-1
Factor -139 + 185*h + 79 - 114*h**2 - 76*h**2 - 5*h**5 + 5*h**4 + 5*h**4 + 60*h**3.
-5*(h - 3)*(h - 1)**3*(h + 4)
Let y(n) = 5*n**3 + 2*n**2 - 8*n + 7. Let v be y(1). Let s(o) be the first derivative of -v + o**3 - 1/4*o**4 + 0*o**2 - 4*o. What is m in s(m) = 0?
-1, 2
Let a = 20 - 13. Suppose a*y - 12*y = -25. What is s in 3/4*s**3 - 1/4*s**y - s - 1/2*s**4 + s**2 + 0 = 0?
-2, 0, 1
Suppose -2*m - 2 = -4*z + 14, -4*z = 3*m - 6. Suppose z*o = -o + 12. Factor -l**2 + o*l - l - 3*l + 3*l.
-l*(l - 2)
Let u be (-21)/(-15) + (-3)/(-5). Factor -2*w**u + 4*w + 2*w + 4*w - 72 + 14*w.
-2*(w - 6)**2
Let k(p) be the third derivative of -p**6/720 + 23*p**5/60 - 529*p**4/12 + 24334*p**3/9 - 610*p**2. Solve k(t) = 0.
46
Let j(s) = -s - 1. Let n be j(-3). Factor z**2 + 12*z**2 + 9*z**3 + 12*z + 13*z**2 - 2*z**n.
3*z*(z + 2)*(3*z + 2)
Let l(z) = 2*z**2 + 64*z + 490. Let o(t) = t**2 + 32*t + 244. Let u(g) = 6*l(g) - 11*o(g). Factor u(i).
(i + 16)**2
Suppose -1 + 43 = 14*p. Let z(q) be the second derivative of -3/35*q**5 + 3/35*q**6 - 4/147*q**7 + 0 + 1/42*q**4 + 0*q**p - 8*q + 0*q**2. Solve z(m) = 0.
0, 1/4, 1
Let t(b) = 2*b**2 - 122*b + 757. Let x be t(54). Determine s so that -x + 1/2*s**3 - s + 3/4*s**2 - 1/4*s**4 = 0.
-1, 2
Let q(g) = g - 5. Let z be q(7). Suppose -x + 4 = -0*x, 3*h - 14 = -z*x. What is t in -4*t - 4*t + t + 3*t**h + t = 0?
0, 2
Let s(g) = g**5 + 8*g**4 + 20*g**3 + 13*g**2 - 3*g + 3. Let t(u) = u**2 + u - 1. Let i(z) = -2*s(z) - 6*t(z). Find k, given that i(k) = 0.
-4, -2, 0
Let d(k) be the second derivative of k**7/840 + k**6/480 - k**5/80 - k**4/96 + k**3/12 + k**2/2 + 4*k. Let i(v) be the first derivative of d(v). Solve i(u) = 0.
-2, -1, 1
Let f(d) be the first derivative of -5*d**6 + 94*d**5/5 - 3*d**4 - 125. Determine b so that f(b) = 0.
0, 2/15, 3
Suppose -4*p + 5*a + 3 = -2, -2*p + 19 = 3*a. Let -47*j**3 - 2*j - 2*j**p + 0*j + 51*j**3 = 0. What is j?
-1, 0, 1
Let c(w) = -2*w**2 - 19*w - 21. Let y be c(-8). What is x in 11/4*x**y - 11/4*x + 2*x**2 - 3/2 - 1/2*x**4 = 0?
-1, -1/2, 1, 6
Factor -2*q**3 + 12 + 66*q**2 - 142*q**2 - 80 - 3*q**3 - 140*q + q**3.
-4*(q + 1)**2*(q + 17)
Let i(a) be the first derivative of -25*a**8/336 - 2*a**7/21 - a**6/30 - 29*a**2/2 + 21. Let v(y) be the second derivative of i(y). Solve v(b) = 0.
-2/5, 0
Let p(s) be the first derivative of 5/4*s**2 - 1/2*s**3 + 1/10*s**5 + 8 - 1/8*s**4 - s. Determine i, given that p(i) = 0.
-2, 1
Let o(w) = w**2 + 7*w + 16. Let x be o(-7). Let m = x + -6. Determine i so that -3*i**2 - 2*i + 3*i**3 - m*i + 6*i = 0.
-1, 0, 2
Let n(h) = -h + 5. Let u be n(4). Suppose -3*z = 2*k - 3 - u, -4 = -5*z - 4*k. Find a such that 72 - 3*a**3 + z*a - a**3 - 80 + 8*a**2 = 0.
-1, 1, 2
Let z(c) be the first derivative of -c**5/300 - c**4/60 - c**3/30 + 25*c**2/2 + 10. Let k(r) be the second derivative of z(r). Find t such that k(t) = 0.
-1
Factor -2*l**3 - 297*l - 27*l**2 + 14*l**2 + 5087 - 44*l**2 - 5330 - l**3.
-3*(l + 1)*(l + 9)**2
Suppose -4*m + 34 = 2*u, u - 5*m - 4 - 13 = 0. Suppose 4*x + p = 4*p + 24, x + u = -5*p. Find r, given that -2*r - 9*r**3 + 3*r**4 + 0*r**x + 7*r**2 + r**3 = 0.
0, 2/3, 1
Let s(b) be the third derivative of -1/140*b**7 - 38*b**2 - 1/16*b**4 + 0*b**3 + 1/16*b**5 + 0*b - 1/160*b**6 + 0. Solve s(j) = 0 for j.
-2, 0, 1/2, 1
Let q be 129/258*5/2. Factor -3/4*b - 1/4*b**3 - q*b**2 + 9/4.
-(b - 1)*(b + 3)**2/4
Let v = 18609/4 + -4652. Solve -r**2 - r - v = 0 for r.
-1/2
Let j = -8227 + 8229. Factor -1/2*y + 0 - 1/4*y**j.
-y*(y + 2)/4
Let y(c) = -2*c**4 + 2*c**3 + 2*c**2 - c + 1. Let v(g) = -17*g**4 + 11*g**3 + 23*g**2 - 2*g + 3. Let b(l) = -2*v(l) + 18*y(l). Let b(o) = 0. Calculate o.
-1, 1, 6
Let l be ((-2)/6)/(8 + 308/(-33)). Let h(d) be the third derivative of -1/540*d**6 + 0*d - d**3 - 1/30*d**5 - l*d**4 + 5*d**2 + 0. Factor h(p).
-2*(p + 3)**3/9
Find x such that 66*x**3 - 57*x**3 - 15 + 16 + 60*x**2 - 27*x - 43 = 0.
-7, -2/3, 1
Suppose -51*n**3 + 51*n + 9/2 - 289/2*n**4 + 140*n**2 = 0. What is n?
-1, -3/17, 1
Let x(y) be the first derivative of 5*y**3/3 - 90*y**2 + 1620*y - 140. Solve x(z) = 0 for z.
18
Let q(h) be the third derivative of h**8/112 + 9*h**7/35 + 29*h**6/40 - 12*h**5/5 + 7*h**2 + 6*h. Let q(b) = 0. What is b?
-16, -3, 0, 1
Find c such that 1/2*c**5 + 4*c**2 - 41/6*c + 19/3*c**3 - 17/3*c**4 + 5/3 = 0.
-1, 1/3, 1, 10
Let p(u) = -264*u**3 + 260*u**2 - 28. Let g(w) = -w**3 + w**2 + w + 1. Let f(z) = -16*g(z) - p(z). What is v in f(v) = 0?
-3/14, 1/5, 1
Let u(v) be the second derivative of -v**7/7560 + v**6/1080 + v**5/1080 - v**4/72 - 5*v**3/6 - v. Let a(b) be the second derivative of u(b). Factor a(d).
-(d - 3)*(d - 1)*(d + 1)/9
Let m(h) be the third derivative of -1/36*h**4 + 0 - 11*h**2 + 0*h - 1/540*h**6 + 1/27*h**3 + 1/90*h**5. Let m(r) = 0. Calculate r.
1
Let w(y) be the second derivative of -1/8*y**3 - 1/2*y**2 + 0 + 1/48*y**4 + y. Determine q, given that w(q) = 0.
-1, 4
Let c(m) = 2*m**3 + 70*m**2 - 84*m - 427. Let d be c(-36). Factor 0*g**4 + 0 - 2/15*g**d + 2/5*g**3 - 4/15*g**2 + 0*g.
-2*g**2*(g - 1)**2*(g + 2)/15
Factor -2/9*r**4 + 8/9*r + 0 - 16/9*r**2 + 10/9*r**3.
-2*r*(r - 2)**2*(r - 1)/9
Let f(v) be the third derivative of v**8/840 + v**7/300 - v**6/200 - 7*v**5/600 + v**4/120 + 23*v**2 + 2*v. Let f(c) = 0. What is c?
-2, -1, 0, 1/4, 1
Let x(j) be the first derivative of 3*j**5/5 - 3*j**4/4 - 10*j**3 - 12*j**2 + 899. Factor x(p).
3*p*(p - 4)*(p + 1)*(p + 2)
Let b(g) be the second derivative of -g**6/15 - g**5/5 + 11*g**4/6 + 4*g**3 - 36*g**2 - 22*g + 2. What is n in b(n) = 0?
-3, 2
Let f(g) = 8*g**2 - 7*g - 10. Let h(z) = z**2 - z - 3. Let q(k) = -2*f(k) + 6*h(k). Solve q(y) = 0 for y.
-1/5, 1
Let x(r) = -2*r - 6. Let o be x(-5). Let q(u) = -24*u - 762. Let j be q(-32). Factor -3*z**o - 8*z + 0*z + j*z**3 + z**4.
-2*z*(z - 2)**2*(z + 1)
Determine l, given that -32400 - 720*l + 8*l**2 - l**2 - 11*l**2 = 0.
-90
Let p be (-2 + 0)/(180/(-63)) + (-7)/(-70). Suppose p*u - 4/5 - 2/5*u**3 - 1/5*u**4 + 3/5*u**2 = 0. Calculate u.
-2, 1
Let c(p) = -2*p + 2 + p - 3*p - p - p**2. Let x be c(-5). Determine n, given that 0 + 12/11*n**3 + 2/11*n + 2/11*n**5 - 8/11*n**x - 8/11*n**4 = 0.
0, 1
Let s(r) be the first derivative of r**4/48 + r**3/4 + 9*r**2/8 - r - 12. Let x(c) be the first derivative of s(c). Determine n, given that x(n) = 0.
-3
Suppose -4*o + 5*o**2 + 33 - 14*o + 7 - 12*o = 0. Calculate o.
2, 4
Suppose -7*j + 30 = -2*j. Let m(g) = g**4 - 3*g**3 + 5*g**2 - g. Let p(w) = -6*w**4 + 18*w**3 - 31*w**2 + 6*w. Let r(d) = j*p(d) + 39*m(d). Factor r(b).
3*b*(b - 1)**3
Let l(u) be the first derivative of -32*u**4/7 - 2720*u**3/21 - 337*u**2/7 - 6*u - 266. Factor l(a).
-2*(a + 21)*(8*a + 1)**2/7
Let y(t) be the second derivative of t**9/756 - t**7/105 + t**5/30 + 2*t**3 + 17*t. Let w(q) be the second derivative of y(q). Factor w(v).
4*v*(v - 1)**2*(v + 1)**2
Let b = 30083 - 30080. Factor -3/7*h**4 + 3/7*h - 3/7*h**b + 0 + 3/7*h**2.
-3*h*(h - 1)*(h + 1)**2/7
Find v, given that -20285 + 101*v - 300*v - 4*v**2 - 10198 - 33021 - 809*v = 0.
-126
Let n(c) be the third derivative of -c**5/15 + 65*c**4/3 - 8450*c**3/3 - 33*c**2 - 3*c. Determine o, given that n(o) = 0.
65
Let b(g) be the third derivative of -g**4 - 7/20*g**5 + 2*g**3 + 0 + 0*g + 1/8*g**6 + 12*g**2. Find a, given that b(a) = 0.
-1, 2/5, 2
Suppose -132*i**3 - 96*i**2 + 322*i**3 + 20*i - 130*i**3 + 16*i**4 = 0. Calculate i.
-5, 0, 1/4, 1
Let v(p) = -p**2 + 8*p - 13. Let q be v(7). Let l be (q/8)/((-90)/80). Factor -10/3*x**3 - l*x**2 + 2/3*x - 2*x**4 + 0.
-2*x*(x + 1)**2*(3*x - 1)/3
Let m(o) = -3*o - 3. Let r be m(-1). Let l be (2/1)/(-2) + r + 1. Suppose -1/3*g**2 + l - 2/3*g = 0. Calculate g.
-2, 0
Let j be (-4)/(-2) - -3*(-27797)/45318. Let h = j + -1/166. Factor -h*i**2 - 18/13 + 12/13*i.
-2*(i - 3)**2/13
Let i(b) = 20*b - 138. Suppose 0 = -u + 5*n + 12, -2*u + 11 = -0*u + 3*n. Let o be i(u). Determine v, given that -1/5 - 4/5*v**o + v = 0.
1/4, 1
Let g(t) = t**3 - 109*t**2 + 679*t - 1211. Let o(q) = -5*q**3 + 655*q**2 - 4075*q + 7265. Let u(a) = -25*g(a) - 4*o(a). Factor u(c).
-5*(c - 9)**2*(c - 3)
Determine x so that 29*x - 15 + 19*x**2 - 18*x**2 - 31*x = 0.
-3, 5
Let n(l) = -3*l**3 + 320*l**2 + 316*l. Let s(w) = -3*w**3 + 318*w**2 + 315*w. Let c(t) = -6*n(t) + 7*s(t). Determine q so t