
Suppose -125*c = -27*c. Let j(x) be the second derivative of -8*x + 0 + 5/24*x**4 + c*x**2 + 0*x**3. Factor j(v).
5*v**2/2
Let o(i) = -11*i**2 - 59*i + 45. Let r(x) = 14*x**2 + 58*x - 42. Let w(q) = 6*o(q) + 5*r(q). Determine v, given that w(v) = 0.
1, 15
Suppose -2*t**2 + 20 - 13068*t + 6532*t + 6530*t = 0. What is t?
-5, 2
Factor -3*m**2 - 1/4*m**3 - 41/4*m - 15/2.
-(m + 1)*(m + 5)*(m + 6)/4
Let v(d) = 14*d**2 + 14*d - 12. Suppose 2*b = -4*x + 5 - 21, 0 = 5*x - 3*b + 31. Let g(p) = -9*p**2 - 9*p + 8. Let r(k) = x*v(k) - 8*g(k). Factor r(l).
2*(l - 1)*(l + 2)
Let r(o) = -130*o - 4396. Let p be r(-34). Let n(q) be the first derivative of -3*q**3 - 15/4*q**2 - 9/8*q**4 - 9/4*q + p - 3/20*q**5. Factor n(v).
-3*(v + 1)**3*(v + 3)/4
Let x(u) be the first derivative of -2*u**6/15 - 184*u**5/25 - 26*u**4 - 32*u**3/3 + 262*u**2/5 + 344*u/5 + 457. Let x(z) = 0. Calculate z.
-43, -2, -1, 1
Factor 1/10*z**3 + 83/5*z**2 + 3526/5*z + 6724/5.
(z + 2)*(z + 82)**2/10
Let l(c) = c**2 - 5*c - 32. Let w be l(-7). Factor 5*i**2 + 87*i - 20 - 50*i - w*i.
5*(i - 4)*(i + 1)
Suppose 66246/5*p - 65522/5 - 726/5*p**2 + 2/5*p**3 = 0. Calculate p.
1, 181
Let w be 111 - ((1 - (-2 + 2)) + 2). Let q be (-2)/(-5)*(w + 12). Find f, given that -55*f - 34*f**2 + 2*f**2 - 36*f**3 + f**3 - 10 - q*f**2 = 0.
-1, -2/7
Let x(y) be the third derivative of 45*y**2 + 0*y + 0 + 1/2016*y**8 + 0*y**4 + 0*y**6 + 1/1260*y**7 + 0*y**3 + 0*y**5. Factor x(c).
c**4*(c + 1)/6
Let a(y) be the second derivative of 5/9*y**3 + 25/6*y**2 + 1/36*y**4 + 170*y + 0. What is o in a(o) = 0?
-5
Let z(k) be the first derivative of k**4/4 - 7*k**3 + 39*k**2/2 - 18*k - 59. Let n(w) be the first derivative of z(w). Determine s, given that n(s) = 0.
1, 13
Let f = 2117 - 2112. Let m(j) be the third derivative of -16/3*j**3 + 0 + 6/5*j**f - 2*j**2 + 1/6*j**6 + 2*j**4 + 0*j. Factor m(c).
4*(c + 2)**2*(5*c - 2)
Let n(w) be the third derivative of w**7/462 + w**6/165 - 13*w**5/220 + 17*w**4/132 - 4*w**3/33 + 2255*w**2. Find b such that n(b) = 0.
-4, 2/5, 1
Suppose h - i = 4 + 2, h = -5*i. Suppose 4*z = -3*a + 32 - 2, 27 = 2*a + h*z. Let -a + 3*x - 10*x**3 + 5*x**4 + 7*x + 1 = 0. What is x?
-1, 1
What is o in -25/8 - 15/8*o + 9/8*o**2 - 1/8*o**3 = 0?
-1, 5
Suppose 99 = 84*o - 97 + 28. Factor -3/2 - 21/4*l - 15/4*l**o.
-3*(l + 1)*(5*l + 2)/4
Suppose 5*z = 5*d - 1690, 20*z = 18*z + 4*d - 672. Let r = 683/2 + z. Factor -9/2*x**2 + 0 - r*x.
-3*x*(3*x + 1)/2
Let f(g) be the third derivative of g**5/60 + 65*g**4/24 + 32*g**3/3 - 860*g**2 + 2*g. What is o in f(o) = 0?
-64, -1
Suppose -4*l = t - 3261, 8*t = -4*l + 3*t + 3281. Let r = -8938/11 + l. Solve -50/11*f**3 - 76/11*f**2 - 16/11*f**4 - 56/11*f - 2/11*f**5 - r = 0.
-2, -1
Let k(w) be the third derivative of -w**8/1680 - w**7/105 - w**6/25 + 8*w**5/75 + 16*w**4/15 + 1795*w**2. Factor k(u).
-u*(u - 2)*(u + 4)**3/5
Let z(h) be the first derivative of h**7/420 - h**6/180 - h**5/15 + h**4/3 + 6*h**3 + 162. Let d(b) be the third derivative of z(b). Factor d(u).
2*(u - 2)*(u - 1)*(u + 2)
Let w(s) be the first derivative of -s**6/120 - s**5/3 + 43*s**4/24 - 11*s**3/3 - s**2/2 + 10*s - 134. Let c(o) be the second derivative of w(o). Factor c(p).
-(p - 1)**2*(p + 22)
Let p(o) be the first derivative of 4/3*o**3 + 96*o - 28*o**2 + 115. Factor p(u).
4*(u - 12)*(u - 2)
Let v(m) be the first derivative of 2*m**6 - 168*m**5/5 + 147*m**4/4 + 43*m**3 - 159*m**2/2 + 39*m + 1855. Determine k, given that v(k) = 0.
-1, 1/2, 1, 13
Let w(k) be the first derivative of k**6/12 - 49*k**5/5 + 523*k**4/2 + 7492*k**3/3 + 7904*k**2 + 10816*k + 564. Factor w(m).
(m - 52)**2*(m + 2)**3/2
Let t(i) be the first derivative of 5/2*i**2 + 5/6*i**6 + 0*i + 15/2*i**4 + 52 + 4*i**5 + 20/3*i**3. Suppose t(o) = 0. Calculate o.
-1, 0
Let m(u) be the first derivative of u**7/1680 + u**6/720 - u**5/120 - 5*u**3/3 - 3*u**2/2 - 4. Let k(q) be the third derivative of m(q). Factor k(f).
f*(f - 1)*(f + 2)/2
Let c(n) be the second derivative of -n**6/36 + 293*n**5/120 + 59*n**4/36 - 5064*n. Determine f, given that c(f) = 0.
-2/5, 0, 59
Let a(d) = -d**2. Let f(v) = v**3 - 21*v**2 - 21*v - 3. Let y(k) = 21*k**2 + 22*k + 4. Let b(s) = 4*f(s) + 5*y(s). Let l(o) = a(o) - b(o). Factor l(z).
-2*(z + 1)*(z + 4)*(2*z + 1)
Let s(i) be the third derivative of i**6/80 - 3*i**5/40 + i**4/8 + 332*i**2. Factor s(b).
3*b*(b - 2)*(b - 1)/2
Let p(h) be the third derivative of -h**5/150 - 47*h**4/30 + h**2 + 104*h + 2. Factor p(l).
-2*l*(l + 94)/5
Let j be 1*(16/24)/((-6)/(-36)). Let u(d) be the second derivative of -2/15*d**j - 1/150*d**6 - 1/20*d**5 + 18*d + 0 + 0*d**2 - 2/15*d**3. Factor u(n).
-n*(n + 1)*(n + 2)**2/5
Suppose 2/7*j**3 + 6*j**2 + 160/7*j + 0 = 0. Calculate j.
-16, -5, 0
Factor -2/15*r**3 - 1397792/5*r - 1672/5*r**2 - 1168554112/15.
-2*(r + 836)**3/15
Let v(c) be the first derivative of 181*c**2 + 3*c + 66*c**2 - 138 + 6000*c**3 + 181*c**2 - 128*c**2 + 2*c. Factor v(g).
5*(60*g + 1)**2
Let m(a) = a**3 - 3*a**2 - 46. Let o be m(5). Suppose 2*y**4 + 9*y**5 - 4*y**3 + 362*y**2 - 11*y**o - 358*y**2 = 0. What is y?
-2/3, 0, 2/3, 1
Let q(n) be the first derivative of -147*n**4/20 - 84*n**3/5 - 54*n**2/5 - 1880. Factor q(x).
-3*x*(7*x + 6)**2/5
Let z be (-7)/(-7)*4 - (54/(-5) - -2). Factor 4/5*l**2 - z*l + 256/5.
4*(l - 8)**2/5
Let v(i) = 3*i**3 - 3*i**2 + 3*i - 18. Let w be v(3). Factor 58*r**3 + 22*r**3 - w*r**4 - 5*r**5 - 30*r**3.
-5*r**3*(r - 1)*(r + 10)
Let m be (2 - 2)/(-4 - -1 - (-43 + 42)). Let s(n) be the second derivative of 1/20*n**5 + m*n**3 + 0*n**2 + 0 + 1/12*n**4 - 18*n. Find a, given that s(a) = 0.
-1, 0
Suppose -21 = -3*n - 3*o, -n + 13 = 14*o - 11*o. Let r(g) be the first derivative of -13 + 5/4*g**n - 10*g**2 + 5/3*g**3 - 20*g. Factor r(y).
5*(y - 2)*(y + 1)*(y + 2)
Suppose q = -q - 4*o + 558, -4*q + 1126 = 3*o. Determine x, given that -132*x**2 + q - 58 - 114*x**2 - 15*x - 7*x**5 + 21*x**4 + 18*x**3 + 3*x**5 + x**5 = 0.
-3, -1, 1, 5
Let n be 1914/(-145) - -6 - (-16)/2. Let p(d) be the first derivative of -3/2*d**2 + 1 + 1/6*d**6 + 1/2*d**4 + 0*d - n*d**5 + 4/3*d**3. Factor p(z).
z*(z - 3)*(z - 1)**2*(z + 1)
Let r = 331/2145 - 3/143. Let n = -9945 - -9947. Factor 0 + 0*w**n - r*w + 2/15*w**3.
2*w*(w - 1)*(w + 1)/15
Factor -428*t**3 - 450*t**4 - 46*t**3 + 5*t**5 + 0*t**5 + 19*t**3.
5*t**3*(t - 91)*(t + 1)
Let q(o) = -180*o + 922. Let u be q(5). Let n(y) be the first derivative of -245/4*y**4 + 14*y**5 + 0*y - u - 5/6*y**6 + 0*y**2 + 0*y**3. Solve n(g) = 0.
0, 7
Let m = -2948 - -2950. Let s(g) be the second derivative of -9/50*g**5 + 16/5*g**m + 0 + 21*g + 44/15*g**3 + 4/5*g**4. Suppose s(x) = 0. What is x?
-2/3, 4
Let f(q) be the second derivative of -3*q**4/16 - 5*q**3/4 + 171*q**2/8 - 1314*q + 2. What is k in f(k) = 0?
-19/3, 3
Let u be (-66)/40*(-2016)/756. Factor -u*w - 24/5 + 4/5*w**2 + 2/5*w**3.
2*(w - 3)*(w + 1)*(w + 4)/5
Factor -163/5*y + 1/5*y**2 - 164/5.
(y - 164)*(y + 1)/5
Let a = 954 + -958. Let p = a - -33/8. Factor 1/4*i + 3/8*i**2 + 0 + p*i**3.
i*(i + 1)*(i + 2)/8
Let u(l) be the second derivative of 3*l**5/140 - l**4/2 - 6*l + 240. Factor u(t).
3*t**2*(t - 14)/7
Determine b, given that 1599/4*b**2 + 3/4*b**3 + 1590*b + 1587 = 0.
-529, -2
Let d = 247 + -244. Factor 0*w + 0*w + 6*w**d + 15797*w**4 - 15794*w**4 - 3*w**5.
-3*w**3*(w - 2)*(w + 1)
Find v, given that 624*v + 10816/5 + 1/5*v**3 + 108/5*v**2 = 0.
-52, -4
Let o(t) be the second derivative of -t**7/315 + 2*t**6/225 + 7*t**5/150 - 2*t**4/9 + 4*t**3/15 - 225*t - 3. Let o(c) = 0. What is c?
-3, 0, 1, 2
Let v(b) = -4*b - 6. Let r be v(-3). Suppose 6 = r*p - 3*p. Solve 0*n + 4*n**p + 3*n - 3*n = 0 for n.
0
Suppose 5*u = -2*q - 8, -8 + 0 = -4*q - 4*u. Suppose 18*f = 13*f, 3*b - q = -2*f. Factor 2/7*n**b + 0 + 0*n.
2*n**2/7
Suppose -4*a + 31 = u, 4*a - 14 = 2. Suppose 8*p - 9 = u. Factor -53*c**3 + 20*c**2 + 15*c + p - 3 - 10*c**4 + 48*c**3.
-5*c*(c + 1)**2*(2*c - 3)
Suppose 89*t - 15/2*t**2 - 440/3 - 1/6*t**3 = 0. What is t?
-55, 2, 8
Let a = 131/59 + -9257/3186. Let k = -1/54 - a. Solve -1/3*u**2 + k*u + 0 = 0 for u.
0, 2
Let k(p) be the second derivative of 3/40*p**6 + 79/80*p**5 + 13*p + 75/16*p**4 + 63/8*p**3 - 27/4*p**2 + 0. Factor k(j).
(j + 3)**3*(9*j - 2)/4
Solve 1252/5*q**4 - 29096/5*q**2 + 13868/5*q**3 + 2290*q + 26/5*q**5 + 500 