
i*(i - 1)**2*(i + 1)*(4*i - 1)
Factor 2*u - 7/2*u**2 - u**3 + 0.
-u*(u + 4)*(2*u - 1)/2
Let q(f) be the first derivative of -4*f**3/3 + 164*f**2 - 6724*f + 240. Determine i, given that q(i) = 0.
41
Determine t so that -2/9*t**5 + 2/9*t**4 + 32/9*t - 56/9*t**2 + 8/3*t**3 + 0 = 0.
-4, 0, 1, 2
Let z(l) be the first derivative of 1/60*l**6 + 0*l**3 + 0*l - 3/2*l**2 - 1/12*l**4 + 0*l**5 - 3. Let m(f) be the second derivative of z(f). Factor m(b).
2*b*(b - 1)*(b + 1)
Let f(r) be the third derivative of -r**8/840 - r**7/105 - r**6/30 - r**5/15 - r**4/12 - r**3/15 + 627*r**2. Factor f(t).
-2*(t + 1)**5/5
Find m such that 3*m**4 + 16*m**3 + 102*m + 3425*m**2 - 3380*m**2 - 70*m**3 = 0.
-1, 0, 2, 17
Let n be (-11)/91 + 3/(-2)*30/(-105). Suppose 0 + 0*t - 2/13*t**4 - n*t**2 + 6/13*t**3 = 0. Calculate t.
0, 1, 2
Let -11*s - 5*s**4 - 510*s**2 + 10*s**3 + s + 515*s**2 = 0. What is s?
-1, 0, 1, 2
Suppose 0 = q + 3, 1 = g - q - 7. Let k be 12 - 1*(0 + -1). Factor -k*i**3 - 6*i**3 + g*i**3 + i**2 - 5*i**2.
-2*i**2*(7*i + 2)
Let w(t) be the first derivative of 3*t**4/28 + 10*t**3/7 + 48*t**2/7 + 96*t/7 - 42. Let w(b) = 0. What is b?
-4, -2
Let d(l) = -l**2 + l. Let o(q) = -5 + q**2 + q + 1 - 7*q + 3*q**2. Let x(p) = 12*d(p) + 4*o(p). Determine n so that x(n) = 0.
-1, 4
Let q(t) be the second derivative of t**5/5 - 14*t**4/3 - 208*t. Factor q(w).
4*w**2*(w - 14)
Let s(q) be the first derivative of 2/3*q**3 - 1 + 10*q - 1/24*q**4 - 4*q**2. Let h(l) be the first derivative of s(l). Determine y, given that h(y) = 0.
4
Let n = 12911/7 - 1829. Factor 20/7*p**3 + n*p + 2/7*p**4 + 72/7*p**2 + 54/7.
2*(p + 1)*(p + 3)**3/7
Let r(d) = -d**2 - 10*d + 4. Let g be r(0). Solve 2/3*v**g + 2/3*v**2 + v**3 + 1/6*v**5 + 0 + 1/6*v = 0.
-1, 0
Let w(b) be the third derivative of -b**8/2800 + b**6/600 + 8*b**3/3 + 17*b**2. Let d(r) be the first derivative of w(r). Factor d(i).
-3*i**2*(i - 1)*(i + 1)/5
Let u(g) be the third derivative of g**8/196 - 4*g**7/21 + 51*g**6/35 + 1172*g**5/105 + 377*g**4/14 + 676*g**3/21 + 45*g**2. Suppose u(b) = 0. Calculate b.
-1, -2/3, 13
Let h(o) be the second derivative of 3*o**6/40 - 7*o**5/20 - 3*o**4/4 - 17*o**2/2 - 11*o. Let u(n) be the first derivative of h(n). Factor u(d).
3*d*(d - 3)*(3*d + 2)
Let h(p) be the third derivative of p**6/24 + p**5 - 65*p**4/24 + 74*p**2. Suppose h(g) = 0. Calculate g.
-13, 0, 1
Let i(n) be the first derivative of n**4/6 - 16*n**3/9 + 5*n**2 + 68. Let i(f) = 0. Calculate f.
0, 3, 5
Suppose -12 = -7*a + 65. Let u = -8 + a. Factor 0*k - k + 5*k**3 + 0*k**u - 4*k**3.
k*(k - 1)*(k + 1)
Let a = 3861 - 3858. Factor 0*n + 1/2*n**a + 0 + n**2.
n**2*(n + 2)/2
Let w(u) = 4*u**2 + u - 3. Suppose 5*m - 3*i - i + 40 = 0, m + 4*i - 16 = 0. Let b(c) = -5*c**2 - 2*c + 4. Let h(j) = m*w(j) - 3*b(j). Solve h(t) = 0.
0, 2
Let m(n) be the third derivative of -n**8/53760 + n**7/4480 + n**6/480 + n**5/20 - 8*n**2. Let d(u) be the third derivative of m(u). Factor d(g).
-3*(g - 4)*(g + 1)/8
Let w(f) be the first derivative of f**4/66 + f**3/33 - 4*f - 21. Let o(t) be the first derivative of w(t). Factor o(r).
2*r*(r + 1)/11
Suppose 22 = 5*k - 2*a, 2*k + 239*a = 240*a + 10. Factor -1/6*n**k - 25/6 - 5/3*n.
-(n + 5)**2/6
Suppose -398 = -m - 0*m - 4*g, g = m - 423. Let p = m + -2082/5. Suppose 8/5 + 2/5*y**2 + p*y = 0. What is y?
-2
Let u(g) = 25*g**2 - 360*g. Let j(c) = -c**2 + 0*c - 2*c**2 + 5*c**2 - 30*c. Let x(s) = -35*j(s) + 3*u(s). Factor x(v).
5*v*(v - 6)
Let o be -2 + 8*(-5)/(-10). Factor 14*b - 4*b**3 - b**3 - 18 - o*b**4 - 3*b**3 + 4*b**2 + 10*b.
-2*(b - 1)**2*(b + 3)**2
Let o(t) be the first derivative of 16/25*t**5 + 16/15*t**3 - 2/5*t**2 - 2/15*t**6 - 8 - 6/5*t**4 + 0*t. Factor o(j).
-4*j*(j - 1)**4/5
Suppose -5*g = 5*a, g + 15 = 5*a - 3*a. Let -z**5 + 4*z**3 + 16*z**2 - 16*z**4 - 206*z + 206*z - 3*z**a = 0. What is z?
-4, -1, 0, 1
Factor 480 + 160*g - 45*g**3 - 5*g**4 - 81*g**3 - 90*g**2 - 54*g**3 + 135*g**3.
-5*(g - 2)*(g + 3)*(g + 4)**2
Suppose 9 = k + 4. Factor 15*l - 7 + 30*l**2 + 6*l**5 + 15*l**4 + 10 + 30*l**3 - 3*l**k.
3*(l + 1)**5
Let v(k) be the first derivative of -2/3*k**2 - 2/27*k**3 + 14/9*k + 57. Let v(h) = 0. Calculate h.
-7, 1
Let o(p) = -28*p + 5. Let y be o(0). Let u(b) be the second derivative of 5*b + 0 - 1/140*b**y + 0*b**3 + 0*b**2 + 1/42*b**4. Factor u(d).
-d**2*(d - 2)/7
Let i be 4 - (-790)/(-40) - -16. Factor i*l**4 - 1/4*l**3 + 1/4*l + 1/2 - 3/4*l**2.
(l - 2)*(l - 1)*(l + 1)**2/4
Let i(o) be the second derivative of 5/27*o**3 - 21*o + 0 - 1/15*o**5 - 1/135*o**6 - 1/27*o**4 + 1/3*o**2 + 1/189*o**7. Factor i(l).
2*(l - 3)*(l - 1)*(l + 1)**3/9
Suppose 33*b = 24*b. Let v(r) be the second derivative of 1/4*r**2 + 3/8*r**3 - 4*r + 7/48*r**4 + b. Solve v(s) = 0.
-1, -2/7
Suppose 4*w = -1 + 17. Factor 75*x**2 - 70*x**2 + 11*x + w*x.
5*x*(x + 3)
Let -356/3*t**3 + 812/3*t**2 + 20/3*t**4 + 352/3*t - 832/3 + 4/3*t**5 = 0. Calculate t.
-13, -1, 1, 4
Let l be 6/(-4)*(-4)/3. Let c = 1 + l. Factor -i**3 - 3*i - 2*i**4 - i + i**c + 4*i**3 + 2.
-2*(i - 1)**3*(i + 1)
Let o(m) = 20*m**2 + 12*m - 18. Let t(k) = -k**3 + k - 1. Let q(s) = o(s) + 2*t(s). Let v(c) be the first derivative of q(c). Factor v(i).
-2*(i - 7)*(3*i + 1)
Let y(m) = m**2 - 8*m + 21. Let r be y(6). Factor 20*b**2 + 3*b**3 + r*b - 32*b**2 + 0*b**3.
3*b*(b - 3)*(b - 1)
Let k(c) be the third derivative of -1/24*c**4 + 0 - 14*c**2 + 1/20*c**5 - 1/3*c**3 + 0*c. Factor k(x).
(x - 1)*(3*x + 2)
Let x = 47 - 45. Factor -9*i + 88*i**2 + 0 - 91*i**x + i**3 - 5.
(i - 5)*(i + 1)**2
Let s = 25640 - 76918/3. Factor -14/3 + 4*n + s*n**2.
2*(n - 1)*(n + 7)/3
Let l be (-1)/8*(-11 + -5 + 15). Let z(a) be the second derivative of -1/20*a**6 + 0*a**3 + 1/28*a**7 + l*a**4 + 7*a + 0*a**2 - 3/40*a**5 + 0. Factor z(f).
3*f**2*(f - 1)**2*(f + 1)/2
Let d(h) = -3*h**5 + 2*h**4 + 15*h**3 - 14*h**2 - 4*h. Let x(o) = o**4 - o**2 + o. Let l(n) = -d(n) - 4*x(n). Factor l(r).
3*r**2*(r - 3)*(r - 1)*(r + 2)
Let s = -358 + 362. Let z(p) be the first derivative of -1/6*p**4 + s + 4/9*p**3 + 0*p - 1/3*p**2. Factor z(a).
-2*a*(a - 1)**2/3
Let p = 3/299 - -269/2990. Let 0*w + 0 + 1/10*w**5 + p*w**4 - 1/10*w**3 - 1/10*w**2 = 0. Calculate w.
-1, 0, 1
Suppose -22*n + n**2 - 48 - 2*n**2 - 73 = 0. What is n?
-11
Let m(g) be the second derivative of -g**7/336 + g**6/15 - 97*g**5/160 + 139*g**4/48 - 95*g**3/12 + 25*g**2/2 - 81*g. Factor m(n).
-(n - 5)**2*(n - 2)**3/8
Let b(o) be the third derivative of 0*o - 21*o**2 + 1/390*o**5 + 0 + 0*o**3 - 1/52*o**4. Factor b(d).
2*d*(d - 3)/13
Suppose 4*w + 2*g - 350 = -138, -12 = 3*g. Let 33*h + w*h - 88*h**5 + 328*h**2 - 188*h**3 + 32 + 64*h + 88*h - 324*h**4 = 0. What is h?
-2, -1/2, -2/11, 1
Let j(a) be the first derivative of -32*a**6/3 + 608*a**5/5 - 409*a**4 + 640*a**3 - 522*a**2 + 216*a + 492. Determine t so that j(t) = 0.
3/4, 1, 6
Let h(a) be the first derivative of 2*a**4/21 + a**3/21 + 13*a - 8. Let f(r) be the first derivative of h(r). Solve f(p) = 0 for p.
-1/4, 0
Let r = -214597 - -2358600/11. Let j = 179 + r. Factor 6/11*m**2 + j + 6/11*m + 2/11*m**3.
2*(m + 1)**3/11
Let m(i) = 7*i**2 - 5*i - 48. Let a be m(3). Factor -2/7*c**2 + a + 6/7*c.
-2*c*(c - 3)/7
What is y in 67/2*y + 1/3*y**2 - 101/6 = 0?
-101, 1/2
Factor 2/9*x**3 - 10/3 + 62/9*x - 34/9*x**2.
2*(x - 15)*(x - 1)**2/9
Let u(k) be the first derivative of 3*k**5/100 + k**4/20 - k**3/10 - 3*k**2/10 - 2*k + 5. Let x(w) be the first derivative of u(w). Factor x(z).
3*(z - 1)*(z + 1)**2/5
Let r(h) = -3*h - 105*h**2 + 4*h + 104*h**2 + 1. Let q(n) = 2*n**2 + 3*n - 12. Let b(g) = -q(g) - 3*r(g). Factor b(z).
(z - 3)**2
Let q(h) = -3*h**3 + 2*h**2 + h - 1. Let f be q(-2). Let -28*x**2 - 1 - 5 - 2*x**2 + 0*x**3 - 7*x**3 - f*x = 0. What is x?
-3, -1, -2/7
Let z(f) = -2*f - 49. Let d(r) = 3*r + 50. Let h(t) = -5*d(t) - 4*z(t). Let k be h(-8). Factor 0 + 0*n - 1/4*n**k.
-n**2/4
Let h be (12/40)/(-4*96/(-20)). Let i = h + 253/192. Determine g so that 0*g + 1/3*g**2 - i = 0.
-2, 2
Let l(w) be the first derivative of w**5 - 5*w**4 - 10*w**3/3 + 30*w**2 + 45*w + 292. Factor l(r).
5*(r - 3)**2*(r + 1)**2
Let x = 9712 + -844916/87. Let a = 10/29 + x. Factor a*t**3 + 0 + 2*t + 8/3*t**2.
2*t*(t + 1)*(t + 3)/3
Suppose 2*g - 3*g = -6*g. Factor g*j + 3*j**2 - 12*j**2 + 12*j + 6 + 3*j.
-3*(j - 2)*(3*j + 1)
Fac