9*i**2. Let m(l) = 0. What is l?
-2, 1
Suppose 6*b - 63 = -15*b. Let j(q) be the first derivative of -3*q**2 + 1/2*q**b + 6*q - 5. What is p in j(p) = 0?
2
Let s(z) = -7*z - 31. Let c be s(-5). Suppose -3*j + 3*q + 12 = 0, j + 4*q = 2*q + 1. Factor -301*k**3 + 295*k**3 + 5*k**4 + 0*k**4 - 2*k**c + j*k**2.
3*k**2*(k - 1)**2
Let w(i) be the first derivative of -i**6/180 + 3*i**5/20 - i**3/3 - 6. Let l(y) be the third derivative of w(y). Determine h, given that l(h) = 0.
0, 9
Let a(x) be the second derivative of -x**6/180 + 2*x**5/15 - 4*x**4/3 + 64*x**3/9 - 13*x**2 - 27*x. Let w(d) be the first derivative of a(d). Factor w(p).
-2*(p - 4)**3/3
Let i(j) be the first derivative of j**4/4 - 7*j**3/3 + 6*j**2 + 80. Solve i(c) = 0.
0, 3, 4
Let x(s) = 4*s**5 + 16*s**4 + 4*s**3 + 8*s**2 + 8*s - 8. Let z(b) = b**4 + b**2 + b - 1. Let r = -24 - -23. Let o(h) = r*x(h) + 8*z(h). Factor o(c).
-4*c**3*(c + 1)**2
Let r be (-9)/((-441)/(-56))*-1. Factor -4/7*s**3 + r*s + 0 + 4/7*s**2.
-4*s*(s - 2)*(s + 1)/7
Let o = 2263/168 + -94/7. Let j(i) be the third derivative of 11/210*i**7 + 0*i**4 + 0*i + 1/84*i**8 - 3*i**2 + o*i**6 + 0*i**3 - 1/30*i**5 + 0. Factor j(s).
s**2*(s + 1)*(s + 2)*(4*s - 1)
Suppose -2092*l - 36 = -2096*l. Let v(h) be the first derivative of 0*h**2 - h**4 - 2*h**6 + 4*h**5 + l + 0*h - 4/3*h**3. Factor v(a).
-4*a**2*(a - 1)**2*(3*a + 1)
Let o(z) = z**2 - 14*z + 1. Let c be o(15). Determine y so that 22*y - y - 4*y**4 - 5*y - 16*y**3 - 12*y**2 + c = 0.
-2, -1, 1
Let o(h) = h - 11. Let d be o(14). Let 0*s - 36/5*s**d + 8/5*s**2 + 0 + 28/5*s**4 = 0. What is s?
0, 2/7, 1
Find i such that 0*i**4 + 55*i**3 + i**2 + 14*i**2 + 130*i**2 - 5*i**4 + 40 + 130*i - 5*i**5 = 0.
-2, -1, 4
Let b(v) be the first derivative of v**5/40 - 3*v**4/16 + v**3/3 - 391. Solve b(t) = 0 for t.
0, 2, 4
Let m(k) be the first derivative of -k**6/180 + k**5/45 + k**4/9 + 26*k**3/3 - 18. Let q(g) be the third derivative of m(g). Determine f, given that q(f) = 0.
-2/3, 2
Suppose -3*q - 3 = -5*v + 20, 3*q = -2*v + 5. Let r(z) = z**2 - 8*z + 18. Let w be r(v). Factor -3/4*y**w - 5/4*y + 1/2.
-(y + 2)*(3*y - 1)/4
Let i = -14287/180 + 397/5. Let h(k) be the third derivative of 13*k**2 - i*k**4 - 1/90*k**5 + 0 + 0*k + 2/9*k**3. Solve h(n) = 0.
-2, 1
Let z(r) be the second derivative of -r**5/45 - r**4/9 + 2*r**3/3 + 5*r**2 + 6*r. Let f(t) be the first derivative of z(t). Factor f(b).
-4*(b - 1)*(b + 3)/3
Let a(f) = -f**2 + f + 2. Let c be a(2). Suppose z = -c*z + 1. Factor 2*v**2 - 6*v**2 + v**2 - z + 4.
-3*(v - 1)*(v + 1)
Suppose -3*s - 31 = -d - 3*d, -d - 5*s + 2 = 0. Let k = 9 - d. Let -2 + 2*o**2 - k*o**5 + o**5 - 4*o + o + 4*o**3 = 0. What is o?
-1, 1, 2
Let p(h) be the first derivative of -h**6/480 - h**5/80 - h**4/48 + 19*h**2 - 12. Let g(v) be the second derivative of p(v). Factor g(w).
-w*(w + 1)*(w + 2)/4
Let i(m) = -30*m**2 + 15*m**3 - 35*m**2 - 11 + 71*m**2 + m**3 - 21*m. Let d(b) = -1 + 2 + 3*b**3 - 3 + b**2 - 4*b. Let l(k) = -11*d(k) + 2*i(k). Factor l(o).
-o*(o - 2)*(o + 1)
Let p(d) be the third derivative of 0*d**4 - 1/240*d**6 - 2*d**2 + 1/24*d**3 - 1/80*d**5 + 0*d + 0. Suppose p(t) = 0. Calculate t.
-1, 1/2
Let x = -4169 - -12509/3. Let q be -2 + ((-14)/(-6) - 0). Factor c - q*c**2 - x.
-(c - 2)*(c - 1)/3
Let v(u) = -u**4 - u**2 - u. Suppose -10 + 2 = 4*d. Let h(g) = -3*g**4 - g**3 - g**2 - g. Suppose -4 = -2*c - 2. Let w(i) = c*h(i) + d*v(i). Factor w(l).
-l*(l - 1)*(l + 1)**2
Let c(z) be the first derivative of -12 - 4/15*z + 4/45*z**3 - 1/30*z**4 + 1/15*z**2. Factor c(d).
-2*(d - 2)*(d - 1)*(d + 1)/15
Let f(h) be the second derivative of h**4/9 + 110*h**3/9 + 36*h**2 - 477*h. Factor f(d).
4*(d + 1)*(d + 54)/3
Let q be (1/7)/(1336/184 - 6). Let s = q + 5/29. Factor 0 - 2/7*f**2 - s*f.
-2*f*(f + 1)/7
Suppose 20 = -4*j + 20. Let u be 18/99 + (-38)/(-154). What is k in j*k + 0 - u*k**2 = 0?
0
Let q(u) be the third derivative of -u**7/525 - 7*u**6/100 - 27*u**5/25 - 9*u**4 - 216*u**3/5 + 22*u**2. Factor q(t).
-2*(t + 3)*(t + 6)**3/5
Let x(t) = t**2 - 8*t - 4. Let w be x(9). Let -w + 2*u**2 + 3 - u**2 - 13*u**2 - 10*u = 0. Calculate u.
-1/2, -1/3
Let s = 1658 - 6631/4. Find m, given that s*m**3 + 0 - 1/2*m**2 + 1/2*m**4 + 0*m - 1/4*m**5 = 0.
-1, 0, 1, 2
Suppose -b - 3*b = t - 19, 5*b = 5*t + 5. Suppose -5*c - 21 = -b*u, -u = 3*u + 2*c - 14. Factor 4*d**3 + 2*d**2 + 0*d**2 + d**5 - 10*d**3 - 3*d**5 + 6*d**u.
-2*d**2*(d - 1)**3
Let u(r) be the second derivative of -3/5*r**2 + 0 + 4/15*r**3 - 3*r - 1/30*r**4. Factor u(q).
-2*(q - 3)*(q - 1)/5
Let x(b) be the third derivative of b**6/840 + b**5/210 + 10*b**2 + b. Find m, given that x(m) = 0.
-2, 0
Let f(m) be the first derivative of -2*m**5/25 - 11*m**4/10 - 2*m**3/3 + 47*m**2/5 - 12*m - 357. Find q such that f(q) = 0.
-10, -3, 1
Factor 3*s**5 - 3*s**4 + 3*s - 5*s**3 - 26 - 25 + 6*s**2 + 68 - s**3 - 20.
3*(s - 1)**3*(s + 1)**2
Let o(u) = 10*u**4 - 8*u**3 - 10*u**2 + 8*u. Let n(t) = -t**3 + 724 - 724 + t**4 - t**2 + t. Let q(m) = -44*n(m) + 4*o(m). Factor q(d).
-4*d*(d - 3)*(d - 1)*(d + 1)
Let h(d) be the third derivative of 1/30*d**6 + 0*d**3 + 15*d**2 + 1/15*d**5 - 1/3*d**4 + 0 + 0*d. Factor h(u).
4*u*(u - 1)*(u + 2)
Let m(r) be the third derivative of r**7/1260 + r**6/135 + r**3/2 - 13*r**2. Let f(h) be the first derivative of m(h). Factor f(t).
2*t**2*(t + 4)/3
Let m(x) be the first derivative of -4/19*x + 12 - 3/19*x**2 + 10/57*x**3. Factor m(r).
2*(r - 1)*(5*r + 2)/19
Let h = 28 + -8. Let s be h/(-195)*(-15)/10. Factor s*i**2 + 0 + 2/13*i.
2*i*(i + 1)/13
Let z(m) be the first derivative of m**4/4 - 8*m**3/3 + m**2/2 - 4*m + 11. Let u be z(8). Factor 3*h**4 + 158*h**5 - 162*h**5 + 5*h**4 - 8*h**2 + u*h.
-4*h*(h - 1)**3*(h + 1)
Let g = 97/140 - -2/35. Let z = 413/540 + -2/135. Factor -z*o + g*o**3 + 3/4*o**2 - 3/4.
3*(o - 1)*(o + 1)**2/4
Let x(h) = h**4 - 5 + 40*h**3 + 5*h**4 - 30*h**3 - h**4. Let m(t) = t**5 + 6*t**4 + 11*t**3 - 6. Let j(a) = 5*m(a) - 6*x(a). Find s, given that j(s) = 0.
-1, 0, 1
Let z(r) = 0*r**2 - 5 + r - r**3 - 7*r**2 + 14*r**2. Let o be z(7). Factor 1 + 3/2*k**o + 9/2*k - 2*k**3.
-(k - 2)*(k + 1)*(4*k + 1)/2
Let j(n) = 2*n**2 + 18*n + 10. Suppose 0 = -m - 0*m. Let k(o) = o - 5 + 6 + m. Let c(y) = -2*j(y) + 36*k(y). Solve c(b) = 0.
-2, 2
Let y be ((-12)/(-14))/((-88)/(-308)). Let t(b) be the third derivative of 4/21*b**y + 0*b + 3/70*b**5 + 0 - 2*b**2 + 1/7*b**4. Factor t(x).
2*(3*x + 2)**2/7
Let d(f) be the third derivative of f**5/270 - 2*f**4/27 + 5*f**3/9 - 3*f**2 - 28. Factor d(v).
2*(v - 5)*(v - 3)/9
Let t(i) be the third derivative of 0 - 1/75*i**5 + 0*i**3 + 0*i**4 + 0*i + 1/300*i**6 - 22*i**2. Solve t(a) = 0 for a.
0, 2
Solve 2*q**2 + 11 + 8*q**2 - 12*q**2 + 32*q + 23 = 0 for q.
-1, 17
Factor 32/3*m + 4/3*m**2 + 16.
4*(m + 2)*(m + 6)/3
Let i be (10 - (-153)/(-15)) + (-11)/(-5). Factor -5/6*j**i + 0 + 5/6*j.
-5*j*(j - 1)/6
Suppose 5*b + 29 = 4*q, -3*q - 4*b + 0*b = -14. Factor -3*c - 2*c + 3*c - q*c**2 + 22*c**2.
2*c*(8*c - 1)
Factor -10*q**2 - 68*q + 5*q**3 - 68*q + 141*q.
5*q*(q - 1)**2
Let w(i) be the third derivative of -i**6/210 + i**5/21 - 2*i**4/21 - 3*i**2 - 16*i. Suppose w(a) = 0. What is a?
0, 1, 4
Let y(d) be the third derivative of d**7/1470 - 9*d**6/280 + 13*d**5/210 + 45*d**2 + d. Determine p so that y(p) = 0.
0, 1, 26
Suppose 14 + 16 + 7*k + 16 + k**3 + 5*k**2 - 51 + 8 = 0. What is k?
-3, -1
Let s = 275/1641 - 1/1094. Let l(u) be the second derivative of 3/80*u**5 + 0 + 0*u**2 + 1/4*u**4 + s*u**3 - 1/24*u**6 + 3*u. Suppose l(i) = 0. What is i?
-1, -2/5, 0, 2
Factor 0 + 10/13*b + 2/13*b**2.
2*b*(b + 5)/13
Let t = 4009/24 + -167. Let g(k) be the first derivative of -t*k**6 + 1/8*k**4 + 0*k**3 + 0*k**2 - 3 - 1/20*k**5 + 0*k. Solve g(s) = 0 for s.
-2, 0, 1
Suppose 4*g + 18 = 10*y - 8*y, g = -5*y + 12. Find j, given that 1/6*j - 1/6*j**y + 0 + 0*j**2 = 0.
-1, 0, 1
Let v(n) be the first derivative of 3*n**5/5 + 9*n**4/2 - 81*n**2 - 243*n + 38. Factor v(q).
3*(q - 3)*(q + 3)**3
Let v(q) be the third derivative of q**7/630 - q**6/72 - q**5/180 + 5*q**4/72 - 61*q**2. Factor v(z).
z*(z - 5)*(z - 1)*(z + 1)/3
Let d = -4/23889 + 13879529/119445. Let b = -113 + d. Factor b*u - 4/5*u**2 - 16/5.
-4*(u - 2)**2/5
Let n be 18/270*6*24. Factor -n*g**2 + 0 + 6/5*g**5 + 0*g + 12/5*g**4 - 24/5