, -1
Let y(p) be the third derivative of -p**7/105 - 11*p**6/20 + 143*p**5/30 - 61*p**4/4 + 74*p**3/3 + 399*p**2. Find k, given that y(k) = 0.
-37, 1, 2
Let c = -513429/1078502 + 1/6497. Let f = 2/83 - c. Suppose 0 - 1/4*a**2 + 1/4*a**3 - f*a = 0. Calculate a.
-1, 0, 2
Factor -183/8 + 9/8*s**2 + 273/4*s.
3*(s + 61)*(3*s - 1)/8
Let y = -11283 - -22571/2. Factor -y*o**3 - 5/2*o**2 + 5/2*o + 5/2.
-5*(o - 1)*(o + 1)**2/2
Factor 55*c - 15*c**3 - 9 + 5*c**4 - 24 - 15*c**2 + 3.
5*(c - 3)*(c - 1)**2*(c + 2)
Suppose -29 = -v + z, 2*v - 5*v + 92 = -4*z. Let j be v/180 - (0 + (-28)/15). Let -3/4*y**j + 0 - 1/2*y + 3/4*y**4 + 1/4*y**3 + 1/4*y**5 = 0. Calculate y.
-2, -1, 0, 1
Let q(d) be the first derivative of -d**7/4620 + d**5/220 - d**4/66 - 7*d**3/3 + 7. Let k(l) be the third derivative of q(l). Factor k(t).
-2*(t - 1)**2*(t + 2)/11
Let u(c) be the first derivative of 3/2*c**3 - 7 + 1/4*c**4 + 4*c + 27/8*c**2. Let l(v) be the first derivative of u(v). Find o, given that l(o) = 0.
-3/2
Let w(r) be the first derivative of r**5/60 + r**4/18 + r**3/18 + 5*r + 2. Let j(g) be the first derivative of w(g). Factor j(h).
h*(h + 1)**2/3
Let l(p) be the first derivative of -p**7/294 + p**6/120 - p**5/210 - 9*p**2 + 5. Let y(i) be the second derivative of l(i). Factor y(o).
-o**2*(o - 1)*(5*o - 2)/7
Let k(c) = 10*c**3 - 10*c**2 - 6. Let j(a) = -11*a**2 - 6*a**2 - 7*a**2 + 15*a**2 - 5 + 9*a**3. Let q(f) = 6*j(f) - 5*k(f). Factor q(v).
4*v**2*(v - 1)
Let c = -141 + 145. Let z be (2 + (1 - c))/((-1)/2). Factor 0*x - 1/3*x**z + 0 - 1/3*x**4 + 2/3*x**3.
-x**2*(x - 1)**2/3
Let i(l) = 2 - 7*l + l**3 - 4*l**2 + 14*l - 12*l. Let y be i(5). Factor 4*v - 6 - 2/3*v**y.
-2*(v - 3)**2/3
Factor 0*s**2 + 64/5*s - 4/5*s**3 + 0.
-4*s*(s - 4)*(s + 4)/5
Let p(i) be the second derivative of i**6/165 - i**5/110 - 3*i**4/22 + 3*i**3/11 + 426*i. Factor p(j).
2*j*(j - 3)*(j - 1)*(j + 3)/11
Let m(z) be the third derivative of z**7/1260 - z**6/360 - z**5/30 - z**4/3 + 15*z**2. Let i(o) be the second derivative of m(o). Factor i(b).
2*(b - 2)*(b + 1)
Let q(f) be the first derivative of 5/4*f**4 + 0*f**2 + 0*f + 13 - 5*f**3. Find a, given that q(a) = 0.
0, 3
Suppose -p - 8 = -9. Let s(j) = 7*j + j**2 - j - j**4 - 5*j + j**3. Let x(g) = -12*g**4 + 12*g**3 + 10*g**2 + 10*g. Let w(u) = p*x(u) - 10*s(u). Factor w(z).
-2*z**3*(z - 1)
Factor 13*m - 3*m + 4*m**3 - 9*m**3 + 2*m - 8*m**2 + m**4.
m*(m - 6)*(m - 1)*(m + 2)
Let f(u) be the first derivative of -5*u**3/3 + 20*u + 95. Factor f(t).
-5*(t - 2)*(t + 2)
Suppose 18 = -6*k + 12*k. Let 6*f**3 + 1 - f**4 - f**3 - 17*f**2 - 7 + 2*f**k + 17*f = 0. Calculate f.
1, 2, 3
Let i(m) be the first derivative of -5/2*m**2 + 14 - 2*m**5 - 25/4*m**4 - 20/3*m**3 + 0*m. Factor i(d).
-5*d*(d + 1)**2*(2*d + 1)
Let m = -30 - -24. Let p be m/9 + (-280)/(-150). Determine l so that -3/5*l**2 + p*l - 6/5*l**3 + 0 + 3/5*l**4 = 0.
-1, 0, 1, 2
Factor 0*k**3 - k**3 - k - 2*k**2 + k.
-k**2*(k + 2)
Let h(q) be the third derivative of q**8/336 - 2*q**7/35 + 7*q**6/30 - q**5/10 - 29*q**4/24 + 3*q**3 - 7*q**2 + 20. Solve h(s) = 0.
-1, 1, 2, 9
What is b in -35*b**3 - 45*b**4 - 326*b + 1086*b + 184*b**2 + 3*b**5 + 161*b**2 - 8*b**5 + 420 = 0?
-7, -2, -1, 3
Let j(o) be the first derivative of -o**6/20 - 3*o**5/10 - o**4/2 - 2*o + 12. Let f(d) be the first derivative of j(d). Factor f(c).
-3*c**2*(c + 2)**2/2
Suppose 0 = 4*d - 5*a + 1 - 8, -3*d - a - 9 = 0. Let j = d - -11. Suppose -8*l**2 + j*l**4 + 3*l**3 - 6*l - l**2 + 7*l**5 - 4*l**5 + 0*l**2 = 0. What is l?
-2, -1, 0, 1
Let g(s) = 42*s - 292. Let o be g(7). Find h such that 19/4*h**3 + 17/4*h**4 - 7/2*h + o - 5/4*h**5 - 25/4*h**2 = 0.
-1, 2/5, 1, 4
Let j = 10 - 8. Suppose 2*a + h = j, -5*a + 0*h + 31 = -4*h. Factor c**a + 11*c**4 - 8*c**4 + 2*c**3.
3*c**3*(c + 1)
Let r(x) be the first derivative of -x**6/24 - x**5/4 - 9*x**2/2 + 20. Let l(m) be the second derivative of r(m). Determine s so that l(s) = 0.
-3, 0
Let t(k) be the second derivative of k**7/840 - k**6/240 + k**4/6 - 18*k. Let m(x) be the third derivative of t(x). Factor m(c).
3*c*(c - 1)
Find o such that -14*o**2 - 64*o - 9787*o**3 + 9786*o**3 - 2*o**2 = 0.
-8, 0
Find d such that 3*d**4 + 10*d + 2*d**4 - 10*d**3 - 274*d**2 + 269*d**2 = 0.
-1, 0, 1, 2
Suppose 31*f - 136 = -43. Factor 0 + 2/5*r**f + 2/5*r**2 - 4/5*r.
2*r*(r - 1)*(r + 2)/5
Let r(x) be the second derivative of -x**7/42 - 3*x**6/10 - 7*x**5/10 - 175*x + 1. Factor r(z).
-z**3*(z + 2)*(z + 7)
Suppose -3*m + 2*x - 5*x + 348 = 0, -5*x + 112 = m. Suppose m*v + 8 = 121*v. Suppose 12/7*c**v - 3/7*c**3 - 15/7*c + 6/7 = 0. What is c?
1, 2
Solve 146*r + 3*r**2 - 632*r + 19174 + 509 = 0.
81
Let j = -44 + 56. Suppose 6*i + 24 = j*i. Find l such that 2/7*l**3 + 0 + 2/7*l**i - 2/7*l**2 - 2/7*l = 0.
-1, 0, 1
Determine l so that -729 - 26*l + 21*l - l**2 - 49*l = 0.
-27
Let w be 40/(-140) + (-836)/(-770). Factor 48/5 + 32/5*q - 4/5*q**2 - w*q**3.
-4*(q - 3)*(q + 2)**2/5
Let v(p) = 2*p**2 + p + 3. Let a be v(-1). Suppose 3*z = 3*s + 21, a*z + 2*s + 2 = -0*z. Factor 4/5 - 6/5*w - 2*w**z.
-2*(w + 1)*(5*w - 2)/5
Find a such that 58*a**3 - 5*a**5 + 142*a**3 + 180*a - 336*a**2 + 9*a**5 - 23*a**4 - 25*a**4 = 0.
0, 1, 3, 5
Let a(w) = w**3 + 125*w**2 + 3838*w - 4004. Let q(r) = -r**3 - 125*r**2 - 3837*r + 4011. Let v(u) = 6*a(u) + 5*q(u). Find c such that v(c) = 0.
-63, 1
Let w = 81 - 66. Determine v, given that 100*v**3 - 51*v**3 + w*v**2 - 52*v**3 = 0.
0, 5
Factor -10*c**4 - 2*c**2 - 2*c**2 + 17*c**4 + 6*c**3 - 9*c**4.
-2*c**2*(c - 2)*(c - 1)
Let x(g) be the second derivative of 0*g**2 - 24*g + 1/3*g**3 - 1/21*g**7 - 1 - 2/15*g**6 + 0*g**5 + 1/3*g**4. Factor x(j).
-2*j*(j - 1)*(j + 1)**3
Suppose 16 = 7*c + 2. Suppose -14*k - 5*k**c + 13*k**3 + 12*k - 2*k**3 - 4*k**4 = 0. What is k?
-1/4, 0, 1, 2
Let w = -449 - -451. Let c(i) be the first derivative of 4*i**2 + 12*i - 4/3*i**3 - w. Suppose c(t) = 0. What is t?
-1, 3
Let -9/5*b + 24/5*b**2 + 0 - 3*b**3 = 0. What is b?
0, 3/5, 1
Let j(i) = 3*i**3 - i**2 + 4*i + 18. Let y(c) = -7*c**3 + 3*c**2 - 9*c - 36. Let w(n) = -9*j(n) - 4*y(n). Let s(t) be the first derivative of w(t). Factor s(p).
3*p*(p - 2)
Let p(y) = -6*y**2 + 13*y + 5. Let a(j) be the first derivative of j**3 - 7*j**2/2 - 2*j + 2. Let q(b) = -5*a(b) - 2*p(b). Factor q(t).
-3*t*(t - 3)
Factor -522 + 12*v**2 - 4*v**2 + 746 - 4*v**2 - 228*v.
4*(v - 56)*(v - 1)
Let s(i) = -8*i - 327. Let c be s(-41). Determine x, given that 1/2*x + c - 1/2*x**2 = 0.
-1, 2
Let n(m) = -80*m**3 - 525*m**2 + 15*m. Let p(s) = 21*s**3 + 131*s**2 - 4*s. Let k(f) = -4*n(f) - 15*p(f). Factor k(h).
5*h**2*(h + 27)
Let l(p) be the second derivative of 17*p + 1 - 2/15*p**3 - 1/15*p**2 - 1/10*p**4. Factor l(q).
-2*(3*q + 1)**2/15
Factor -75*j**3 + 10*j**2 + 39*j**3 + 41*j**3.
5*j**2*(j + 2)
Let s(p) be the first derivative of -p**6/72 - 5*p**5/24 - 5*p**4/4 + 5*p**3 + 44. Let v(m) be the third derivative of s(m). Determine i, given that v(i) = 0.
-3, -2
Let 4*l**4 + 8*l - 22/3*l**3 - 2/3*l**5 - 16/3 + 4/3*l**2 = 0. What is l?
-1, 1, 2
Let b(m) be the first derivative of -1/330*m**5 + 0*m**3 + 3/2*m**2 + 1/132*m**4 + 4 + 0*m. Let j(t) be the second derivative of b(t). Let j(k) = 0. What is k?
0, 1
Let n(o) = 73*o**5 + 91*o**4 + 10*o**3 - 16*o + 8. Let r(j) = -24*j**5 - 30*j**4 - 3*j**3 + 6*j - 3. Let m(u) = 3*n(u) + 8*r(u). Factor m(a).
3*a**3*(a + 1)*(9*a + 2)
Factor p**3 - p**3 + 4*p**3 + 0*p**3.
4*p**3
Let c(x) = 7*x**4 - 56*x**3 + 955*x**2 - 6. Let a(j) = j**4 + j**3 - j**2 - 1. Let p(w) = 6*a(w) - c(w). Factor p(y).
-y**2*(y - 31)**2
Let v(n) = -n**2 + n - 1. Let f(y) = 30*y - 2. Let o(i) = f(i) - 2*v(i). Find g, given that o(g) = 0.
-14, 0
Let j(d) be the first derivative of -d**5/20 + d**4/4 - 13*d**2/2 + 4. Let c(u) be the second derivative of j(u). Solve c(y) = 0.
0, 2
Let t be -3 - (26/(-3) - 10/(-15)). Let a be t - ((-425)/(-65) + -2). Factor 0 + 2/13*n**3 + 0*n + a*n**2.
2*n**2*(n + 3)/13
Suppose -11*o - 25 + 78 = 31. Suppose -o*q - 3/2*q**2 + 0 + 1/2*q**3 = 0. What is q?
-1, 0, 4
Let m be 2 - 43/25 - (-28)/(-140). Let y(o) be the first derivative of -2 + 0*o - 2/15*o**3 + 0*o**4 + m*o**5 + 0*o**2. Determine v so that y(v) = 0.
-1, 0, 1
Let z(c) = 13*c**2 + 9*c - 4. Let p(v) = 4*v**2 + 77 - 78 - v**2 + 2*v. Let x(q) = 9*p(q) - 2*z(q). Fa