r(v) be the second derivative of 0*v**2 + 1/27*v**3 - 1/90*v**5 + 0 - 13*v + 0*v**4. Determine u so that r(u) = 0.
-1, 0, 1
Suppose -h + 5 = 2*r - 20, -3*h = 2*r - 55. Let v be 18/h*35/21. Determine q, given that q**v - 2/3 + 1/3*q = 0.
-1, 2/3
Factor 0*v + 243*v**2 + 27*v**3 + 0 + 3/4*v**4.
3*v**2*(v + 18)**2/4
Solve -21*f**2 - 28 + 3 - 3*f**3 - 48*f - 10 - 1 = 0 for f.
-3, -2
Let w(d) be the second derivative of 0 - 17*d + 9/10*d**2 + 1/5*d**3 - 1/20*d**4. Factor w(n).
-3*(n - 3)*(n + 1)/5
Solve 4598/5*a - 2662/5 - 62/5*a**4 - 1276/5*a**2 - 596/5*a**3 - 2/5*a**5 = 0 for a.
-11, 1
Let c = 1208 + -1205. What is z in 9/2*z - 5*z**2 + 3/2*z**c - 1 = 0?
1/3, 1, 2
Suppose 24*h**4 + 6 + 291/2*h**2 - 54*h - 108*h**3 = 0. What is h?
1/4, 2
Let h(p) be the first derivative of p**5/30 + p**4/4 + 2*p**3/3 - 9*p**2/2 - 19. Let n(y) be the second derivative of h(y). Factor n(w).
2*(w + 1)*(w + 2)
Factor 12/13*a**2 + 2/13*a**3 - 20/13 + 6/13*a.
2*(a - 1)*(a + 2)*(a + 5)/13
Suppose -b**2 + 4*b**2 + 63 - 408*b + 342*b = 0. What is b?
1, 21
Let n(q) be the third derivative of q**6/30 + 7*q**5/15 - 4*q**4/3 - 45*q**2. Factor n(f).
4*f*(f - 1)*(f + 8)
Let v = -103 + 121. Let s = v + -87/5. Let -1/5*x**2 - s + 4/5*x = 0. What is x?
1, 3
Let v(n) = -11*n**2 + 46*n + 104. Let j(s) = 4*s**2 - 15*s - 34. Let t(f) = -8*j(f) - 3*v(f). Factor t(y).
(y - 20)*(y + 2)
Let y(c) = -2*c**4 - c**3 + c**2 + 1. Let t(z) = -2*z**4 - 8*z**3 + 8*z**2 - 2*z + 2. Let i(x) = t(x) - 2*y(x). Factor i(d).
2*d*(d - 1)**3
Let p(u) be the second derivative of 126/5*u**5 + 16/3*u**3 + 68/3*u**4 - 54/5*u**6 + 0 + 10*u + 0*u**2. Determine k so that p(k) = 0.
-2/9, 0, 2
Suppose -18*f = -5*f + 156. Let c be (((-6)/54)/(-1))/((-2)/f). Suppose 0*g + 4/3*g**3 + 0 + c*g**4 + 2/3*g**2 = 0. What is g?
-1, 0
Let u(t) be the third derivative of -t**5/100 - t**4/5 - 6*t**3/5 - 3*t**2 - 33*t. Factor u(p).
-3*(p + 2)*(p + 6)/5
Factor 0 + 0*g + 4/7*g**4 + 12/7*g**2 - 20/7*g**3 + 4/7*g**5.
4*g**2*(g - 1)**2*(g + 3)/7
Suppose -3*n = -9*n + 450. Factor -3*m**3 + m**5 + n*m**2 + 2*m**5 - 60*m**2 - 15*m**4.
3*m**2*(m - 5)*(m - 1)*(m + 1)
Let r be ((-20)/(-7))/10*(-210)/(-45). Factor -24*d - 108 - r*d**2.
-4*(d + 9)**2/3
Factor g**4 + 3*g - 2*g**2 - 8*g**3 + g - 3*g**4 + 8*g.
-2*g*(g - 1)*(g + 2)*(g + 3)
Factor -11/3*b**2 + 4 - 13/3*b**3 - 1/3*b**4 + 13/3*b.
-(b - 1)*(b + 1)**2*(b + 12)/3
Let w = 1/59 + 883/118. Let z(p) be the first derivative of w*p**2 + 21/4*p**4 - 9*p**3 - 3*p - 6/5*p**5 + 1. Factor z(n).
-3*(n - 1)**3*(2*n - 1)
Let s(z) = z**3 - 3*z**2 - 2*z + 4. Let j be s(1). Let y(i) be the third derivative of 3*i**2 - 1/3*i**4 + j*i + 0*i**3 + 1/15*i**5 + 0. Factor y(k).
4*k*(k - 2)
Let u(d) = -31*d**3 + d**2 + 22*d + 2. Let m(k) = 92*k**3 - 2*k**2 - 65*k - 5. Let t(x) = 6*m(x) + 17*u(x). What is s in t(s) = 0?
-1, 2/5
Let m(g) be the first derivative of g**6/3 - 4*g**5/5 - 2*g**4 + 4*g**3/3 + 3*g**2 - 11. Let m(u) = 0. What is u?
-1, 0, 1, 3
Let f(t) = -10*t - 46. Let m be f(-6). Suppose m*y + 25 = 19*y. What is l in -87/4*l**3 + 27/4*l**y - 3/2*l**2 + 15*l - 9/2*l**4 + 6 = 0?
-1, -2/3, 1, 2
Let l be (-2 + 1)*-19*2. Let y = l + -113/3. What is d in -1/3*d + 0 - y*d**2 = 0?
-1, 0
Suppose -p + 4*j + 32 = j, -5*j = 5*p - 60. Suppose -y = 15 - p. Factor -2/5*k**3 + 0*k + 0*k**y + 0.
-2*k**3/5
Let z = 3574 - 1715519/480. Let x(k) be the third derivative of -z*k**6 + 0*k - 1/840*k**7 - k**2 + 0 + 0*k**4 + 1/120*k**5 + 0*k**3. What is v in x(v) = 0?
-2, 0, 1
Factor -3 + 1/4*n**2 + 1/4*n.
(n - 3)*(n + 4)/4
Let v(c) be the second derivative of c**6/30 - 47*c**5/100 + 29*c**4/30 - 8*c**3/15 - 540*c. Determine o, given that v(o) = 0.
0, 2/5, 1, 8
Let z = 18 + -12. Suppose 2 = 7*d - z*d. Find n such that 1/3*n + 0 - 1/3*n**d = 0.
0, 1
Let p(a) = -14*a**5 - 21*a**4 + 27*a**3 + 11*a**2. Let v(z) = -z**2 - 117 - z**3 + z**4 + 117. Let w(j) = -p(j) - 3*v(j). Suppose w(k) = 0. What is k?
-2, -2/7, 0, 1
Let o(d) be the third derivative of d**9/151200 - d**7/4200 + d**6/900 + 13*d**5/60 + 9*d**2. Let r(z) be the third derivative of o(z). Let r(n) = 0. What is n?
-2, 1
Let w(b) = -3*b**2 + 6*b**2 + 7 + 167*b + 1029 - 8*b**2. Let t(m) = -2*m**2 + 56*m + 346. Let k(n) = -11*t(n) + 4*w(n). Factor k(p).
2*(p + 13)**2
What is t in -1350 - 4*t**3 - 20*t**2 - 4*t + 1358 - 4*t**3 = 0?
-2, -1, 1/2
Let c(z) be the first derivative of -z**7/735 + z**5/105 - z**3/21 - 5*z**2/2 + 11. Let s(d) be the second derivative of c(d). Factor s(q).
-2*(q - 1)**2*(q + 1)**2/7
Let l(r) be the third derivative of 5/3*r**3 - 1/24*r**6 + 1/3*r**5 + 0 - 25/24*r**4 - 3*r**2 + 0*r. Determine y so that l(y) = 0.
1, 2
Let s(k) be the third derivative of -1/504*k**8 + 0*k**3 + 0*k**4 + 0*k + 0 - 11*k**2 + 4/315*k**7 + 1/45*k**5 - 1/36*k**6. Factor s(y).
-2*y**2*(y - 2)*(y - 1)**2/3
Let 27/7*j + 0 - 51/7*j**3 + 9/7*j**2 + 15/7*j**4 = 0. What is j?
-3/5, 0, 1, 3
Factor 0 - 1/6*y**5 - 5/6*y**3 + 2/3*y**4 + 1/3*y**2 + 0*y.
-y**2*(y - 2)*(y - 1)**2/6
Let w(h) be the second derivative of h**10/2520 - 2*h**9/945 + h**8/240 - h**7/315 - h**4/3 - 9*h. Let o(v) be the third derivative of w(v). Factor o(y).
4*y**2*(y - 1)**2*(3*y - 2)
Let i = 347 + -155. Suppose 16 + 32 + 240*k - 12*k**5 - 5*k**3 + i*k**2 - 51*k**4 - 7*k**3 = 0. Calculate k.
-2, -1/4, 2
Let s = 718/17 + -2086/51. Find w, given that s*w**2 - 1/4*w**3 - 17/12*w + 1/3 = 0.
1/3, 1, 4
Solve 357 - g**2 - 1271 + 152*g - 668 - 3*g**2 + 138 = 0.
19
Let o(p) be the second derivative of -p**6/40 + 33*p**5/40 - 15*p**4/4 + 29*p**3/4 - 57*p**2/8 - 120*p. Factor o(k).
-3*(k - 19)*(k - 1)**3/4
Let s be (-1656)/299 - -6 - 816/(-260). Factor 2/5*v**2 - 12/5*v + s.
2*(v - 3)**2/5
Let s(r) be the second derivative of 0 + 8/3*r**3 + 8*r - 17/12*r**4 - 2*r**2 + 1/4*r**5. Let s(h) = 0. Calculate h.
2/5, 1, 2
Let p = -36/55 - -2509/220. Factor 73/4*w**3 + 11/4*w + 1/4 + p*w**2 + 4*w**5 + 14*w**4.
(w + 1)**3*(4*w + 1)**2/4
Let w(r) be the first derivative of -r**3 + 252*r**2 - 21168*r + 77. Determine f so that w(f) = 0.
84
Let 128/3 + 2/3*u**2 + 32/3*u = 0. What is u?
-8
Let z(s) be the first derivative of 2*s**3/9 - 104*s**2/3 + 5408*s/3 + 327. Find r, given that z(r) = 0.
52
Let j(d) = d**3 - 12*d**2 - 13*d + 30. Let h be j(-2). Let h + 0*r - 3/7*r**2 + 1/7*r**3 = 0. What is r?
0, 3
Let t(j) be the third derivative of -1/48*j**4 + 0 - 1/240*j**5 + 0*j - 26*j**2 + 0*j**3. Factor t(m).
-m*(m + 2)/4
Let g = 4176 + -4173. Factor -35/2*u - 1/2*u**g - 11/2*u**2 - 25/2.
-(u + 1)*(u + 5)**2/2
Let n(d) be the third derivative of d**7/2100 - 7*d**6/1200 + 7*d**5/300 - d**4/30 - d**2 + 31*d. Factor n(y).
y*(y - 4)*(y - 2)*(y - 1)/10
Let g = -7 - -10. Let i(y) be the second derivative of 1/36*y**4 + 2/3*y**2 + 0 - 2/9*y**g - 4*y. Let i(t) = 0. Calculate t.
2
Let p(i) be the first derivative of i**5/630 + i**2 + 10. Let l(q) be the second derivative of p(q). Suppose l(b) = 0. What is b?
0
Let 2*s**4 + 6*s**2 - 6*s**4 + 2*s**4 - 9*s + 5*s = 0. Calculate s.
-2, 0, 1
Let m = -123 - -132. Let v be (-4 + 2 + -2)/(0 - m). Suppose -2/3*g**5 + v*g**3 + 0 - 8/9*g**4 + 8/9*g**2 + 2/9*g = 0. What is g?
-1, -1/3, 0, 1
Suppose -m = 4*m - 25. Let i = -3 + m. Let 2*f**5 - 5*f**2 - 8*f**4 - f**2 + 12*f**3 + 2*f - 2*f**i = 0. Calculate f.
0, 1
Let m(s) be the third derivative of 2*s**7/105 - 23*s**6/15 + 481*s**5/15 + 184*s**4 + 384*s**3 + 78*s**2. Solve m(t) = 0 for t.
-1, 24
Let o(a) = 25*a**3 + a**2 - 32*a - 8. Suppose 0*g - i = g - 1, 3*g - 18 = 2*i. Let s(t) = 12*t**3 - 16*t - 4. Let b(k) = g*o(k) - 7*s(k). Factor b(l).
4*(l - 1)*(l + 1)*(4*l + 1)
Let u(b) be the second derivative of -b**5/20 - 5*b**4/8 - 2*b**3 - 19*b**2/2 + 5*b. Let j(q) be the first derivative of u(q). Suppose j(z) = 0. Calculate z.
-4, -1
Suppose 10*p + 3*p = -3*p + 48. Factor 0 + 4/3*d**2 + 1/3*d**p + d.
d*(d + 1)*(d + 3)/3
Let 62*g**3 - 151*g**3 + 90*g**3 + 60 - 4*g - 15*g**2 = 0. Calculate g.
-2, 2, 15
Let j(v) be the first derivative of v**2 + 0*v - v**4 + 0*v**5 + 6 + 1/3*v**6 + 0*v**3. Let j(s) = 0. Calculate s.
-1, 0, 1
Let p(g) = 3*g**2 + g - 1. Let d be p(1). Let s be (-14)/(-4)*(-2 - 126/(-49)). Find n, given that 3*n**5 + n**4 - 3*n**d - s*n**2 + 5*n**2 - 4*n**4 = 0.
-1, 0, 1
Let d(x) be the third derivative of 0*x**6 + 0*x**4 + 0*x**5 + 0*x**3 - 1/315*x**7 +