of q(l). Suppose f(h) = 0. What is h?
-2
Let t(g) be the first derivative of -15/2*g**2 - 7 - 6*g + 3*g**3. Factor t(z).
3*(z - 2)*(3*z + 1)
Let z(l) be the third derivative of -1/324*l**6 + 0*l + 1/27*l**4 - 2*l**2 + 0 + 2/135*l**5 + 1/6*l**3. Let i(r) be the first derivative of z(r). Factor i(v).
-2*(v - 2)*(5*v + 2)/9
Let u(h) be the third derivative of 0*h**3 + 25/336*h**8 + 0*h - 1/3*h**7 + 23/40*h**6 - 7/15*h**5 + 1/6*h**4 + 0 + 7*h**2. Let u(d) = 0. What is d?
0, 2/5, 1
Determine c, given that 0 + 4/3*c**4 + 0*c**2 - 2/3*c**3 + 0*c = 0.
0, 1/2
Let a(b) be the second derivative of -5*b**4/12 + 5*b**3/2 - 5*b**2 - 15*b. Find h, given that a(h) = 0.
1, 2
Let n(p) be the first derivative of -p**5/30 + p**4/3 - 3*p**2/2 + 5. Let v(x) be the second derivative of n(x). Factor v(s).
-2*s*(s - 4)
Suppose 0 = 2*l - 4*m - 18, 0*m = -2*l + m + 9. Let a be (7/56)/(l/6). Factor -1/2 - g**2 + 5/4*g + a*g**3.
(g - 2)*(g - 1)**2/4
Let n(g) be the third derivative of -g**7/70 + g**5/10 - g**3/2 - 31*g**2. Factor n(o).
-3*(o - 1)**2*(o + 1)**2
Suppose 0*x + 4*x - 52 = 0. Suppose 4*a - x - 3 = 0. Factor -2/7*k**a + 2/7*k**2 + 0*k + 0*k**3 + 0.
-2*k**2*(k - 1)*(k + 1)/7
Suppose 3*u = 4*x + 4*u - 11, -4*x + 2*u + 2 = 0. Let t(b) be the first derivative of -1/12*b**4 - 1/2*b**x - 1/3*b - 1/3*b**3 + 1. Find v, given that t(v) = 0.
-1
Let n(q) be the third derivative of -q**5/390 + q**4/78 - q**3/39 - 4*q**2. Factor n(x).
-2*(x - 1)**2/13
Suppose 4*u - 64 - 56 = 0. Let c be (-25)/u - (1 - 2). Factor -g**2 + c*g + 1/6*g**3 + 1/3*g**4 + 1/3.
(g - 1)**2*(g + 2)*(2*g + 1)/6
Suppose 6*t - t = 0. Let z(y) be the first derivative of -2/21*y**3 + 4 + t*y + 1/7*y**2. Factor z(x).
-2*x*(x - 1)/7
Let g(b) be the second derivative of b**5/110 - b**4/22 + 2*b**3/33 + b. Let g(o) = 0. Calculate o.
0, 1, 2
Let d(n) be the second derivative of 0*n**2 - n + 1/21*n**7 + 1/24*n**3 + 0 - 7/48*n**4 - 1/6*n**6 + 9/40*n**5. Solve d(m) = 0 for m.
0, 1/2, 1
Let y(n) be the second derivative of -n**6/120 - n**5/30 - n**4/24 + 3*n**2/2 + 4*n. Let h(j) be the first derivative of y(j). Factor h(o).
-o*(o + 1)**2
Suppose 0 = -3*x - x + 8. Suppose 4/5*l**4 + 0 + 4/5*l**x - 6/5*l**3 - 1/5*l - 1/5*l**5 = 0. What is l?
0, 1
Let a be (-4)/6*(-2 - 4). Let j be (-1)/a*(-2)/1. Factor -j*o**3 - 1/2*o**2 + 0 + o.
-o*(o - 1)*(o + 2)/2
Let u = -50 - -55. Let i(p) be the second derivative of -1/10*p**u - 1/15*p**6 + 2/3*p**4 - 7/6*p**3 + p**2 + 1/42*p**7 + 0 - 2*p. Factor i(g).
(g - 1)**4*(g + 2)
Let n be ((-3)/(-12))/(2/(-126)). Let i = n + 16. Factor -i + t**2 + 3/4*t.
(t + 1)*(4*t - 1)/4
Let a be (0 + 7)/(-7)*-2. Solve 0 + 2/11*h**3 + 2/11*h**a - 2/11*h - 2/11*h**4 = 0 for h.
-1, 0, 1
Let u(y) be the third derivative of y**8/1008 - y**7/315 - y**6/180 + 2*y**5/45 - 7*y**4/72 + y**3/9 + 5*y**2. Let u(w) = 0. Calculate w.
-2, 1
Factor 2/5*c**3 + 0*c + 1/5*c**4 - 3/5*c**5 + 0*c**2 + 0.
-c**3*(c - 1)*(3*c + 2)/5
Let g(x) be the second derivative of 3*x**5/20 - x**4/4 - x**3/2 + 3*x**2/2 + 42*x. Factor g(i).
3*(i - 1)**2*(i + 1)
Factor -2/11*u**3 + 0 + 2/11*u**5 + 0*u + 0*u**2 + 0*u**4.
2*u**3*(u - 1)*(u + 1)/11
Let a(q) be the second derivative of 2*q**6/75 - 7*q**5/150 - 2*q**4/45 + 7*q**3/45 - 2*q**2/15 + 23*q. Determine t so that a(t) = 0.
-1, 1/2, 2/3, 1
Suppose 2*r + 14 = -2*m, -5*r + m = -1 + 6. Let j be (3/r)/((-6)/8). Factor 4*o - 2*o**3 - 4*o + j*o**2.
-2*o**2*(o - 1)
Let m be 1/(1 + 5/(-4)). Let o = 21/5 + m. Solve -o*u + 1/5*u**2 + 0 = 0 for u.
0, 1
Let w be ((-12)/4 - -5) + 25/(-15). Let f(p) be the first derivative of -8/45*p**3 + w*p**2 + 3 + 1/30*p**4 - 4/15*p. Factor f(g).
2*(g - 2)*(g - 1)**2/15
Let w(d) = -4*d**4 + 3*d**3 + 33*d**2 + 11*d - 5. Let a(s) = 4*s**4 - 4*s**3 - 32*s**2 - 12*s + 4. Let c(m) = 5*a(m) + 4*w(m). Factor c(g).
4*g*(g - 4)*(g + 1)**2
Let n(f) be the first derivative of -f**7/18 + f**6/10 - f**5/30 + 5*f - 5. Let r(d) be the first derivative of n(d). Determine t so that r(t) = 0.
0, 2/7, 1
Let 5*x + 7*x**3 + 5*x**3 - x - 2*x**2 - 4*x**4 - 10*x**2 = 0. What is x?
0, 1
Let b(c) = 17*c**4 - 5*c**3 - 13*c**2 - 21*c - 17. Let g(m) = 3*m**2 + 10*m + 3 + 2 + 3 + 2*m**3 + 3*m**2 - 8*m**4. Let t(r) = -6*b(r) - 13*g(r). Factor t(i).
2*(i - 1)*(i + 1)**3
Suppose -5*l = 363 + 17. Let t be (-2)/5 - l/90. Factor -2/9*f**2 + 0 - t*f**3 + 0*f - 2/9*f**4.
-2*f**2*(f + 1)**2/9
Let q(x) = x**3 - x**2 - 1. Let h(k) = 4*k**3 - k**2 - k - 2. Let b(w) = h(w) - 2*q(w). Factor b(z).
z*(z + 1)*(2*z - 1)
Suppose h - l - 4 = -0*h, 0 = -4*h + 3*l + 15. Determine d, given that 2/5*d - 2/5*d**h - 2/5*d**2 + 0 + 2/5*d**4 = 0.
-1, 0, 1
Let n(a) = 9*a. Let x be n(1). What is y in -6 - 3*y**2 - y**2 - x*y + y**2 = 0?
-2, -1
Let o(h) be the third derivative of -h**9/1008 + h**8/2240 + h**7/168 - h**6/240 + h**4/12 + h**2. Let n(z) be the second derivative of o(z). Factor n(q).
-3*q*(q - 1)*(q + 1)*(5*q - 1)
Let o(z) = -z**2 + 1. Let h(v) = 6*v**2 + 4*v - 5. Let s(u) = h(u) + 5*o(u). Factor s(b).
b*(b + 4)
Suppose p = -3 + 101. Let h = p - 36. Find a, given that -35*a**2 - 368*a**4 - 294*a**3 + 25*a**4 - h*a**2 - 8*a + 13*a**2 = 0.
-2/7, 0
Let w(n) be the first derivative of 7*n**3 - 6*n**2 + 12*n/7 - 2. Factor w(t).
3*(7*t - 2)**2/7
Suppose -4*h = -6*z + 3*z + 9, 15 = 5*z - 3*h. Factor 0*q - 3*q**3 + z*q + 0*q**3.
-3*q*(q - 1)*(q + 1)
Let g be (4/(-5))/(1/(-5)). Suppose -6*q = -14*q + 24. Determine l so that -36*l**q - 27*l**5 + 0*l**2 - 46*l**g - 10*l**2 - 8*l**4 - l = 0.
-1, -1/3, 0
Let j(c) be the first derivative of c**6/15 - c**4/6 + 6*c + 7. Let z(o) be the first derivative of j(o). Solve z(w) = 0 for w.
-1, 0, 1
Let i(r) be the second derivative of 0*r**3 - 16/45*r**6 + 2/9*r**4 - 10/63*r**7 + 7*r + 0 - 1/15*r**5 + 0*r**2. Find z, given that i(z) = 0.
-1, 0, 2/5
Suppose -48 = -2*p - p. Let j = -12 + p. Determine g so that -14/5*g**2 - 26/5*g**j + 2/5*g + 8/5*g**5 + 6*g**3 + 0 = 0.
0, 1/4, 1
Let r(k) = k**3 - 11*k**2 - 7*k - 7. Let z(f) = 4*f**3 - 34*f**2 - 20*f - 22. Let m(b) = 20*r(b) - 6*z(b). Factor m(w).
-4*(w + 1)**2*(w + 2)
Let j = -6 - -13. Let i = 349 - 209. Let 109*a**3 - 10*a**3 - 16 - 250*a**4 + i*a**2 - j*a - 17*a + 51*a**3 = 0. Calculate a.
-2/5, 2/5, 1
Let l(b) be the third derivative of -b**5/240 - b**4/96 + b**3/12 - 9*b**2. Factor l(m).
-(m - 1)*(m + 2)/4
Let c(p) be the third derivative of 0*p - 1/9*p**3 + 8*p**2 - 1/90*p**5 + 0 - 1/18*p**4. Find s, given that c(s) = 0.
-1
Let u(j) be the first derivative of -2/3*j + 1/12*j**4 - 4/9*j**3 + 5/6*j**2 - 5. Factor u(a).
(a - 2)*(a - 1)**2/3
Let j(l) be the third derivative of -l**8/2240 + l**7/560 - l**6/480 + l**3/2 - 5*l**2. Let n(i) be the first derivative of j(i). Solve n(x) = 0.
0, 1
Let k(v) be the second derivative of -v**5/5 - 2*v**4/3 + 2*v**3/3 + 4*v**2 + 2*v. Factor k(y).
-4*(y - 1)*(y + 1)*(y + 2)
Let l(q) be the second derivative of 1/3*q**4 - 3/5*q**5 - q**2 + 0 + q**3 + 1/7*q**7 - 1/15*q**6 - 4*q. Let l(u) = 0. Calculate u.
-1, 1/3, 1
Let u(g) be the first derivative of g**3/5 - 6*g**2/5 - 3*g + 41. Determine v, given that u(v) = 0.
-1, 5
Factor -3/8*p**4 + 0 + 3/8*p**2 + 0*p - 3/8*p**3 + 3/8*p**5.
3*p**2*(p - 1)**2*