o**2 + h.
-3*o*(o - 1)/5
Let g(f) be the first derivative of -f**8/1680 + f**6/180 - f**4/24 + 5*f**3/3 - 5. Let k(q) be the third derivative of g(q). Let k(r) = 0. Calculate r.
-1, 1
Let h(x) be the first derivative of -x**5 - 5*x**4 - 5*x**3 + 39. Find i, given that h(i) = 0.
-3, -1, 0
Let g(m) be the second derivative of -1/60*m**5 + 8*m + 0*m**2 + 1/18*m**4 + 0*m**3 + 0. Find h such that g(h) = 0.
0, 2
Let 16/7*l**3 + 6*l**2 - 5/7 + 16/7*l - 5/7*l**4 = 0. What is l?
-1, 1/5, 5
Let c(t) be the third derivative of t**6/1440 - t**5/60 + t**4/6 - 7*t**3/6 + 7*t**2. Let n(x) be the first derivative of c(x). Let n(b) = 0. What is b?
4
Factor -9*w**4 + 3*w**5 + w**5 + 5*w**4 - 12*w**4 - 16*w**2 + 4*w + 24*w**3.
4*w*(w - 1)**4
Suppose -7*x + 8 = -5*x. Let j(a) be the third derivative of 1/210*a**7 + 0*a**3 + 2*a**2 + 0*a + 0*a**x + 0*a**6 + 0 - 1/60*a**5. Factor j(p).
p**2*(p - 1)*(p + 1)
Let n(p) be the second derivative of -p**5/20 + 5*p**4/12 + 13*p**3/6 + 7*p**2/2 - 8*p - 4. Solve n(j) = 0 for j.
-1, 7
Find j, given that -3*j**5 + 4 + 8*j**4 + 15*j**3 - 3*j**2 - 3*j**4 - 16 - 24*j - 2*j**4 = 0.
-1, 2
Find l, given that 2/7*l**2 + 2/7 - 4/7*l = 0.
1
Let f(t) be the third derivative of -t**6/540 + t**5/135 - t**4/108 - 7*t**2. Solve f(n) = 0.
0, 1
Let o(k) be the third derivative of -k**7/210 + k**6/240 - k**4/8 - 2*k**2. Let z(n) be the second derivative of o(n). Solve z(b) = 0 for b.
0, 1/4
Let b(o) be the third derivative of o**6/54 - 2*o**5/45 - o**4/6 + 4*o**3/27 - 7*o**2. Suppose b(s) = 0. What is s?
-1, 1/5, 2
Determine d so that 2/9*d**4 - 8/9*d**3 + 0 + 0*d + 8/9*d**2 = 0.
0, 2
Let s = 395 + -4735/12. Let r(b) be the first derivative of -b - s*b**3 - 3/2*b**2 + 3/4*b**4 + 9/20*b**5 - 2. Factor r(x).
(x - 1)*(x + 1)*(3*x + 2)**2/4
Factor 0*c - 5/2*c**4 + 0 + 1/2*c**5 - 2*c**2 + 4*c**3.
c**2*(c - 2)**2*(c - 1)/2
Suppose 1/4*c**2 + 0 - 1/2*c = 0. What is c?
0, 2
Let g(h) be the second derivative of h**6/255 - h**4/34 + 2*h**3/51 - 25*h. Factor g(r).
2*r*(r - 1)**2*(r + 2)/17
Suppose 2*q = 6*q + 4. Let v(o) = -o**4 + o**2 + 1. Let c(a) = -6*a**4 + a**3 + 6*a**2 - a + 5. Suppose -3 - 2 = -g. Let h(j) = g*v(j) + q*c(j). Factor h(z).
z*(z - 1)**2*(z + 1)
Let v(z) be the first derivative of 2/5*z**5 - 1/2*z**2 + 0*z**4 + 1/6*z**6 + 0*z + 6 - 2/3*z**3. Factor v(j).
j*(j - 1)*(j + 1)**3
Find w such that 0*w - 1/3*w**2 - 1/3*w**4 - 2/3*w**3 + 0 = 0.
-1, 0
Factor 1/2*z**4 + 3/4*z**3 - 1/4 - 3/4*z - 1/4*z**2.
(z - 1)*(z + 1)**2*(2*z + 1)/4
Suppose 4*t = 4*b + 64, 5*b + 5*t + 88 = -2. Let n = 19 + b. Determine u, given that -n*u**2 - 2*u - 1/2*u**3 + 0 = 0.
-2, 0
Let k(u) be the second derivative of u**4/20 - 7*u**3/15 - u**2/2 - 14*u. Factor k(n).
(n - 5)*(3*n + 1)/5
Let g(l) = l**3 - 15*l**2 - 17*l + 16. Let z(j) = j**2 - 3*j - 12. Let w be z(7). Let i be g(w). Suppose -3*o**2 - 3/4*o**3 - 3*o + i = 0. Calculate o.
-2, 0
Let d(u) = -u**2 + 3*u + 3. Let s be d(0). Let v(a) be the third derivative of 0 + 0*a + 7/150*a**5 - 2*a**2 + 0*a**s - 1/30*a**4. Factor v(k).
2*k*(7*k - 2)/5
Let m(l) be the second derivative of -l**7/147 - 2*l**6/105 + l**4/21 + l**3/21 + 8*l. Suppose m(n) = 0. What is n?
-1, 0, 1
Let a = -20 + 12. Let j = -5 - a. Factor 1/4*g + 0 + 3/4*g**j + 1/4*g**4 + 3/4*g**2.
g*(g + 1)**3/4
Suppose -4*i - 3 = j, -2*i - 3*j = -2*j + 3. Factor z**3 + i - 1/2*z + 0*z**4 + 0*z**2 - 1/2*z**5.
-z*(z - 1)**2*(z + 1)**2/2
Let -24/11*c - 72/11 - 2/11*c**2 = 0. What is c?
-6
Let l(y) be the first derivative of 5*y**4/2 + y**3/2 - 3*y**2 - 9*y - 6. Let b(w) be the first derivative of l(w). Let b(s) = 0. Calculate s.
-1/2, 2/5
Let b(y) be the first derivative of y**6/180 - y**5/90 - y**4/36 + y**3/9 + 2*y**2 - 5. Let w(j) be the second derivative of b(j). Factor w(i).
2*(i - 1)**2*(i + 1)/3
Let h(m) = 7*m**2 + 3. Suppose 0 = -a - 1 - 2. Let b(q) = -4*q**2 - 2. Let k(d) = a*h(d) - 5*b(d). Factor k(v).
-(v - 1)*(v + 1)
Let o(d) be the second derivative of -d**8/3360 + d**7/1260 - d**4/12 - 3*d. Let g(j) be the third derivative of o(j). Solve g(y) = 0 for y.
0, 1
Let n(s) be the first derivative of -5*s**4/4 + 25*s**3/3 - 20*s**2 + 20*s - 6. Factor n(k).
-5*(k - 2)**2*(k - 1)
Suppose 136 - 136 + 12*b**3 - 33*b**2 - 6*b - 3*b = 0. Calculate b.
-1/4, 0, 3
Let q(x) be the first derivative of -x**6/1260 + x**5/210 - x**4/84 + 5*x**3/3 + 4. Let u(t) be the third derivative of q(t). Suppose u(d) = 0. Calculate d.
1
Suppose 5*s = 4*t + 6 + 1, 0 = t + 3*s - 11. Let h(p) be the second derivative of -1/54*p**4 + 1/9*p**t - 1/90*p**5 + 0 - 2*p + 1/27*p**3. Factor h(n).
-2*(n - 1)*(n + 1)**2/9
Suppose -2*l + 3*g + 1 + 15 = 0, -4*l = -4*g - 24. Let k = -61 - -307/5. What is r in 0 - 2/5*r - k*r**3 - 4/5*r**l = 0?
-1, 0
Let k(c) = 2*c**2 - 2*c - 4. Let p(z) = 18 - 9 - 8. Let f(n) = -k(n) - 4*p(n). Factor f(a).
-2*a*(a - 1)
Let y(u) be the first derivative of 0*u + 1/3*u**3 - 9 + 1/2*u**2. Solve y(p) = 0 for p.
-1, 0
Let a be 2/(-9) + (-4512)/(-4590). Let p = 2/51 + a. Factor 0 + 1/5*q**4 + 0*q**2 - 3/5*q**3 + p*q.
q*(q - 2)**2*(q + 1)/5
Let a(b) be the second derivative of b**5/100 + b**4/60 - 8*b. Let a(d) = 0. Calculate d.
-1, 0
Let t = -5368 - -16253/3. Let r = t + -49. What is w in -5/3*w**4 + w**3 + 1/3*w**2 - 1/3*w + r*w**5 + 0 = 0?
-1/2, 0, 1
Let z(f) be the first derivative of 7*f**5/5 + f**4/2 - 7*f**3/3 - f**2 + 1. What is b in z(b) = 0?
-1, -2/7, 0, 1
Let o = -14/9 - -65/36. What is l in 0 + 0*l + 0*l**3 - 1/4*l**4 + 0*l**2 - o*l**5 = 0?
-1, 0
Let p be 2 + -3 + (-10)/(-6). Let 0 - 1/3*l**4 + 2/3*l**3 + 1/3*l**2 - p*l = 0. Calculate l.
-1, 0, 1, 2
Suppose 2*j = -j. Let v(g) = -2*g**2 - 25*g - 9. Let n be v(-12). Suppose 1/5*i**2 - 3/5*i**n + 2/5*i + j = 0. Calculate i.
-2/3, 0, 1
Let k(j) be the second derivative of j**4/30 - 4*j**2/5 + 2*j. Factor k(u).
2*(u - 2)*(u + 2)/5
Factor -2/15*y**2 + 0 - 2/15*y.
-2*y*(y + 1)/15
Let p(f) = -f**2 - 13*f - 30. Let h be p(-10). Let m(z) be the second derivative of h*z**2 - z + 1/30*z**4 - 1/15*z**3 + 0. What is w in m(w) = 0?
0, 1
Let y = 8 + -4. Find a, given that 0*a**4 - 4*a**2 - a**y + 3*a**2 + 10*a**3 - 8*a**3 = 0.
0, 1
Let r be 21 - (1 + 0 + 1). Suppose -2 + 15*a - 8*a**2 + r*a - 6 = 0. What is a?
1/4, 4
What is w in 0*w**2 + 0 - 1/7*w**3 - 1/7*w**4 + 0*w = 0?
-1, 0
Let o(l) be the first derivative of 2*l**5/5 + 2*l**4 + 4*l**3 + 4*l**2 + 2*l + 7. Suppose o(k) = 0. Calculate k.
-1
Let z be 1/(-4)*((-594)/(-63) + -10). Factor 1/7*a - z*a**2 - 1/7*a**3 + 1/7*a**4 + 0.
a*(a - 1)**2*(a + 1)/7
Let z = 13/180 + 3/20. Let m(j) be the first derivative of 0*j - 2 - z*j**3 + 1/12*j**4 + 1/6*j**2. Factor m(g).
g*(g - 1)**2/3
Let k be 24/(-84) - (-1082)/3640. Let n(j) be the third derivative of -k*j**6 + 0 + j**2 + 0*j**3 - 1/156*j**4 + 0*j - 1/65*j**5 - 4/1365*j**7. Factor n(h).
-2*h*(h + 1)**2*(4*h + 1)/13
Let i(v) be the third derivative of -v**5/120 - v**4/48 - 8*v**2. What is y in i(y) = 0?
-1, 0
Let q(m) be the first derivative of 2*m**5/15 - 5*m**4/6 + 16*m**3/9 - 4*m**2/3 - 25. Factor q(t).
2*t*(t - 2)**2*(t - 1)/3
Let m be (-14)/(-12) - 1/2. Let s be 4/10*(-5)/(-3). Solve -4/3*k**4 + 0*k**2 + 0 - m*k**5 + 0*k - s*k**3 = 0 for k.
-1, 0
Let b(q) = 5*q**4 + 4*q**3 - 19*q**2 + 14*q + 4. Let k(z) = 10*z**4 + 7*z**3 - 37*z**2 + 27*z + 7. Let x(p) = 7*b(p) - 4*k(p). Suppose x(d) = 0. Calculate d.
-2, 0, 1
Let n = -4 + 6. Determine t, given that 2*t**4 + n + 4*t - 3*t**4 - 4*t**3 - t**4 + 0*t**4 = 0.
-1, 1
Let f(l) be the second derivative of l**7/14 + 2*l**6/5 + 9*l**5/10 + l**4 + l**3/2 + 3*l. Factor f(b).
3*b*(b + 1)**4
Let d = -4 - -10. Let m be 3/9 - (-10)/d. Factor -5/4*n - 1/2 + 5/4*n**3 + 1/2*n**m.
(n - 1)*(n + 1)*(5*n + 2)/4
Let m(w) = -w**3 - 12*w**2 + 14*w + 16. Let f be m(-13). Let b - b**3 + 0*b - 3*b**2 - 3*b**f + 0*b**3 = 0. Calculate b.
-1, 0, 1/4
Let k(f) be the second derivative of -1/18*f**3 + 0*f**2 - 3*f + 0 - 1/36*f**4. What is v in k(v) = 0?
-1, 0
Factor 6/11 + 12/11*w**3 + 2/11*w**4 + 20/11*w + 24/11*w**2.
2*(w + 1)**3*(w + 3)/11
Solve -1/2 + 1/4*u**2 + 1/4*u = 0 for u.
-2, 1
Suppose 35*y - 38*y = 0. Let z(r) be the third derivative of y + 0*r**3 + 0*r + 1/30*r**5 - 1/120*r**6 - 3*r**2 + 0*r**4. Solve z(l) = 0.
0, 2
Let u be (-4)/(-6)*3/25*5. Let a(n) = n + 5. Let g be a(-5). Factor u*l + g + 2/5