*5 + p*c**3 + 2*c - 3/2*c**2 - 3/2*c**4. Suppose i(h) = 0. What is h?
1
Let c(f) be the third derivative of f**8/181440 - f**7/7560 + f**6/720 + 3*f**5/10 + 16*f**2. Let b(v) be the third derivative of c(v). What is u in b(u) = 0?
3
Let m(n) be the second derivative of -n**6/10 + 6*n**5/5 - n**4/2 - 16*n**3 - 63*n**2/2 - 254*n. Factor m(h).
-3*(h - 7)*(h - 3)*(h + 1)**2
Factor -44 - 170/3*h - 12*h**2 + 2/3*h**3.
2*(h - 22)*(h + 1)*(h + 3)/3
Factor 0 - 2*u**2 + 60/13*u + 2/13*u**3.
2*u*(u - 10)*(u - 3)/13
Let d = 65 + -46. Factor 36 + 56 - 11 + s**2 - s + d*s.
(s + 9)**2
Factor -24/5*b**4 - 72/5*b**3 + 0 - 48/5*b - 96/5*b**2 - 3/5*b**5.
-3*b*(b + 2)**4/5
Suppose -19*q + 20 = -14*q. Factor -32*k**3 + 5*k**4 - 34*k**4 + 3*k**4 - 10*k**q - 4*k**5.
-4*k**3*(k + 1)*(k + 8)
Let m(x) be the second derivative of -1/12*x**4 - 1/20*x**5 + 1/2*x**2 + 0 + 1/6*x**3 - 3*x. Factor m(f).
-(f - 1)*(f + 1)**2
Factor -264/5 + 276/5*r - 78/5*r**2 + 3/5*r**3.
3*(r - 22)*(r - 2)**2/5
Let m(l) = l**2 + 16*l + 20. Let y be m(-15). Determine s, given that 14 + 22*s**3 + 50*s + 56*s**2 + y*s**4 + 4*s**2 + 1 + 8*s**3 = 0.
-3, -1
Suppose 10*p + 25*p**4 + 29*p**3 + 35*p**2 + 2626*p**5 + 10*p**3 - 2621*p**5 + 6*p**3 = 0. Calculate p.
-2, -1, 0
Let s(y) be the first derivative of -7*y**5/240 - y**4/6 - y**3/6 - 9*y**2 - y + 48. Let x(q) be the second derivative of s(q). Let x(h) = 0. What is h?
-2, -2/7
Let i(j) = j**3 + 2*j**2 - j. Let y(g) = 2*g**3 + 122*g**2 - 1684*g + 1568. Let s(f) = -4*i(f) + y(f). Find n, given that s(n) = 0.
1, 28
Factor -2/9*h**2 + 0 - 2/9*h**4 + 0*h + 4/9*h**3.
-2*h**2*(h - 1)**2/9
Determine y so that 552*y**3 + 24*y**5 - 13*y**5 + 1044*y - 7*y**5 - 1663*y**2 - 324 - 84*y**4 + 471*y**2 = 0.
1, 9
Let f be 2/(-8) + (-539)/(-2380). Let q = f + 89/170. Determine j, given that -q - 1/2*j**3 - 3/2*j**2 - 3/2*j = 0.
-1
Let q be (-5 + 6)*(1 - -2). Suppose -q*j = 4*z - 4, 1 = 4*j + 4*z - 7. Suppose -38*a - j*a**3 + 16 + 16*a**2 + 6*a + 4*a**2 = 0. What is a?
1, 2
Let k = -33797/5 + 6733. Let o = -26 - k. Factor 1/5*h**5 - o*h**3 + 1/5*h + 1/5*h**4 + 1/5 - 2/5*h**2.
(h - 1)**2*(h + 1)**3/5
Let k(b) be the first derivative of 3/5*b**2 - 1/5*b**3 + 0*b + 11. Solve k(g) = 0 for g.
0, 2
Let d be 6 - (8 - (9 + -3)). Let f(v) be the first derivative of d + 1/18*v**3 - 1/3*v**2 + 2/3*v. Factor f(t).
(t - 2)**2/6
Suppose 0*k - 7 = x + 5*k, -3*x - 5*k = 31. Let y = x + 15. Factor 3*r + 6*r**2 + y*r - 3 + 2*r**3 + 5.
2*(r + 1)**3
Let w = -10174 - -91568/9. Solve -2/9*u**2 - w*u + 4/3 = 0.
-3, 2
Let j(t) = 4*t**5 + 11*t**4 + 17*t**3 + t**2 + 2*t - 1. Let l(a) = -2*a**5 + a**4 - a**3 - a**2 - 2*a + 1. Let i(x) = 2*j(x) + 2*l(x). Factor i(v).
4*v**3*(v + 2)*(v + 4)
Let i(q) be the third derivative of q**5/15 + 31*q**4/3 - 90*q**2. Factor i(m).
4*m*(m + 62)
Suppose 3*j - 2*z = 0, 3*j + 2*z + 3*z = 21. Suppose 7*r + 3*k - 20 = 2*r, j*k = -2*r + 8. Factor -4*p**4 + 185 - 185 - 8*p**3 - r*p**2.
-4*p**2*(p + 1)**2
Let b(k) = 11*k**2 + 11*k - 17. Let q(t) = -4*t + 16. Let r be q(5). Let x(u) = -6*u**2 - 6*u + 8. Let a(i) = r*b(i) - 7*x(i). Let a(n) = 0. Calculate n.
-3, 2
Let f(m) be the first derivative of 2*m**3/7 - 17*m**2/7 + 20*m/7 - 86. Factor f(q).
2*(q - 5)*(3*q - 2)/7
Determine r so that 2/7*r - 6/7*r**2 + 6/7*r**3 + 0 - 2/7*r**4 = 0.
0, 1
Let c(q) = -32*q**2 + 16*q + 1. Let o(y) = 128*y**2 - 64*y - 5. Let i(n) = -26*c(n) - 6*o(n). Factor i(j).
4*(4*j - 1)**2
Suppose 3*w + 0*w = 18. Let v(t) be the second derivative of -1/10*t**5 + 0*t**2 + 0 + 0*t**3 + 0*t**4 + 2*t + 0*t**w + 1/21*t**7. Factor v(p).
2*p**3*(p - 1)*(p + 1)
Let g(s) be the second derivative of -s**7/210 - 11*s**3/3 + 15*s. Let c(n) be the second derivative of g(n). Factor c(m).
-4*m**3
Let a(g) be the first derivative of -7/2*g**2 + 0*g + 23 + 1/3*g**3. Factor a(m).
m*(m - 7)
Let g(c) be the second derivative of -c**6/105 - c**5/105 + c**4/21 + 2*c**3/21 + 3*c**2/2 + 7*c. Let b(y) be the first derivative of g(y). Factor b(m).
-4*(m - 1)*(m + 1)*(2*m + 1)/7
Let b = 0 - 1. Let g be (b - (-15)/2 - 3) + -3. Factor -5/2*o**2 - g*o**4 + 0 - o - 2*o**3.
-o*(o + 1)**2*(o + 2)/2
Let s be 75/(-65) - 6/(-39). Let q be (2 - -1) + (0 - s). Solve -4*a**2 + 3*a**4 - 2*a**5 + a**q - 7*a**5 + 5*a**5 + 4*a**3 = 0 for a.
-1, 0, 1
Let v be (-8)/(-590)*(-2 - 45/(-10)). Let m = v - -55/118. Let -1/4*p - m + 1/4*p**2 = 0. Calculate p.
-1, 2
Let m(z) = -2*z**2 - 16*z - 11. Let r be m(-6). Suppose 12 = -r*y + 38. Factor 5/2 - 5/4*x - 5/4*x**y.
-5*(x - 1)*(x + 2)/4
Let c(s) = 6*s**3 - 26*s**2 - 24*s + 52. Let r(g) = 2*g**3 - 2*g**2 + g + 1. Let u(z) = -c(z) + 4*r(z). Factor u(v).
2*(v - 1)*(v + 4)*(v + 6)
Factor 20 + 29*j**2 + 18*j**2 + 31*j**2 - 6*j**2 + 64*j + 4*j**4 + 32*j**3.
4*(j + 1)**3*(j + 5)
Let o(f) = -3*f**2 + 21*f + 24. Let i(g) = 2*g**2 - 22*g - 24. Suppose -9*x + 36 = -18. Let m(a) = x*i(a) + 5*o(a). Factor m(p).
-3*(p + 1)*(p + 8)
What is v in 0 + 3/8*v**4 + 30*v + 21*v**2 + 39/8*v**3 = 0?
-5, -4, 0
Let z(b) be the third derivative of b**8/6720 - b**7/1120 + b**6/480 - b**5/480 - 5*b**3/2 + 8*b**2. Let g(c) be the first derivative of z(c). Factor g(d).
d*(d - 1)**3/4
Let t(b) be the third derivative of 0*b**3 + 0*b**4 - 1/12*b**5 + 0*b - 5*b**2 + 1/48*b**6 + 0 + 1/84*b**7. Find v, given that t(v) = 0.
-2, 0, 1
Factor 2784/7*w + 107648/7*w**2 + 18/7.
2*(232*w + 3)**2/7
Let o(v) be the second derivative of -25/3*v**2 - 1/18*v**4 + 3*v + 10/9*v**3 + 0. Factor o(j).
-2*(j - 5)**2/3
Let l = -649 + 4547/7. Suppose -8/7 + 6/7*g**2 + l*g**3 - 8/7*g - 2/7*g**4 = 0. What is g?
-1, 2
Factor -1320*i - 59 - 44*i**3 + 1859 + 176*i**2 + 186*i**2 + 2*i**4.
2*(i - 6)**2*(i - 5)**2
Let m(v) be the second derivative of v - 1/20*v**5 + 1/2*v**3 + 0*v**4 - 2*v**2 + 0. Let g(w) be the first derivative of m(w). Factor g(q).
-3*(q - 1)*(q + 1)
Factor 0*r - 24/5*r**2 + 2/5*r**3 + 0.
2*r**2*(r - 12)/5
Let n(z) = 3*z**4 - 67*z**3 + 75*z**2 + 29*z - 5. Let m(y) = 5*y**4 - 100*y**3 + 113*y**2 + 43*y - 7. Let k(l) = -5*m(l) + 7*n(l). Let k(w) = 0. What is w?
-1/4, 0, 2, 6
Let b(u) be the second derivative of 0*u**3 + 12*u + 0*u**2 - 1/3*u**4 + 0 - 1/15*u**6 + 3/10*u**5. Find p such that b(p) = 0.
0, 1, 2
Let o(g) be the third derivative of -g**6/30 + 8*g**5/15 - 148*g**2. Let o(p) = 0. What is p?
0, 8
Let c = 1876 + -11219/6. Let p = -17/3 + c. Let 0 - 1/2*t**3 - p*t**5 - 3/2*t**4 + t + 3/2*t**2 = 0. What is t?
-2, -1, 0, 1
Let p(d) be the third derivative of -d**6/600 + d**5/75 + d**4/120 - 2*d**3/15 + 309*d**2. Factor p(b).
-(b - 4)*(b - 1)*(b + 1)/5
Let w(c) be the second derivative of -25/6*c**3 - 1/4*c**5 + 5*c**2 + 0 + 29*c + 5/3*c**4. Solve w(b) = 0.
1, 2
Let w(m) be the first derivative of 2*m**3/21 + 10*m**2/7 - 48*m/7 - 20. Factor w(h).
2*(h - 2)*(h + 12)/7
Let s(z) = -8*z**4 + 8*z**3 + 16*z**2 - 8*z - 12. Let v(x) = 9*x**4 - 10*x**3 - 15*x**2 + 10*x + 11. Let f(o) = 5*s(o) + 4*v(o). Solve f(h) = 0 for h.
-2, -1, 1, 2
What is g in 35/2*g**2 + 10 + 55/2*g = 0?
-1, -4/7
Let -5/3*g**3 + 85/3*g + 35/3*g**2 + 15 = 0. What is g?
-1, 9
Suppose 18/17*g**2 - 2/17*g**3 - 28/17*g + 0 = 0. Calculate g.
0, 2, 7
Let v(y) be the first derivative of -y**5/25 - 3*y**4/20 + y**3/15 + 3*y**2/10 + 492. Suppose v(j) = 0. What is j?
-3, -1, 0, 1
Let b(r) = -r**3 + 6*r**2 + 18*r - 13. Let d be b(8). Let w(j) be the first derivative of 1/12*j**d + 0*j - 2 + 0*j**2. Solve w(x) = 0.
0
Let w = -66 - -200/3. Let s(j) = -j**3 - 5*j**2 + 3*j + 15. Let v be s(-5). Factor 0*y - 1/3*y**2 + w*y**3 + v - 1/3*y**4.
-y**2*(y - 1)**2/3
Let h be (1/2)/((-33)/(-330)). Let l(a) be the third derivative of 0*a**3 + 0*a**4 + 1/90*a**h + 0 + 7*a**2 + 0*a. Factor l(t).
2*t**2/3
Let o(i) be the first derivative of 5*i**3/3 - 105*i**2/2 + 340*i - 192. Let o(u) = 0. What is u?
4, 17
Let d(k) be the first derivative of -7/25*k**5 - 3/5*k - 9/10*k**4 - 1 - 13/10*k**2 - 1/30*k**6 - 22/15*k**3. Suppose d(c) = 0. What is c?
-3, -1
Let p(j) = -15*j**4 + 60*j**3 - 120*j**2 - 50*j + 125. Let a(o) = o**4 - o**3. Let d(c) = 10*a(c) + p(c). Suppose d(r) = 0. What is r?
-1, 1, 5
Let d be 5 + (4 - (-1 - -5))/(-2). Let w(c) be the second derivative of 3*c + 1/8*c**4 + 0 - 1/80*c**d - 3/8*c**3 + 0*c**2. Solve w(v) = 0.
0, 3
Let i(h) = -4*h**2 - 9*h - 1. Let r(g) be the third derivative of g