**4/16 - 45*x**3/4 + 6075*x**2/8 + 339*x. Suppose h(c) = 0. Calculate c.
45
Suppose 0 = -b + 5 - 2. Suppose 5*h = 7*h - 12. Factor -3 - 2*s - h*s - 3 + 3*s**b - s.
3*(s - 2)*(s + 1)**2
Let a = 58932 + -412520/7. Factor 0*v - a*v**3 - 2/7*v**2 + 0 - 2/7*v**4.
-2*v**2*(v + 1)**2/7
Let d(y) be the first derivative of y**6/48 + 3*y**5/40 - y**4/8 - 2*y**3/3 + 2*y - 17. Find o, given that d(o) = 0.
-2, 1, 2
Factor 363/2 + 3/2*o**2 + 33*o.
3*(o + 11)**2/2
Let f(z) be the third derivative of z**5/60 - z**4/8 + z**3/3 - z**2 + 2*z. What is y in f(y) = 0?
1, 2
Let x(k) be the third derivative of k**7/630 - k**6/40 + 5*k**5/36 - 3*k**4/8 + 5*k**3/9 + 7*k**2 + 12. Suppose x(f) = 0. Calculate f.
1, 2, 5
Let b(a) = -a - 4. Let r be b(-8). What is n in 8*n**2 - 12*n + 6 - 2 + 10*n**3 + 2*n**5 - 9*n**r - 3*n**2 = 0?
-1, 1/2, 1, 2
Let j(q) be the first derivative of -q**6/3 + 6*q**5/5 + q**4 - 8*q**3 + 8*q**2 + 120. Determine p, given that j(p) = 0.
-2, 0, 1, 2
Suppose 4*w - 16 = -2*d, -6 = -w - 7*d + 11. Determine f, given that 1/3*f**w - 2/3*f + 0 + 1/3*f**2 = 0.
-2, 0, 1
Let l(g) = 3*g**3 + 54*g**2 + 33*g - 210. Let j(k) = 2*k**3 + 35*k**2 + 22*k - 140. Let f(i) = 8*j(i) - 5*l(i). Solve f(u) = 0 for u.
-7, -5, 2
Let x(w) be the first derivative of w**6/18 - 16*w**5/15 + 13*w**4/2 - 112*w**3/9 + 49*w**2/6 + 61. Factor x(b).
b*(b - 7)**2*(b - 1)**2/3
Let d(y) be the second derivative of -1/23*y**4 + 3*y + 5/69*y**3 + 1/23*y**2 + 0. Factor d(k).
-2*(k - 1)*(6*k + 1)/23
Let i be (-169)/(-1014) - (-19)/(-120). Let q(w) be the third derivative of 0*w + 0 + i*w**5 - 1/240*w**6 - 1/12*w**3 + 1/48*w**4 - 12*w**2. Factor q(r).
-(r - 1)**2*(r + 1)/2
Let y(o) be the second derivative of -o**5/5 - 25*o**4/3 - 16*o**3 - 34*o. Solve y(h) = 0 for h.
-24, -1, 0
Factor -48 + 16*a + 48 - 7*a + 3*a**2 + 0*a**2.
3*a*(a + 3)
Let p(q) be the third derivative of 0 + 5/6*q**4 + 11/40*q**5 + 1/420*q**7 + 22*q**2 + 4/3*q**3 + 0*q + 1/24*q**6. Factor p(g).
(g + 1)**2*(g + 4)**2/2
Let q(m) be the first derivative of 0*m + 0*m**3 + 0*m**2 + 2/15*m**6 + 4/5*m**4 - 16/25*m**5 + 10. Factor q(a).
4*a**3*(a - 2)**2/5
Suppose 3*q + q + 644 = -4*j, 5*j + 4*q + 809 = 0. Let z = j - -168. Factor 1/2*i**2 + 0*i + 0 - 1/2*i**z.
-i**2*(i - 1)/2
Suppose 33 = 2*f - 3*u, -3*u + 0 = 3*f - 27. Let o be 368/f + (-2)/3. Find s such that -3*s**3 - o*s**5 - 3*s**2 + 5*s**2 + 31*s**5 = 0.
-2, 0, 1
Suppose -1176 - 746/3*t**2 - 952*t - 68/3*t**3 - 2/3*t**4 = 0. Calculate t.
-14, -3
Let m(h) be the second derivative of h**6/70 + 2*h**5/35 - 2*h**4/3 + 16*h**3/21 + 24*h**2/7 - 344*h. Factor m(w).
(w - 2)**2*(w + 6)*(3*w + 2)/7
Let g be ((-180)/75)/((-3)/20). Let 20*i**3 - 2*i**4 - 77*i**2 - 16*i - g - 4*i**5 + 97*i**2 - 2*i**4 = 0. Calculate i.
-2, -1, 1, 2
Let q(w) = w**2 + 10*w + 12. Let i be q(-9). Factor -2*v**3 + 0*v**i - 16*v + 31*v**2 - 8 - 41*v**2.
-2*(v + 1)*(v + 2)**2
Let o(t) be the second derivative of 1/24*t**6 + 0*t**3 + 0 - t + 5/6*t**4 - 1/3*t**5 + t**2. Let x(d) be the first derivative of o(d). Solve x(q) = 0 for q.
0, 2
Let i(t) = -3*t + 22. Suppose -2*u = -5*u + 18. Let c be i(u). Find a, given that 0*a**2 + 0*a + 0 - 2/5*a**3 + 8/5*a**c - 6/5*a**5 = 0.
0, 1/3, 1
Let d be (-17)/((-1989)/26) - (-158)/18. Let o(b) be the first derivative of -8/9*b - d + 2/27*b**3 - 1/3*b**2. Factor o(c).
2*(c - 4)*(c + 1)/9
Let o be 104/91*3 - 3. Factor -12/7*r + o*r**2 + 9/7.
3*(r - 3)*(r - 1)/7
Let f(c) be the first derivative of c**4/24 - c**2/4 - c/3 - 195. Factor f(s).
(s - 2)*(s + 1)**2/6
Let l(z) = z**3 + 5*z**2 + z - 9. Let v be l(-4). Suppose 3*h - 96 = -v*h. Factor h*p**3 + 4 + 2*p**5 - 18*p - 9 - 12*p**4 + 5 + 12*p**2.
2*p*(p - 3)**2*(p - 1)*(p + 1)
Let y(s) = -5*s**2 + 68*s + 1357. Let b(m) = -m**2 - m - 2. Let l(z) = 6*b(z) - y(z). Factor l(p).
-(p + 37)**2
Let o(n) be the second derivative of 0*n**3 + 0 + 9/80*n**5 + 1/40*n**6 + 0*n**2 + 1/8*n**4 - 19*n. Solve o(j) = 0 for j.
-2, -1, 0
Let g(s) be the first derivative of 2/5*s**3 - 8/5*s + 1/2*s**4 + 28 - s**2 + 2/25*s**5. Solve g(w) = 0.
-4, -1, 1
Let g = 2 - -3. Factor 5*q**4 - 3*q - 3*q - 5*q**2 + 11*q - g*q**3.
5*q*(q - 1)**2*(q + 1)
Factor -172*u**3 - u**2 + u**4 + 2*u - 171*u**3 + 341*u**3.
u*(u - 2)*(u - 1)*(u + 1)
Determine r, given that 76/5*r - 62/5*r**3 - 58/5*r**2 + 74/5*r**4 - 14/5*r**5 - 16/5 = 0.
-1, 2/7, 1, 4
Let p(m) be the third derivative of -m**8/168 - m**7/105 - 140*m**2. Let p(a) = 0. What is a?
-1, 0
Let c be (-4)/(-14) + 4/(-14) - -79. Solve -3*f**3 + 9*f**5 - 21*f**2 - 74*f + 21*f**4 + 147*f - c*f = 0.
-2, -1, -1/3, 0, 1
Suppose 2*r = -3*r - 80. Let s = -8 - r. Let t(h) = h**2 + 3*h - 1. Let i(c) = -4*c**2 - 8*c + 4. Let x(f) = s*t(f) + 3*i(f). Determine d so that x(d) = 0.
-1, 1
Suppose 4*c + 3*c = 2*c - 0*c. Let 0 + c*t - 1/5*t**2 = 0. What is t?
0
Suppose 109*w - 100*w - 36 = 0. Let o(v) be the second derivative of v + 1/105*v**7 - 2/15*v**w + 1/15*v**3 + 0 + 0*v**2 - 4/75*v**6 + 3/25*v**5. Factor o(b).
2*b*(b - 1)**4/5
Factor 3*o**4 + 212*o**2 + 228*o**2 + 16*o - 428*o**2 - 4*o**4.
-o*(o - 4)*(o + 2)**2
Suppose -2*d + 97 = 5*u, -u + d = -8 - 17. Let i = -19 + u. What is c in 2*c**2 + 0*c**i + 1 - 8*c + 7 = 0?
2
Solve -41*j**2 - 34*j**2 - 31*j**2 - 5*j**5 - 35*j**4 + 166*j**2 - 20*j**3 = 0.
-6, -2, 0, 1
Let f(c) be the third derivative of c**7/840 + 11*c**6/480 + 7*c**5/48 + 25*c**4/96 + 3*c**2 + 14*c. Find u such that f(u) = 0.
-5, -1, 0
Factor -468*j**2 + 111*j**3 + 1060 + 179*j**3 + 23816*j + 5*j**4 + 1833*j**2 - 21676*j.
5*(j + 1)*(j + 2)**2*(j + 53)
Let l = 3340/7 - 474. Let x = -290 + 2034/7. Factor -18/7*s - x + l*s**2.
2*(s - 1)*(11*s + 2)/7
Factor 1/3*b**3 - 17/3*b**2 + 56/3*b - 52/3.
(b - 13)*(b - 2)**2/3
Let x(q) be the second derivative of q**4/36 - 3*q**3 + 53*q**2/6 - 196*q. Factor x(f).
(f - 53)*(f - 1)/3
Let t(n) be the first derivative of -9*n**2 - 64 + 12 + 20 - n**3 + 22 + 21*n. Factor t(f).
-3*(f - 1)*(f + 7)
Let b(y) be the second derivative of -y**7/42 + y**6/15 + y**5/4 - 5*y**4/6 - 2*y**3/3 + 4*y**2 - 14*y - 5. Determine f, given that b(f) = 0.
-2, -1, 1, 2
Let v = 42/31 - 1103/837. Let k(g) be the third derivative of -g**2 + 0 - v*g**3 - 1/54*g**4 - 1/270*g**5 + 0*g. What is s in k(s) = 0?
-1
Let q(u) be the second derivative of 0 + 1/48*u**4 + 0*u**2 - 1/24*u**3 - 8*u. Factor q(p).
p*(p - 1)/4
Let n = -152/13 + 18253/1560. Let v(b) be the third derivative of 0*b - 5*b**2 + 0 + 1/96*b**4 - n*b**5 + 0*b**3 + 1/480*b**6. Factor v(l).
l*(l - 1)**2/4
Let o(i) be the first derivative of 58*i**3/21 - 8*i**2 - 8*i/7 - 203. Factor o(q).
2*(q - 2)*(29*q + 2)/7
Let s(a) be the second derivative of -a**5/30 - 5*a**2 + 12*a. Let c(m) be the first derivative of s(m). Suppose c(n) = 0. What is n?
0
Let z(t) be the first derivative of -9/25*t**5 + 12 - 12/5*t + 0*t**2 - 1/10*t**6 + 3/20*t**4 + 7/5*t**3. Let z(m) = 0. Calculate m.
-2, -1, 1
Solve 18 - 6*s + 1253*s**2 - 1251*s**2 - 6*s = 0.
3
Suppose -63/5*m - 24/5*m**2 + 6 - 6/5*m**4 + 63/5*m**3 = 0. Calculate m.
-1, 1/2, 1, 10
Let i(t) = t + 1. Let c = -13 - -17. Let z be i(c). Let 14/11*l + 4/11*l**3 - 4/11*l**4 + 16/11*l**2 - 2/11*l**z + 4/11 = 0. What is l?
-1, 2
Let p(y) = -5*y**3 + 44*y**2 - 14*y + 6. Let x(l) = 5*l**3 - 40*l**2 + 15*l - 5. Let a(k) = -5*p(k) - 6*x(k). Factor a(g).
-5*g*(g - 2)**2
Factor -104/7*c - 32*c**3 - 20/7 - 116/7*c**4 - 216/7*c**2 - 24/7*c**5.
-4*(c + 1)**4*(6*c + 5)/7
Let q be (-156)/(-15) + (-96)/12. Let s(n) be the first derivative of -8/5*n + 18/5*n**3 - q*n**2 - 18/25*n**5 - 10 - 1/5*n**4. Let s(r) = 0. Calculate r.
-2, -2/9, 1
Let b(o) = o**2. Let w be b(2). Suppose -k = -w*r - 0*r + 10, 0 = k - 2*r + 4. Factor -v**4 - 6*v**2 - v + 6*v**2 - 3*v**3 - 3*v**k.
-v*(v + 1)**3
Let o(m) be the third derivative of m**7/105 - 7*m**6/30 + 26*m**5/15 - 11*m**4/2 + 9*m**3 - m**2 - 130. Factor o(c).
2*(c - 9)*(c - 3)*(c - 1)**2
Let r(n) = 2*n**2 - 11*n - 182. Let d(m) = m**2 - 5*m - 87. Let j(x) = -14*d(x) + 6*r(x). Factor j(b).
-2*(b - 9)*(b + 7)
Suppose 0 = 236*q - 248*q + 24. Factor 1/2*n**q - 1/2*n**4 - 1/4*n + 1/4*n**5 + 0 + 0*n**3.
n*(n - 1)**3*(n + 1)/4
Let h(c) = -5*c + 60. Let y be h(12). Let m(o) be the second derivative of -3/40*o**5 - 1/28*o**7 + y*o**2 + 0*o**4 - 1/10*o**6 + 0 + 2*o + 0*o**3. Factor m(s).
-3*s**3*(s + 1