171*q**4/2 + 2*q**3 + 459*q**2/2 - 243*q + 184. Suppose z(n) = 0. Calculate n.
-9/5, 1
Let f(q) be the first derivative of q**7/189 + 2*q**6/135 + q**5/90 + 13*q + 7. Let p(a) be the first derivative of f(a). Factor p(y).
2*y**3*(y + 1)**2/9
Let a(k) be the second derivative of -k**6/330 + 3*k**5/220 + k**4/132 - k**3/22 - 85*k + 2. Factor a(c).
-c*(c - 3)*(c - 1)*(c + 1)/11
Suppose -5/2*c + 75/2 - 7/2*c**2 + 1/2*c**3 = 0. What is c?
-3, 5
Let k be 0/(-4*(-5 - 22/(-4))). Let x(r) be the second derivative of 0*r**3 + 0 - 3*r + 1/10*r**5 - 1/6*r**4 + k*r**2. Let x(q) = 0. What is q?
0, 1
Let g(l) be the second derivative of l**6/2340 - l**5/195 - 8*l**3/3 + l. Let z(n) be the second derivative of g(n). What is w in z(w) = 0?
0, 4
What is d in 5/2*d**2 + 7*d + 4 = 0?
-2, -4/5
Suppose 118*o + 18*o**2 + 119*o + 14*o**4 + 30*o**3 + 116*o - 351*o = 0. What is o?
-1, -1/7, 0
Let b(r) = 9*r + r**3 + 12*r**2 + 0*r - 5 + 5*r. Let x be b(-10). Solve q**2 - 55 + x + q = 0.
-1, 0
Let a(j) = 5*j**4 + 47*j**3 - 275*j**2 + 521*j - 294. Let t(c) = 18*c**4 + 189*c**3 - 1101*c**2 + 2085*c - 1176. Let b(h) = 15*a(h) - 4*t(h). Solve b(x) = 0.
1, 2, 7
Let m = -201 + 111. Let v be (-56)/m + (-10)/25*1. Determine q, given that -2/9*q**3 + 2/9*q - 2/9*q**2 + v = 0.
-1, 1
Let b(v) be the third derivative of -v**5/20 - v**4/4 - 60*v**2. Find w, given that b(w) = 0.
-2, 0
Let n(k) be the first derivative of 3*k**5/25 + 78*k**4/5 + 2374*k**3/5 - 5148*k**2 + 16335*k + 212. Solve n(w) = 0.
-55, 3
Let l be ((273/13)/(-63))/(-1 + 0). Let u(j) be the first derivative of 1/3*j + 1/9*j**3 - l*j**2 - 3. What is k in u(k) = 0?
1
Suppose -z - 19 = -4*n, z - 5*n + 26 - 3 = 0. Let y be z/(-12)*(6 + -6). Let y - 2/3*t**3 + 0*t - 4/3*t**2 = 0. What is t?
-2, 0
Let z(g) = -g**2 - 10*g - 16. Let s be z(-8). Let h(o) = -o + 2. Let j be h(s). What is m in 23*m - 3*m - 20*m**3 - 8 + 12*m**4 - 3*m**2 - m**j = 0?
-1, 2/3, 1
Let z = -46 + 45. Let q be 2*z/(-3)*(-21)/(-70). Factor 1/5*x**3 + 1/5*x**2 - 1/5*x - q.
(x - 1)*(x + 1)**2/5
Let j(k) = -2*k**3 - 4*k**2 + 4*k - 7. Let w be j(-5). Let x = 126 - w. Solve -1/4*b**x + 1/2*b**2 + 0 - 1/4*b = 0.
0, 1
Let i = -7 - -11. Suppose 3*l + 3 = i*l. Factor -22*u**l - 46*u**2 - 27*u - 4 - 3*u - 2*u**2.
-2*(u + 1)**2*(11*u + 2)
Let n(d) be the first derivative of 4*d**3/15 - 28*d**2/5 - 204*d/5 + 8. Factor n(o).
4*(o - 17)*(o + 3)/5
Let q = 138 - 115. Suppose 0 = -5*y - 2 + 27, d = 5*y - q. Suppose -5/4*p + p**d + 1/2 - 1/4*p**3 = 0. What is p?
1, 2
Suppose 3*l = 5*l - 126. Suppose -5*m = 2*b - l, 59 = 5*m + b - 0*b. What is j in 0*j**4 + m*j**3 + 3*j - 14*j**3 + 3*j**2 - 3*j**4 = 0?
-1, 0, 1
Let p(d) be the first derivative of 2/9*d**3 - 3 + 0*d - d**2. Determine j so that p(j) = 0.
0, 3
Suppose 4*q - q - 4*b + 11 = 0, -b + 14 = 3*q. Find x such that -3*x**3 + 5*x + 0*x + 3*x**2 - q + 2*x - 4*x = 0.
-1, 1
Let x(i) be the third derivative of 0*i - 5*i**2 + 1/120*i**5 + 0 - 1/480*i**6 + 0*i**3 - 1/96*i**4. Suppose x(t) = 0. What is t?
0, 1
Factor -1/6*m**2 - m + 9/2.
-(m - 3)*(m + 9)/6
Let m(d) be the third derivative of -d**5/75 - 11*d**4/60 - d**3 - 39*d**2 - 2*d. Factor m(o).
-2*(o + 3)*(2*o + 5)/5
What is j in -13/6*j - 5 - 1/6*j**2 = 0?
-10, -3
Factor -19503*y**4 + 1 - 7*y**3 - 1 + 11*y**2 + 2*y + 19504*y**4 - 7*y.
y*(y - 5)*(y - 1)**2
Let x(p) be the third derivative of 1/840*p**7 + 0*p**3 + 0*p + 3*p**2 - 1/80*p**5 - 1/48*p**4 + 0*p**6 + 0. Factor x(a).
a*(a - 2)*(a + 1)**2/4
Let u(g) be the third derivative of 0*g**3 + 4*g**2 + 0*g + 1/8*g**4 + 1/56*g**8 - 1/70*g**7 + 1/20*g**5 - 3/40*g**6 + 0. Suppose u(a) = 0. Calculate a.
-1, -1/2, 0, 1
Let z(x) be the third derivative of 0*x + 1/15*x**6 + 0*x**5 - 1/3*x**4 + 0 + 2/105*x**7 + 16*x**2 - 2/3*x**3. Factor z(m).
4*(m - 1)*(m + 1)**3
Let a(l) = 2*l**2 + 29*l + 27. Let j(v) = -2*v**2 - 15*v - 13. Let z(u) = -3*a(u) - 5*j(u). Determine x so that z(x) = 0.
-1, 4
Factor -17/3*c**2 + 9*c + 1/3*c**3 + 15.
(c - 15)*(c - 3)*(c + 1)/3
Suppose 6*u = 4*u - u. Let d(x) be the first derivative of u*x**2 - 1 + 1/18*x**6 + 1/9*x**3 - 1/12*x**4 + 0*x - 1/15*x**5. Factor d(s).
s**2*(s - 1)**2*(s + 1)/3
Let i be 72/(-7) - -1 - -5. Let c = 40/7 + i. Factor 2/7*y**5 - c*y**3 - 2/7*y**4 + 2/7*y**2 + 8/7 + 16/7*y.
2*(y - 2)**2*(y + 1)**3/7
Suppose 0 = 4*d + x - 12, -19*d + 22*d - 4*x = -10. Factor 0*i**3 + 8/5*i**d - 4/5 + 0*i - 4/5*i**4.
-4*(i - 1)**2*(i + 1)**2/5
Let 2*n**5 + 3*n**5 + 8*n**3 - 4*n**5 + 321*n**4 - 2*n**5 + 12*n**2 - 326*n**4 = 0. What is n?
-6, -1, 0, 2
Let u(k) be the second derivative of k**5/8 + 145*k**4/24 + 1235*k**3/12 + 2535*k**2/4 - 146*k. Factor u(s).
5*(s + 3)*(s + 13)**2/2
Let m(r) be the second derivative of 1/25*r**5 + 0 + 1/10*r**4 - 4/5*r**2 - 1/75*r**6 + 3*r - 4/15*r**3. Let m(l) = 0. Calculate l.
-1, 2
Let v(t) be the first derivative of -2/15*t**3 + 13 - 18/5*t - 6/5*t**2. Find k such that v(k) = 0.
-3
Let v(j) be the third derivative of -j**6/180 - j**5/45 + 7*j**4/36 - 4*j**3/9 - 69*j**2. Let v(z) = 0. Calculate z.
-4, 1
Let y = 69 + -55. Suppose 4*b = -v + 1 - y, 3*b = 2*v - 18. Factor 0*d**v + 0 + 3/7*d - 3/7*d**5 - 6/7*d**2 + 6/7*d**4.
-3*d*(d - 1)**3*(d + 1)/7
Let x(c) be the first derivative of -18 - 2/19*c**2 + 2/19*c - 2/57*c**3 + 1/19*c**4. Factor x(w).
2*(w - 1)*(w + 1)*(2*w - 1)/19
Let o be ((-27)/36)/(108/(-48)). Factor -5/3*d + o*d**2 + 2.
(d - 3)*(d - 2)/3
Let y(r) be the first derivative of r**9/3024 - r**7/280 + r**6/180 - r**3/3 + 3. Let o(j) be the third derivative of y(j). Factor o(z).
z**2*(z - 1)**2*(z + 2)
Let u be (2/6)/((-2)/(-4)). Let o = -3272/19 - -9892/57. Factor -2*z**2 + 2/3*z**3 - u*z + o + 2/3*z**4.
2*(z - 1)**2*(z + 1)*(z + 2)/3
Suppose 15 + 17 = 8*n. Factor h**4 + 4*h**4 - h**n.
4*h**4
Let i(b) be the first derivative of -2*b**2 + 1/150*b**5 + 0*b**3 + 0*b - 1 - 1/30*b**4. Let g(k) be the second derivative of i(k). Factor g(y).
2*y*(y - 2)/5
Let v(n) = n**2 - 5*n + 6. Let f be v(6). Let i be (-5)/(-20) - (-3)/f. Suppose 1/2*d**4 - 1/6*d**3 + 0 - i*d**2 + 1/6*d = 0. Calculate d.
-1, 0, 1/3, 1
Let q(j) = -j + 33. Let b be q(17). Determine k, given that b*k**3 - 34*k**3 + 16*k**3 + 2*k + k**4 - k**2 = 0.
-1, 0, 1, 2
Let l(c) be the second derivative of 3*c**5/70 + 13*c**4/28 + 3*c**3/7 - 16*c. Factor l(q).
3*q*(q + 6)*(2*q + 1)/7
Let o(w) = 9*w**3 + 6*w**2 + 13*w. Let a be o(-3). Let d be 3/((-15)/20) - a/51. Factor 12/17*u**2 + 8/17*u**3 + d*u + 2/17 + 2/17*u**4.
2*(u + 1)**4/17
Let w(p) be the third derivative of 1/270*p**5 + 1/1080*p**6 + 0*p**3 + 0*p + 0*p**4 + 3*p**2 + 0. Suppose w(t) = 0. What is t?
-2, 0
Determine k so that -49*k**2 - 45*k**2 - k**4 + 103*k**2 + 12*k - 12 - 2*k**4 - 6*k**3 = 0.
-2, 1
Let t = 440 + -815. Let g = -731/2 - t. Solve -7/2*f**4 - 25/2*f**2 - g*f**3 - 1/2*f**5 - 8*f - 2 = 0.
-2, -1
Let v(l) = -l**3 + 6*l**2 - 10. Let i be v(5). Factor 5*p**4 - p - 6*p + 5*p**5 - p - 25*p**2 - 2*p - i*p**3.
5*p*(p - 2)*(p + 1)**3
Let b(o) = 2*o**3 + 2*o**2 - 8*o - 5. Let l be b(-3). Let d = l + 23. Factor -10 - 2*m**4 + 2*m + 4*m**3 - 6*m**3 + 6*m**2 + d.
-2*(m - 1)**2*(m + 1)*(m + 2)
Suppose -5*q + q = -20. Let a = -2 + q. Solve u**3 + u**a - 3*u**3 - u**4 + u**2 + 0*u**5 + u**5 = 0 for u.
-1, 0, 1
Suppose -3 - 126 = -43*i. Let h(t) be the third derivative of 0 + i*t**2 - 1/12*t**4 + 1/180*t**5 + 0*t + 1/2*t**3. Suppose h(o) = 0. What is o?
3
Let i be (2/(-39))/((-352)/1144). Suppose -8 = -5*f + 7. Factor 0*s**2 + 0 + 0*s + 0*s**f + i*s**4.
s**4/6
Let o = -1783 + 8931/5. What is t in -8/5*t - 2/5 - 2/5*t**4 - 8/5*t**5 + o*t**3 + 4/5*t**2 = 0?
-1, -1/4, 1
Let v(s) be the third derivative of 0*s + 0 - 1/540*s**6 + 1/108*s**4 + 1/27*s**3 + 19*s**2 - 1/270*s**5. Determine y, given that v(y) = 0.
-1, 1
Let r(i) be the second derivative of -i**7/7 + 17*i**6/15 - 23*i**5/15 - 34*i**4/9 + 40*i**3/9 + 32*i**2/3 + 38*i + 1. What is d in r(d) = 0?
-2/3, 1, 2, 4
Let g = 3088 + -40174/13. Let a = 133/52 + g. Let -1/4*z**4 + 1/4*z + a*z**5 + 1/2*z**2 - 1/2*z**3 - 1/4 = 0. Calculate z.
-1, 1
Let y(q) be the second derivative of 10*q**7/21 + 13*q**6/6 + 5*q**5/2 - 10*q**4/3 - 35*q**3/3 - 25*q**2/2 - 212*q. What is b in y(b) = 0?
-5/4, -1, 1
Let b be (-1)/((-8)/6 + 2 + -1). Factor -2*a**b + 0*a + 0*a**3 + 4 + 6*a.
-2*(a - 2)*(a + 1)**2
Solve 0 - 2/7