2, 0, 2
Let b(n) be the third derivative of -n**7/2415 + n**6/345 - 2*n**5/345 - 179*n**2. Find f, given that b(f) = 0.
0, 2
Suppose 1/3 - 3/2*z**4 + 7/6*z**2 - 11/6*z**3 + 11/6*z = 0. What is z?
-1, -2/9, 1
Let n(y) be the third derivative of -y**5/240 + 5*y**4/96 - y**3/6 - 106*y**2. Factor n(r).
-(r - 4)*(r - 1)/4
Let x(g) be the second derivative of g**5/180 - 23*g**4/54 + 286*g**3/27 - 484*g**2/9 + 19*g - 2. Factor x(o).
(o - 22)**2*(o - 2)/9
Factor -39/7*v - 6*v**2 - 9/7*v**3 + 18/7.
-3*(v + 2)*(v + 3)*(3*v - 1)/7
Let t be (7089/60)/(-17) + 7. Let c(k) be the third derivative of t*k**6 - 1/14*k**7 - 2*k**2 + 0 + 0*k**3 + 1/4*k**5 + 0*k - 1/4*k**4. Factor c(b).
-3*b*(b - 1)*(b + 1)*(5*b - 2)
Factor 4 - 25/3*g - 1/3*g**3 + 14/3*g**2.
-(g - 12)*(g - 1)**2/3
Let i be -1*(-6 + (6 - 3)). Suppose -d + 3*b = -18, -i*d + 2*b = 4 - 23. Factor -3*g**2 + 4*g**3 + d*g**4 + 2*g**3 + 3*g - 9*g.
3*g*(g - 1)*(g + 1)*(g + 2)
Let n = 1378 - 1373. Let f(a) be the third derivative of -16/3*a**3 + 0 + 0*a - 1/30*a**n - 2*a**2 - 2/3*a**4. Factor f(l).
-2*(l + 4)**2
Let h(u) = -u + 24. Let m be h(11). Factor -15*x**2 + 13*x + 10*x - 25*x**3 - m*x.
-5*x*(x + 1)*(5*x - 2)
Solve 25 - 4*c**4 + 139*c**2 - 61 - 99*c**2 = 0 for c.
-3, -1, 1, 3
Suppose 3*o**5 - 7*o**3 - 3*o**3 - 10*o**3 - 7*o**3 = 0. Calculate o.
-3, 0, 3
Let o(s) be the second derivative of -s**7/2940 + s**6/420 - s**5/140 + s**4/84 - 3*s**3/2 + 9*s. Let a(v) be the second derivative of o(v). Factor a(i).
-2*(i - 1)**3/7
Let j be (-619)/471 - 56/(-42). Let p = j - -293/1099. Let 2/7*f + 4/7*f**2 - p*f**3 - 4/7 = 0. Calculate f.
-1, 1, 2
Factor o**3 + 12*o + 3773*o**2 - 3760*o**2 + 0*o**3.
o*(o + 1)*(o + 12)
Let m be (3 - 1)/6*42. Suppose -m = n - 4*h, -5*n + 28 = -n + 5*h. Factor 8/5 - 8/5*k + 2/5*k**n.
2*(k - 2)**2/5
Let u(a) be the second derivative of -a**6/15 + 29*a**5/6 - 392*a**4/3 + 4352*a**3/3 - 4096*a**2/3 + 2*a - 29. What is k in u(k) = 0?
1/3, 16
Let r(d) be the first derivative of d**7/84 + d**6/60 - d**5/40 - d**4/24 - 15*d - 11. Let c(v) be the first derivative of r(v). Factor c(t).
t**2*(t - 1)*(t + 1)**2/2
Let l(u) = 36*u**4 + 81*u**3 + 96*u**2 + 51*u + 21. Let o(j) = -7*j**4 - 16*j**3 - 19*j**2 - 10*j - 4. Let c(b) = 4*l(b) + 21*o(b). Factor c(d).
-3*d*(d + 1)**2*(d + 2)
Let a(z) be the first derivative of -z**5/60 - z**4/4 - 5*z**3/6 - 16*z**2 - 13. Let q(t) be the second derivative of a(t). Factor q(s).
-(s + 1)*(s + 5)
Let y be (-38)/8 + (3 - 6). Let i = -21/4 - y. Let i*x**2 + 3/2*x - 1 = 0. What is x?
-1, 2/5
Let u = -35 + 141/4. Let c be (6*1/60)/((-4)/(-10)). Determine h so that c*h**2 + 0 + u*h = 0.
-1, 0
Let y(j) = 9*j**2 - 3*j. Let m = -85 + 63. Let q(i) = i**2 + i. Let p(x) = m*q(x) + 2*y(x). Factor p(z).
-4*z*(z + 7)
Suppose 18 = -103*t + 224. Find b, given that 1/3*b**5 + 1/3*b**t + b**4 + 0*b + b**3 + 0 = 0.
-1, 0
Let h(f) be the second derivative of f**7/720 + f**6/432 - f**5/360 + 2*f**3/3 + 6*f. Let g(p) be the second derivative of h(p). Solve g(b) = 0 for b.
-1, 0, 2/7
Let y(z) be the first derivative of -7*z**4/24 + 29*z**3/6 - 4*z**2 - 28*z - 25. Let o(g) be the first derivative of y(g). Factor o(h).
-(h - 8)*(7*h - 2)/2
Factor 12/7*i + 0 + 2/7*i**3 + 2*i**2.
2*i*(i + 1)*(i + 6)/7
Let z be 10/(-15) - (-104)/39. Let 22/19*j**z + 26/19*j + 4/19 = 0. What is j?
-1, -2/11
Let q(u) be the second derivative of -u**7/1890 + u**6/270 - u**5/90 + u**4/6 - 5*u. Let k(w) be the third derivative of q(w). Factor k(i).
-4*(i - 1)**2/3
Let x be 124/(-32) - (-3)/(-24). Let p be x + 7 + (-25)/9. Solve 0*a**2 - 4/9*a**3 + p - 2/9*a**4 + 4/9*a = 0 for a.
-1, 1
Let u be (1 - 4) + (-1040)/(-208). Factor 2/7 + 1/7*g**u + 3/7*g.
(g + 1)*(g + 2)/7
Let o(q) be the first derivative of -1/2*q**2 - 3/4*q + 31 - 1/12*q**3. Factor o(l).
-(l + 1)*(l + 3)/4
Suppose 8*k - 20 = 12. Find w, given that -3*w**2 - 219*w**3 + k*w**2 + 220*w**3 - 2*w = 0.
-2, 0, 1
Let r(b) be the second derivative of 0*b**3 + 0*b**2 - 1/6*b**5 - 1/6*b**4 - 18*b + 0. Factor r(n).
-2*n**2*(5*n + 3)/3
Let t(k) = -k**3 - k**2 - 26*k - 17. Let r(m) = -3*m**3 - m**2 - 52*m - 33. Let l(j) = 3*r(j) - 7*t(j). Factor l(v).
-2*(v - 5)*(v + 1)*(v + 2)
Let j = -4/229 - -6898/1603. Solve 8/7*u + 58/7*u**2 - 8/7 - j*u**3 = 0 for u.
-2/5, 1/3, 2
Factor -2/13*g**4 + 12/13*g**3 - 48/13*g - 32/13 - 2/13*g**2.
-2*(g - 4)**2*(g + 1)**2/13
Let c(b) be the first derivative of -3*b**5/35 + 9*b**4/28 + 8. Factor c(n).
-3*n**3*(n - 3)/7
Let v(a) be the third derivative of 0 + 0*a**3 + 1/8*a**4 + 0*a + 1/120*a**6 - 1/15*a**5 - 9*a**2. Factor v(z).
z*(z - 3)*(z - 1)
Let q be ((-8)/10)/(2 + 36/(-15)). Let w(l) be the first derivative of q + 4*l**2 - 1/2*l**4 - 16*l - 6/5*l**5 + 28/3*l**3. Suppose w(u) = 0. Calculate u.
-2, -1, 2/3, 2
Suppose -11 = -3*q + b, 5*b = -4*q + b + 20. Let d(z) be the first derivative of 3/5*z**2 - 1/10*z**q + 0*z**3 + 4/5*z - 4. Factor d(m).
-2*(m - 2)*(m + 1)**2/5
Let t(a) be the first derivative of -a**5/15 + a**4/6 + 13*a**3/3 - 76*a**2/3 + 112*a/3 + 95. Solve t(v) = 0.
-7, 1, 4
Let l(g) be the first derivative of 3*g**4/4 - 12*g**3 + 66*g**2 - 144*g - 102. Factor l(q).
3*(q - 6)*(q - 4)*(q - 2)
Let j(d) be the second derivative of d**4/108 - 17*d**3/27 + 94*d. Factor j(i).
i*(i - 34)/9
Let y(h) be the third derivative of -5*h**8/336 - 3*h**7/14 - 5*h**6/4 - 11*h**5/3 - 5*h**4 - 8*h**2 + 4. What is z in y(z) = 0?
-3, -2, 0
Let 2*n**3 - 4*n**2 - n**2 - 10*n + 17*n**2 - 4*n = 0. Calculate n.
-7, 0, 1
Let r(y) be the first derivative of 25*y**3/12 - 23*y**2/8 - y/2 + 102. Let r(p) = 0. What is p?
-2/25, 1
Let t = -145 - -150. Suppose 11 - 1 = t*p - 5*d, -2*p - 5*d = 10. Solve 0*y**2 + 2/5*y + p - 2/5*y**3 = 0.
-1, 0, 1
Suppose 0 = p - 3*v + 5, -9 = 3*p + v - 4. Let j be p/((-20)/(-6) + -4). Let -6*y + 0*y**3 - 2*y**j + 4*y + 4*y**2 = 0. What is y?
0, 1
Let n(t) be the third derivative of t**6/40 - 147*t**5/20 + 7203*t**4/8 - 117649*t**3/2 - 57*t**2 - t. Factor n(i).
3*(i - 49)**3
Let n(o) be the third derivative of o**8/1680 + 13*o**7/1050 + 47*o**6/600 + 23*o**5/300 - 2*o**4/5 - 6*o**3/5 - 90*o**2. Determine r, given that n(r) = 0.
-6, -1, 1
Let o(c) = 5*c**3 - 18*c**2 + 3*c + 3. Let f(m) = -15*m**3 + 53*m**2 - 8*m - 8. Let a(n) = 3*f(n) + 8*o(n). Factor a(s).
-5*s**2*(s - 3)
Suppose 11 - 6 - 20*r**2 - 2*r**3 - 5 - 50*r = 0. Calculate r.
-5, 0
Let x = 9 - 3. Factor -4 + 9*n + 5*n + x*n - n**2 - 16*n.
-(n - 2)**2
Let l(s) be the third derivative of -s**6/420 + 13*s**3/6 + 10*s**2. Let m(y) be the first derivative of l(y). Factor m(x).
-6*x**2/7
Suppose 4*m = -2*c + 14, 10 = -2*c - m + 21. Let r be 1/c - (-5)/25. What is t in -r*t**3 - 6/5*t + 8/5*t**2 + 0 = 0?
0, 1, 3
Suppose -321*z + 284*z + 111 = 0. What is g in -z*g**2 - 5/3*g**3 - 2/3*g + 7/3*g**5 + 0 + 3*g**4 = 0?
-1, -2/7, 0, 1
Let a = 27 - 23. Factor 2*w**5 - 3*w**4 + 0*w**4 + 2 - 2*w - 4*w + a*w**3 + 4*w**2 - 3*w**4.
2*(w - 1)**4*(w + 1)
Let t = 128 + -115. Let s(f) be the first derivative of 2*f - t - 4*f**4 - 4*f**3 + 0*f**2 - 6/5*f**5. Factor s(p).
-2*(p + 1)**3*(3*p - 1)
Let g(c) be the second derivative of 7*c**4/108 - 20*c**3/27 - 2*c**2/3 + 38*c. Factor g(d).
(d - 6)*(7*d + 2)/9
Suppose -36 = 5*s - 26. Let r be (-40)/630 - s/7. Let 0*l + 0 - 2/9*l**4 + 2/9*l**2 - r*l**5 + 2/9*l**3 = 0. Calculate l.
-1, 0, 1
Factor -3/2*f + 0 + 3/4*f**2.
3*f*(f - 2)/4
Let o(w) be the first derivative of 3*w**4/4 + 3*w**3 - 27*w**2/2 - 81*w - 222. Factor o(n).
3*(n - 3)*(n + 3)**2
Let o(c) = -c**2 + 9*c + 9. Let v be o(10). Let n be v/(-5) - 319/(-145). Factor -4/5 + n*b - b**2.
-(b - 2)*(5*b - 2)/5
Let y(o) be the third derivative of 19*o**5/10 + 15*o**4/8 - o**3 - o**2 - 262*o. Determine g so that y(g) = 0.
-1/2, 2/19
Let i(r) = -r**4 + 12*r**3 - 6*r**2 - 5*r. Let u(m) = -m**4 + 6*m**3 - 3*m**2 - 2*m. Let c(t) = 4*i(t) - 7*u(t). Determine b so that c(b) = 0.
-2, -1, 0, 1
Let w(u) be the third derivative of 0 + 5/12*u**4 - 1/4*u**5 + 0*u - 10*u**2 + 0*u**3 + 1/24*u**6. Let w(x) = 0. What is x?
0, 1, 2
Let w(c) be the second derivative of 3*c**5/50 - 4*c**4/15 - 41*c**3/15 + 6*c**2 - 325*c. Solve w(u) = 0.
-3, 2/3, 5
Let l(r) be the first derivative of 2*r**5/15 - 3*r**4 + 34*r**3/9 - 64. Factor l(f).
2*f**2*(f - 17)*(f - 1)/3
Let h(x) be the second derivative of -x**8/47