)**2*(k + 1)**2/6
Let m(s) be the third derivative of s**9/15120 - s**7/1260 - 13*s**5/60 - 7*s**2. Let f(q) be the third derivative of m(q). Solve f(v) = 0 for v.
-1, 0, 1
Let i(h) = -2*h**2 - 13*h - 9. Let g be i(-5). Determine d, given that 20*d**2 - 3*d**3 - g*d**3 + 4*d**3 = 0.
0, 4
Let n = 8733/7 + -1247. Factor 1/7*t**4 - 8/7 - 5/7*t**3 + 6/7*t**2 + n*t.
(t - 2)**3*(t + 1)/7
Let h(f) be the first derivative of f**7/210 - f**6/30 - f**5/30 + f**4/2 - 23*f**3/3 - 8. Let w(i) be the third derivative of h(i). Factor w(a).
4*(a - 3)*(a - 1)*(a + 1)
Let n(c) = c**3 - 12*c**2 + 9*c. Let o be n(8). Let a = o - -2394/13. Factor 180/13*m**3 + 540/13*m**2 + a*m**5 + 810/13*m + 30/13*m**4 + 486/13.
2*(m + 3)**5/13
Suppose 105*c**5 + 213605 - 213605 - 6*c**4 = 0. Calculate c.
0, 2/35
Factor 94*o + 90*o**2 - 4 + 48 - 12 + 26*o**3 - 2*o**4.
-2*(o - 16)*(o + 1)**3
Let w(f) be the first derivative of -f**5/10 - f**4 - 23*f**3/6 - 7*f**2 - 6*f - 425. Find y such that w(y) = 0.
-3, -2, -1
Let f(y) = -5*y**2 + y. Let t be f(1). Let d be (-2)/t + (-12)/(-8). Factor 9 + 41 + 2*o**2 + 75 + 3*o**d + 50*o.
5*(o + 5)**2
Let s(c) be the second derivative of 2*c**7/21 + 52*c**6/15 + 44*c**5/5 - 104*c**4/3 - 128*c**3 + 10*c + 3. Let s(r) = 0. Calculate r.
-24, -2, 0, 2
Let z = 31 - 36. Let b be ((-6)/z)/((-2)/(-5)). Factor -1/2*r**b + 1/2*r + 1/2 - 1/2*r**2.
-(r - 1)*(r + 1)**2/2
Suppose -35 = 7*b - 3*b + z, 0 = b + 3*z + 17. Let k(o) = o**2 + 9*o + 11. Let s be k(b). Factor -15/4*v - 3/4*v**2 + 3/2*v**s - 3/2.
3*(v - 2)*(v + 1)*(2*v + 1)/4
Let r(d) be the third derivative of d**8/3360 + d**7/252 + 7*d**6/360 + d**5/20 - 5*d**4/24 + 4*d**2. Let u(o) be the second derivative of r(o). Factor u(k).
2*(k + 1)**2*(k + 3)
Let q(d) be the second derivative of -d**5/10 + 5*d**4/3 + 23*d**3/3 + 12*d**2 + 2*d - 42. Find a such that q(a) = 0.
-1, 12
Suppose w = 2*w + 1. Let y = 3 + w. Let 49 + 6*r**2 + y*r**4 - 49 + 2*r + 6*r**3 = 0. What is r?
-1, 0
Let n(c) be the third derivative of c**8/84 + 2*c**7/105 - c**6/30 - c**5/15 - 5*c**2 + 6. Solve n(y) = 0 for y.
-1, 0, 1
Let k(f) = -f**3 + 2*f + 1. Let i be k(-3). Suppose -2*n - 62 + 102 = 0. Solve -16*o**5 + 21*o**5 + 33*o**3 + o - 3*o + 6*o + n*o**2 + i*o**4 = 0.
-2, -1, -2/5, 0
Let s(m) be the third derivative of 1/60*m**5 - 1/210*m**7 + 1/336*m**8 + 1/12*m**4 - 22*m**2 - 1/40*m**6 + 0*m**3 + 0 + 0*m. Factor s(q).
q*(q - 2)*(q - 1)*(q + 1)**2
Factor 20*q**3 - 8*q - 12*q**2 + 10 - 7*q - 5*q**5 + 2*q**2.
-5*(q - 1)**3*(q + 1)*(q + 2)
Let j = 1046 + -13596/13. Factor -2/13*a**4 + 0 - j*a**3 + 0*a**2 + 0*a.
-2*a**3*(a + 1)/13
Let a = -53383 + 53386. Find s such that -8/7 - 4/7*s**a + 6/7*s**2 + 8/7*s - 2/7*s**4 = 0.
-2, 1
Let i be (-3)/(90/75) + (-4)/2 - -5. Factor -9/2 - 3*d - i*d**2.
-(d + 3)**2/2
Let q be (-12)/63 + (-249)/(-21) + -11. Determine a, given that q*a**2 + 1/2*a - 1/6 = 0.
-1, 1/4
Let n(b) be the second derivative of b**4 - 8*b**2 - 1/5*b**5 - b + 0 + 0*b**3. Factor n(t).
-4*(t - 2)**2*(t + 1)
Let k(y) be the first derivative of 56/9*y**3 - 25/6*y**2 + y - 4/3*y**4 - 42. Factor k(w).
-(w - 3)*(4*w - 1)**2/3
Let x(j) be the first derivative of -5*j**2 + 5/4*j**4 - 5/3*j**3 + 0*j + 6. Solve x(q) = 0 for q.
-1, 0, 2
Let q = -397 - -397. Let s(i) be the first derivative of 0*i + 2/21*i**3 - 5/14*i**4 + q*i**2 - 1 + 8/35*i**5. Factor s(m).
2*m**2*(m - 1)*(4*m - 1)/7
Let y be (-3)/((-12)/8) + -2. Suppose y = 4*v - 2*m + m - 5, -v - m + 5 = 0. Factor -9/2*b + v*b**2 + 1.
(b - 2)*(4*b - 1)/2
Let x(q) be the first derivative of -12/5*q**5 + 13/2*q**4 + 31 - 8*q**3 + 1/3*q**6 + 0*q + 4*q**2. Factor x(c).
2*c*(c - 2)**2*(c - 1)**2
Find v such that -4/3*v - 4*v**2 - v**3 + 0 + 5/3*v**4 = 0.
-1, -2/5, 0, 2
Let a be (46 + -42)*(-1 + 0)*-1. Let q(b) be the third derivative of -2*b**2 + 0 + 0*b + 11/360*b**5 + 1/36*b**3 + 7/144*b**a + 1/144*b**6. Factor q(v).
(v + 1)**2*(5*v + 1)/6
Let n(t) = t**2 - 2*t + t - 8*t + 0*t**2 + 3. Let y be n(9). Suppose -4*g**3 + g**3 + 4*g**4 + 5*g**4 - 6*g**2 + 0*g**y = 0. What is g?
-2/3, 0, 1
Let o(r) be the first derivative of r**5/25 - 3*r**4/5 - 9*r**3/5 - 7*r**2/5 + 39. Factor o(t).
t*(t - 14)*(t + 1)**2/5
Let a(k) = 3*k**2 + 3*k + 4. Let o be a(-1). Determine y, given that 3*y**5 - 30*y**o + 20*y - 60*y**2 + 65*y**3 - y**5 + 3*y**5 = 0.
0, 1, 2
Let n(c) be the first derivative of -27/5*c - 1/5*c**3 + 9/5*c**2 - 12. Factor n(a).
-3*(a - 3)**2/5
Let l = -166 + 166. Let z(f) be the second derivative of 0*f**4 + 0*f**2 + 0*f**6 + l*f**3 + 0 - 1/10*f**5 + 1/21*f**7 + f. Solve z(j) = 0.
-1, 0, 1
Let b(o) = -o. Let s(c) = 3*c**3 + 3*c**2 - 12*c. Let n(r) = -6*b(r) - s(r). Let n(i) = 0. What is i?
-3, 0, 2
Let b(z) = -2*z**5 - 6*z**4 + z**3 + z. Let p(y) = -3*y**5 - 11*y**4 + 2*y**3 + y**2 + y. Let j = 89 - 92. Let k(f) = j*p(f) + 5*b(f). Solve k(h) = 0.
-1, 0, 1, 2
Let x be (60/(-80))/((-45)/12). Let h(a) be the third derivative of 0*a**3 - 2*a**2 + 0 + 0*a + 1/6*a**4 + 1/10*a**6 + 2/105*a**7 + x*a**5. Factor h(k).
4*k*(k + 1)**3
Let i(g) = -2*g**4 - 27*g**3 + 20*g**2 + 96*g - 141. Let x(j) = -20*j**4 - 296*j**3 + 220*j**2 + 1056*j - 1552. Let u(p) = 32*i(p) - 3*x(p). Factor u(o).
-4*(o - 3)**2*(o - 2)*(o + 2)
Let m(w) be the third derivative of 10/3*w**4 + 1/336*w**8 + 1/21*w**7 + 1/3*w**6 + 16*w**2 + 16/3*w**3 + 0*w + 0 + 4/3*w**5. Find v such that m(v) = 0.
-2
Suppose -59 = -11*w + 7. Let i(q) be the second derivative of -1/2*q**2 + 1/6*q**4 + 1/42*q**7 - q + 0 + 1/6*q**3 - 1/10*q**5 - 1/30*q**w. Factor i(k).
(k - 1)**3*(k + 1)**2
Suppose -3*a + 18 = 4*t, -5*a = -4*t + 5*t - 30. Factor -a*d + 4*d**3 + 9*d**2 + 3*d - d**3 - 9.
3*(d - 1)*(d + 1)*(d + 3)
Let w = -263 + 265. Let s(i) be the third derivative of -1/6*i**3 - 3*i**w - 1/240*i**5 + 1/24*i**4 + 0 + 0*i. Find q, given that s(q) = 0.
2
Let m be (-2)/5 - (-44)/10. Suppose -2*q + m*y = 2*y - 32, -29 = -2*q - y. Factor 333*r**2 - 333*r**2 + 12*r**5 + 3*r**3 + q*r**4.
3*r**3*(r + 1)*(4*r + 1)
Let m(k) be the second derivative of -3*k**5/20 - k**4 + 7*k**3/2 + 15*k**2 + 6*k - 1. Let m(t) = 0. Calculate t.
-5, -1, 2
Let b(q) = -q**2 + 1. Let y(i) = -16*i**2 + 32*i - 16. Suppose 2*n - 7 = 17. Let k(g) = n*b(g) - y(g). Let k(r) = 0. What is r?
1, 7
Let i(q) be the first derivative of q**4/6 - 4*q**3/3 - 5*q**2 - 21*q + 11. Let n(w) be the first derivative of i(w). Factor n(x).
2*(x - 5)*(x + 1)
Suppose -k + 8 = 5. Let b be (k/(-10))/(6/(-30)). Factor 9/4*p + 0*p**2 - 3/4*p**3 + b.
-3*(p - 2)*(p + 1)**2/4
Let j(u) = u**3 - u**2 + u - 1. Let m be j(1). Suppose 9*q + q = m. Determine k so that 9/4*k**2 + 3/2*k**3 + q + 3/4*k = 0.
-1, -1/2, 0
Suppose 2*x + 4/7 - 4/7*x**2 - 2*x**3 = 0. Calculate x.
-1, -2/7, 1
Let k(b) be the third derivative of -2/27*b**3 + 0*b + 1/60*b**6 + 0 + 11*b**2 + 1/12*b**4 - 7/135*b**5 - 2/945*b**7. Let k(q) = 0. What is q?
1/2, 1, 2
Let s(v) be the third derivative of v**8/756 + 2*v**7/189 + 7*v**6/270 + v**5/45 + 325*v**2. Factor s(t).
4*t**2*(t + 1)**2*(t + 3)/9
Let q = -376 + 379. Let d(z) be the second derivative of 0*z**3 + q*z + 0*z**2 + 0 + 1/6*z**4 + 1/3*z**6 + 9/20*z**5 + 1/14*z**7. Factor d(j).
j**2*(j + 1)*(j + 2)*(3*j + 1)
Let g(r) be the first derivative of r**4/20 + 23*r**3/15 + 59*r**2/5 + 96*r/5 + 854. Factor g(d).
(d + 1)*(d + 6)*(d + 16)/5
Let b = -2/261 + 176/261. Let z(q) be the second derivative of 2/3*q**4 + 0 - 6*q - b*q**3 - 1/4*q**5 + 0*q**2 + 1/30*q**6. Factor z(h).
h*(h - 2)**2*(h - 1)
Let s be (4/5)/((-42)/5925). Let i = 113 + s. Factor 16/7 - 8/7*r + i*r**2.
(r - 4)**2/7
Factor 652*l**2 + 88*l**2 - 42*l**3 + 46*l**3 - 34596 + 33852*l.
4*(l - 1)*(l + 93)**2
Let c(h) = -2*h + 18. Let p = 17 - 9. Let k be c(p). Factor 2/9*v**k + 4/9 - 2/3*v.
2*(v - 2)*(v - 1)/9
Let m(g) be the second derivative of 4*g + 18*g**2 + 0 + 20*g**3 + 25/3*g**4. Factor m(q).
4*(5*q + 3)**2
Let l = -49979/11 - -4545. Factor l*d + 8/11 + 10/11*d**2 + 2/11*d**3.
2*(d + 1)*(d + 2)**2/11
Let b(y) be the third derivative of y**7/175 + y**6/30 - 29*y**5/150 - 4*y**4/15 + 4*y**3/3 + 8*y**2 + 4. Solve b(c) = 0.
-5, -1, 2/3, 2
Solve -5/3*a**2 + 1/3*a - 1/3*a**3 + 5/3 = 0.
-5, -1, 1
Factor -25*z**2 - 5*z**5 - 10*z**4 + 20*z**4 + 10*z - 5*z**4 + 15*z**3.
-5*z*(z - 1)**3*(z + 2)
Determine o so that 0 + 12/5*o + 42/5*o**2 - 24/5*o**