.
2*g**3*(g + 1)/5
Let s(i) be the second derivative of 0 + 6*i + 0*i**3 - 1/12*i**4 + 1/20*i**5 + 1/30*i**6 - 1/42*i**7 + 0*i**2. Determine m, given that s(m) = 0.
-1, 0, 1
Let m(k) = -4*k**3 + 16*k**2 - 4*k + 24. Let o(f) = 6 + 0 - 5 - 2 - f**2. Let y(i) = -m(i) - 24*o(i). Suppose y(n) = 0. What is n?
-1, 0
Let c be 204/(-32)*1 + 4. Let f = -15/8 - c. Find y, given that 0 + 1/2*y**2 - y + f*y**3 = 0.
-2, 0, 1
Let q(z) be the second derivative of 0*z**2 + 0 + 1/40*z**5 + 0*z**4 - z - 1/12*z**3. Factor q(r).
r*(r - 1)*(r + 1)/2
Let q(g) be the first derivative of g**6/10 + 12*g**5/25 + 3*g**4/10 - 4*g**3/5 - 9*g**2/10 - 3. Find o such that q(o) = 0.
-3, -1, 0, 1
Let u(f) = -f**2 - f. Let q = 12 + -9. Suppose -3*h + w = -8*h + 5, -w + 3 = q*h. Let i(l) = 2*l**2 - 4*l - 8. Let m(x) = h*i(x) + 4*u(x). Solve m(t) = 0.
-2
Let u(m) be the second derivative of 0 - 2/21*m**7 - 8*m**2 + 2/15*m**6 + m**5 - 16/3*m**3 - 1/3*m**4 + 9*m. Let u(c) = 0. What is c?
-1, 2
Let x = 171 - 2733/16. Let p(g) be the first derivative of -3/2*g + 1/2*g**3 + 2 + 3/8*g**2 - x*g**4. Find v such that p(v) = 0.
-1, 1, 2
Let a be (-1)/(-1) - (-12)/24. Suppose 1/2 - a*z + 3/2*z**2 - 1/2*z**3 = 0. What is z?
1
Let t(a) be the first derivative of -1/2*a**2 - a + 1/12*a**4 + 0*a**3 - 1. Let c(u) be the first derivative of t(u). Factor c(k).
(k - 1)*(k + 1)
Let d(w) = -w**4 + 12*w**3 - 7*w**2 + 2*w + 2. Let v(o) = o**4 + o**3 + o**2 + 1. Let m(k) = d(k) - 2*v(k). Let m(x) = 0. Calculate x.
0, 1/3, 1, 2
Let j = -34 + 36. Suppose -4*f + 29 = 3*c + 5, j*c = 4*f - 4. Factor 0*r + 10/9*r**f + 4/9*r**2 + 0.
2*r**2*(5*r + 2)/9
Let h(o) be the first derivative of o**7/105 + o**6/60 - o**5/30 - o**4/12 + 3*o**2/2 - 1. Let c(a) be the second derivative of h(a). Factor c(x).
2*x*(x - 1)*(x + 1)**2
Let r(c) be the first derivative of c**5/20 - c**4/6 - 2*c**3/3 + 4*c**2 + 5*c + 5. Let l(n) be the first derivative of r(n). What is d in l(d) = 0?
-2, 2
Let g = 1831/15 - 122. Let h(l) be the second derivative of l + 0*l**3 - 1/5*l**5 - g*l**6 + 0*l**2 - 1/6*l**4 + 0. Factor h(c).
-2*c**2*(c + 1)**2
Let l(w) be the second derivative of 0*w**3 + 0 + 1/2*w**2 + w + 1/30*w**5 + 0*w**4. Let z(m) be the first derivative of l(m). Factor z(q).
2*q**2
Let l = 6 + -2. Factor -k**2 + 4*k**l + 4*k**2 + 5*k**3 + 3*k**2 - k - 14*k**3.
k*(k - 1)**2*(4*k - 1)
Let b(g) be the third derivative of 0*g**3 + 0*g**5 + 1/60*g**4 - 3*g**2 + 0 + 0*g - 1/300*g**6. Determine u so that b(u) = 0.
-1, 0, 1
Let p(n) be the first derivative of 0*n**2 + 0*n**6 + 0*n**3 + 2 + 3*n + 0*n**5 + 0*n**4 - 1/21*n**7. Let l(g) be the first derivative of p(g). Solve l(k) = 0.
0
Let i(q) = -q**2 + 8*q + 37. Let l be i(11). Let h(r) be the second derivative of 1/9*r**2 + 0 + 0*r**3 + 2*r - 1/54*r**l. Factor h(z).
-2*(z - 1)*(z + 1)/9
Let f(m) = m + 9. Let i be f(-9). Let b be 4/(-2) - (-5 + i). Factor -2*g**2 + 0*g**2 - 8*g**4 - 4*g**3 - 6*g**b.
-2*g**2*(g + 1)*(4*g + 1)
Let p(c) be the third derivative of -c**6/540 - 2*c**5/135 - c**4/36 + 23*c**2. Let p(n) = 0. What is n?
-3, -1, 0
Solve 1/6*d**2 + 5/6 + d = 0 for d.
-5, -1
Let i(b) = -16*b**3 - 20*b**2 - 31*b + 11. Let v = 10 - 12. Let g(m) = 3*m**3 + 4*m**2 + 6*m - 2. Let h(n) = v*i(n) - 11*g(n). Factor h(u).
-u*(u + 2)**2
Determine l, given that 0*l - 2*l**3 - 12*l - l**3 + 7*l**3 + 8 = 0.
-2, 1
Suppose x = 6*x - 15. Find w such that w**3 - 3*w + x*w**2 + 3*w**2 - 4*w**3 = 0.
0, 1
Let t be 6/(-39) + 4/26. Suppose -v - 3*q = -15, -4*v = -t*q - 3*q. Solve -3/2*b**2 - 3/4*b - 3/4*b**v + 0 = 0 for b.
-1, 0
Determine r, given that -17*r**3 + 12*r**4 + 3*r**2 - 2*r**3 + 4*r**3 = 0.
0, 1/4, 1
Let t(n) be the second derivative of 2*n + 0*n**2 + 0*n**4 + 1/6*n**3 - 1/360*n**6 - 1/120*n**5 + 0. Let w(y) be the second derivative of t(y). Factor w(x).
-x*(x + 1)
Let c(u) be the third derivative of -u**6/200 - 3*u**5/100 - 3*u**4/40 - u**3/10 - 8*u**2. Suppose c(h) = 0. What is h?
-1
Let i(g) be the first derivative of 0*g**3 + 5 + 0*g**2 - 1/4*g**4 + 0*g + 1/2*g**5 - 1/4*g**6. Factor i(r).
-r**3*(r - 1)*(3*r - 2)/2
Let s be (-3 - -1)/(((-60)/(-9))/(-2)). Factor 39/5*g**2 + 12/5*g**4 + s - 36/5*g**3 - 18/5*g.
3*(g - 1)**2*(2*g - 1)**2/5
Let o(l) be the first derivative of l**8/560 - l**7/168 + 11*l**6/1440 - l**5/240 + 8*l**3/3 - 10. Let g(z) be the third derivative of o(z). Factor g(k).
k*(2*k - 1)**2*(3*k - 2)/4
Let o(m) be the third derivative of 1/315*m**7 + 1/60*m**6 + m**2 - 1/18*m**5 + 0 + 0*m + 0*m**3 - 1/504*m**8 + 1/18*m**4. Factor o(v).
-2*v*(v - 1)**3*(v + 2)/3
Let i(b) = -b + 1. Let m(j) = 3*j**2 + 30*j + 114. Let x(k) = 6*i(k) - m(k). Determine d, given that x(d) = 0.
-6
Let q(f) = f**3 - 7*f**2 - 35*f + 50. Let l be q(10). Let -9/7*x - 6/7 + l*x**2 + 3/7*x**3 = 0. Calculate x.
-1, 2
Let u(d) be the third derivative of -1/80*d**6 + 3*d**2 + 0 + 1/40*d**5 + 0*d**3 + 1/8*d**4 + 0*d. Let u(f) = 0. Calculate f.
-1, 0, 2
Let t be (-4)/((-72)/2254) - 1. Let z = -124 + t. Factor -4/9*i - 2/9*i**2 - z.
-2*(i + 1)**2/9
Let o(q) be the second derivative of -q**5/140 - q**4/42 - 33*q + 2. Factor o(b).
-b**2*(b + 2)/7
Let t = -7 - -9. Factor -11*x + x**4 + 4*x**3 - 1 + 9*x - t*x**3.
(x - 1)*(x + 1)**3
Suppose -5*l = 2 - 12. Factor 11*v**2 - 52*v + 49*v**3 + 8 + 36*v**l + 23*v**2.
(v + 2)*(7*v - 2)**2
Solve -9/2*h - 3/2 - 15/8*h**2 = 0 for h.
-2, -2/5
Let q = -3 + 5. Let i(j) = -3*j**3 - 2*j**2 - j. Let s(d) = d**3 + d**2 + d. Let u(k) = q*s(k) + i(k). Determine n so that u(n) = 0.
-1, 0, 1
Let n(d) be the third derivative of -d**8/2184 + 2*d**7/1365 - d**5/195 + d**4/156 + 23*d**2. Suppose n(c) = 0. Calculate c.
-1, 0, 1
Let p(q) = 48*q**4 + 33*q**3 - 81*q**2 + 33*q. Let b(u) = 5*u**2 - 2*u + 5*u - 3*u**4 + 0*u - 2*u**3 - 5*u. Let l(s) = 33*b(s) + 2*p(s). Factor l(f).
-3*f**2*(f - 1)*(f + 1)
Let r(u) be the first derivative of -u**5/60 - u**4/24 + 2*u**2 - 1. Let p(q) be the second derivative of r(q). Factor p(v).
-v*(v + 1)
Let i be ((-3)/6)/((-1)/2). Let u be (-20)/35*7/(-2). Solve -4*x**u + 0*x**2 + i + x**2 + 2*x**2 + x**3 - x = 0.
-1, 1
Let m be (2 - 1)*(-42)/(-70). Let c(z) be the first derivative of 3 - 2/15*z**3 - 4/5*z + m*z**2. Factor c(k).
-2*(k - 2)*(k - 1)/5
Suppose -w - 15 = -4*w, 4*w - 26 = -3*a. Let 5*q**3 - 4*q**5 - 1/2*q**a - 2*q - 1/2 + 2*q**4 = 0. What is q?
-1/2, 1
Let c(n) be the first derivative of -n**3/2 + 9*n**2/4 - 1. Find v such that c(v) = 0.
0, 3
Let x(l) be the third derivative of -l**6/900 + 2*l**5/225 - l**4/45 + 35*l**2. Determine v, given that x(v) = 0.
0, 2
Let u(n) be the second derivative of -n**6/30 + n**5/20 + n**4/12 - n**3/6 + n. Factor u(f).
-f*(f - 1)**2*(f + 1)
Let u(n) be the first derivative of n**9/1296 - n**8/168 + n**7/70 - n**6/135 + 4*n**3/3 + 5. Let d(w) be the third derivative of u(w). Factor d(g).
g**2*(g - 2)**2*(7*g - 2)/3
Let s be (1/159)/(-1)*2. Let x = s + 328/795. Factor -2/5*i**4 + 0*i - x*i**2 + 0 + 4/5*i**3.
-2*i**2*(i - 1)**2/5
Let d(f) be the first derivative of 3/5*f**3 + 2/5*f + 1/4*f**4 + 7/10*f**2 - 4 + 1/25*f**5. Let d(q) = 0. Calculate q.
-2, -1
Let v = 1/146 + 289/438. Find u such that -4/3*u + v*u**2 + 2/3 = 0.
1
Let w(h) = -h**3 - 19*h - h**2 - 17*h**4 + h**5 + 19*h. Let l(z) = 4*z**4. Let u(v) = 9*l(v) + 2*w(v). Find g such that u(g) = 0.
-1, 0, 1
Let y be 2 + (-16)/4 - -3. Let l be (0/y)/(-1 - -2). Factor -2/7*z**3 + l - 4/7*z**2 - 2/7*z.
-2*z*(z + 1)**2/7
Let h(z) be the first derivative of -2*z**3/27 + 8*z**2/9 + 2*z - 40. Determine k, given that h(k) = 0.
-1, 9
Let s(r) be the third derivative of 0*r - 1/360*r**6 + 1/24*r**4 + 0 + 0*r**5 + 1/9*r**3 + 4*r**2. Factor s(z).
-(z - 2)*(z + 1)**2/3
Let k(l) be the first derivative of -2*l**5/5 + 2*l**3 - 2*l**2 - 26. Factor k(p).
-2*p*(p - 1)**2*(p + 2)
Let p(n) = n + 4. Let r be (6/(-2) - -3) + -2. Let q be p(r). Factor 2/3*y + 2*y**2 + 2/3*y**4 + 0 + q*y**3.
2*y*(y + 1)**3/3
Let c(x) be the third derivative of 125*x**8/84 - 395*x**7/42 + 101*x**6/8 - 121*x**5/30 - 23*x**4/6 + 4*x**3 - 8*x**2. Factor c(s).
(s - 3)*(4*s + 1)*(5*s - 2)**3
Let y be 10/(-1) + (-4524)/(-390). Determine f so that -y*f**3 + 12/5*f + 8/5*f**2 - 12/5*f**4 + 4/5 - 4/5*f**5 = 0.
-1, 1
Let m(w) be the third derivative of -w**5/420 - w**4/168 + 5*w**2. Factor m(k).
-k*(k + 1)/7
Let f be (-8 + 6)