nd derivative of f**7/378 + f**6/27 + 8*f**5/45 + 8*f**4/27 + 88*f. Find t, given that i(t) = 0.
-4, -2, 0
What is f in -2*f + 6*f**2 + 2*f**2 - 1 - 2 = 0?
-1/2, 3/4
Let a = -523 - -523. Let k(j) be the third derivative of 1/24*j**6 + 1/210*j**7 + 0*j**3 + 0 - 4*j**2 + 2/15*j**5 + a*j + 1/6*j**4. Factor k(y).
y*(y + 1)*(y + 2)**2
Let v(u) be the second derivative of -u**5/20 + 7*u**4/12 - u**3 + 60*u. Factor v(a).
-a*(a - 6)*(a - 1)
Let a = 36 + -26. Let y = a - 4. Factor -4*n**3 + y*n**3 + 2*n**2 + 0*n**3.
2*n**2*(n + 1)
Let g be (-2)/(-7)*(17 - 10). Let v(m) be the third derivative of g*m**2 - 1/240*m**5 + 0*m + 0 + 1/24*m**3 + 0*m**4. Suppose v(d) = 0. Calculate d.
-1, 1
Let u(b) = b**3 + 6*b**2 + 10*b + 14. Let t be u(-4). Let w(j) = j**3 - 5*j**2 + j - 1. Let z be w(5). Factor t*s**2 + 15/4*s**3 + 3/4*s**z + 3*s + 0.
3*s*(s + 1)*(s + 2)**2/4
Let f be 10/8*8/28*192/40. Factor 2/7*a**2 + 10/7*a - f.
2*(a - 1)*(a + 6)/7
Suppose 0 = -9*c + 34 + 20. Let f be (-1)/(-4)*368/c. Factor f*m**2 + 8/3 + 40/3*m + 14/3*m**3.
2*(m + 1)*(m + 2)*(7*m + 2)/3
Suppose 0*q = q - 10. Suppose -2*a = -2 - q. Solve a*j**3 - 1 + 1 + 8*j**2 - 6*j**2 = 0.
-1/3, 0
Let w(z) be the third derivative of z**7/11340 - z**6/1080 + z**5/270 + z**4/8 + 14*z**2. Let m(g) be the second derivative of w(g). Factor m(b).
2*(b - 2)*(b - 1)/9
Suppose 2*r - 14 = -4*h + h, -3*h + 4*r = 10. Let x be -1 - -10*1/h. Factor x*w**2 - 108*w - 4*w**4 + 108*w.
-4*w**2*(w - 1)*(w + 1)
Let p(v) be the second derivative of 9*v**5/20 - v**4/4 - 2*v**3 - 6*v. Factor p(o).
3*o*(o + 1)*(3*o - 4)
Let t(j) = -j**2 + 14*j - 11. Let g be t(11). Suppose 4*u + 5*v = -9 - 3, -3*v = -5*u + g. Factor -20*z - z**2 - 4 + 12*z - 3*z**u + 0*z**2.
-4*(z + 1)**2
Let w = 866 - 866. Let v(f) be the first derivative of 81/10*f**5 - 81/8*f**4 + 9/2*f**3 - 6 - 3/4*f**2 + w*f. Let v(n) = 0. What is n?
0, 1/3
Suppose c + 13 = 17. Factor -c*p + p**2 - p**2 + 5*p - p**2.
-p*(p - 1)
Let l(r) = -140*r**3 - 230*r**2 - 94*r - 4. Let f(y) = -47*y**3 - 77*y**2 - 31*y - 1. Let u(v) = -8*f(v) + 3*l(v). Suppose u(z) = 0. What is z?
-1, -1/2, -2/11
Let v be 656/60 + (-168)/630. Suppose v + 80/3*y - 328/3*y**2 - 60*y**3 = 0. What is y?
-2, -2/9, 2/5
Suppose -14*j = -8*j + 216. Let u be (-3)/(2/(-9) - (-46)/j). Find x such that -3/5*x**4 - 3/5*x**3 + 3/5*x**5 + 3/5*x**u + 0*x + 0 = 0.
-1, 0, 1
Let k(h) = 47*h**4 - 169*h**3 + 97*h**2 - 15*h. Let v(c) = -48*c**4 + 171*c**3 - 98*c**2 + 15*c. Let m(u) = -3*k(u) - 2*v(u). Solve m(b) = 0 for b.
0, 1/3, 3
Let k(z) be the first derivative of 1/30*z**6 + 1/25*z**5 - 1/10*z**4 + 1/5*z + 1/10*z**2 + 36 - 2/15*z**3. Factor k(t).
(t - 1)**2*(t + 1)**3/5
Let f(b) be the first derivative of -b**6/33 + 6*b**5/55 + 9*b**4/11 - 422. Factor f(s).
-2*s**3*(s - 6)*(s + 3)/11
Let i(a) be the third derivative of a**11/554400 + a**10/50400 - 19*a**5/20 - 10*a**2 - 3*a. Let w(g) be the third derivative of i(g). Factor w(k).
3*k**4*(k + 5)/5
Suppose 6*i = 4*i + 156. Suppose -3*r + 4 = 2*u, -r - 3*u + 0*u - 8 = 0. Factor o**r + o**3 + i*o - 78*o.
o**3*(o + 1)
Let p(a) be the second derivative of -a**8/210 - a**7/60 - a**6/60 + 29*a**3/6 - 29*a. Let b(t) be the second derivative of p(t). Factor b(q).
-2*q**2*(q + 1)*(4*q + 3)
Let u(k) be the third derivative of -1/8*k**4 + 1/40*k**6 - 1/3*k**3 + 0 + 23*k**2 + 0*k + 1/60*k**5 + 1/210*k**7. Solve u(b) = 0 for b.
-2, -1, 1
Let u(i) be the third derivative of i**8/2352 - i**7/1470 - 5*i**6/168 + i**5/420 + i**4 + 24*i**3/7 - 2*i**2 - 387. Determine v so that u(v) = 0.
-3, -1, 4
Suppose 6*u - 2*u = 28. Suppose 0 = -6*t + u*t - 6. Factor -15*c - 12*c**2 - t + 6*c**3 - 9*c**3 + 0*c**3.
-3*(c + 1)**2*(c + 2)
Let c = 161410/7 - 23058. Factor 0*x - 2/7*x**4 + 0 - c*x**3 - 2/7*x**2.
-2*x**2*(x + 1)**2/7
Let q(b) be the first derivative of 7*b**6/24 - 3*b**5/4 + 5*b**4/12 + 17*b**2/2 - 17. Let o(p) be the second derivative of q(p). Suppose o(m) = 0. What is m?
0, 2/7, 1
Suppose -3*s + 6 = -0. Factor -s*f + 7*f**2 - f**2 - 4*f**2 - 4 + 0*f**2.
2*(f - 2)*(f + 1)
Factor 0 - 1/3*g**2 + 77/3*g.
-g*(g - 77)/3
Let v be (-6)/(7 + 140/(-8)). Let 0 - 4/7*k - 12/7*k**2 - v*k**4 - 12/7*k**3 = 0. What is k?
-1, 0
Suppose 3*s - 19 = 5*k, 0 + 1 = -3*s + k. Let b be ((-1)/3)/(s/(-10)) + 2. Let b*x**5 + 0 - 1/3*x + 0*x**3 - 2/3*x**2 + 2/3*x**4 = 0. Calculate x.
-1, 0, 1
Suppose 4*y = 3*y - u - 2, -3*y + u = -10. Let r = -106 - -108. Factor -12/7 - 38/7*d + y*d**r.
2*(d - 3)*(7*d + 2)/7
Let c be 2/(-9) + 38/90. Suppose -v = -6 + 4. Find o, given that 1/5*o**3 - c*o**v + 1/5 - 1/5*o = 0.
-1, 1
Let r(t) = -6*t**3 - t**2 - 2*t - 2. Let i be r(-1). Suppose 0*j - 5*k = 2*j - 11, -5*k = -i. Let -1 + j*p**2 + 2 + 3 - 7 = 0. Calculate p.
-1, 1
Suppose -5 = 2*f - 3*u, 3*f = -4*u + 1 - 17. Let h be 0 + 0 - (1 + f). Factor 1/7*b**h - 1/7*b**2 - 2/7*b + 0.
b*(b - 2)*(b + 1)/7
Determine c, given that -40*c - 79*c**2 + 2*c**2 - 23*c**2 + 25*c**5 + 34*c**3 - 4*c**3 + 85*c**4 = 0.
-2, -2/5, 0, 1
Factor -222*t + t**4 + 2 + 9*t**3 + 9*t**2 + 0 + 229*t - 4*t**3.
(t + 1)**3*(t + 2)
Find m, given that 6/5*m - 2/5*m**3 + 0 + 4/5*m**2 = 0.
-1, 0, 3
Let u be (15/(-12) + 1)/(-30). Let b(t) be the third derivative of -5*t**2 + 0*t**3 + 0 + 0*t - u*t**6 + 1/30*t**5 - 1/24*t**4. What is p in b(p) = 0?
0, 1
Let i(y) = 20*y**3 - 41*y**2 + 89*y - 7. Let r(b) = -11*b**3 + 20*b**2 - 44*b + 4. Let c(h) = -4*i(h) - 7*r(h). Factor c(t).
-3*t*(t - 4)**2
Let n(v) be the third derivative of -2*v**7/105 - v**6/5 - 4*v**5/5 - 5*v**4/3 - 2*v**3 + 23*v**2 - 2*v. Factor n(d).
-4*(d + 1)**3*(d + 3)
Let s(l) = 2*l - 5. Let x be s(5). Suppose -o + x = -5*t - 2, -1 = -o - t. Factor -9*h - 6*h + 3*h**2 + 20*h + o.
(h + 1)*(3*h + 2)
Let i be (-756)/(-60)*-2*2/(-6). Let d(c) be the first derivative of -i*c**5 - 4/3*c + 6 + 50/9*c**3 + 15/2*c**4 - 5/3*c**2. Find h, given that d(h) = 0.
-1/3, -2/7, 1/3, 1
Factor -4/3*r**2 + 36 - 104/3*r.
-4*(r - 1)*(r + 27)/3
Factor 50*m - 5*m**3 + 9*m**2 + 40 + 4*m**2 - 8*m**2.
-5*(m - 4)*(m + 1)*(m + 2)
Let p(h) be the first derivative of -h**7/210 + h**6/30 - h**5/15 - h**2/2 - 11. Let w(t) be the second derivative of p(t). Determine v, given that w(v) = 0.
0, 2
Let g(i) be the first derivative of i**6/6 - 4*i**5/5 - 3*i**4/2 + 4*i**3/3 + 5*i**2/2 - 73. Factor g(m).
m*(m - 5)*(m - 1)*(m + 1)**2
Determine v so that 23*v**2 - 5*v**2 + 20*v - 16*v**4 - 24*v**3 - 2*v**2 + 4*v**5 = 0.
-1, 0, 1, 5
Suppose -2*d - 849 = -4*d + 5*t, -3*t + 1284 = 3*d. Factor 1266 - 1218 + 99*u**2 - d*u**3 + 64*u**3 + 216*u.
-3*(u - 1)*(11*u + 4)**2
Let i(r) = -10*r - 19. Let z be i(-6). Factor 22*m + z - 4*m + 40 + m**2.
(m + 9)**2
Let i be (0/(9 - 12))/2. Find s such that -1/5*s**3 + 0*s - 2/5*s**2 + i + 1/5*s**4 = 0.
-1, 0, 2
Let s(r) be the first derivative of -r**6/90 + r**5/15 - r**3/3 - 12. Let z(n) be the third derivative of s(n). Factor z(g).
-4*g*(g - 2)
Find o, given that 12*o - 5*o**3 - 7*o + 7*o**2 - o**4 + 97 - 103 = 0.
-6, -1, 1
Let f = 751/5012 - 5/716. Let -f*q + 1/7*q**2 + 0 = 0. Calculate q.
0, 1
Let l(o) be the third derivative of -o**5/570 + 5*o**4/57 + 52*o**3/19 - 4*o**2 - 5*o. Factor l(z).
-2*(z - 26)*(z + 6)/19
Let r(w) = -4*w + 0 + 6*w + 2 + 2 - 6*w**2. Let t(g) = -5*g**2 + 2*g + 3. Let j(c) = 3*r(c) - 4*t(c). Factor j(y).
2*y*(y - 1)
Let j(m) be the first derivative of -m**3/3 + 135*m**2/14 - 38*m/7 + 317. Factor j(x).
-(x - 19)*(7*x - 2)/7
Factor 0*s + 3/5*s**4 - 39/5*s**3 + 0 + 66/5*s**2.
3*s**2*(s - 11)*(s - 2)/5
Let w(u) be the first derivative of 2/9*u**3 - 4/3*u - 11 + 1/3*u**2. Suppose w(h) = 0. Calculate h.
-2, 1
Let v(c) = 274*c + 2. Let l be v(0). Suppose 5/2*w + 1/2 - 13/8*w**3 - 23/8*w**4 + 19/8*w**l - 7/8*w**5 = 0. What is w?
-2, -1, -2/7, 1
Factor -258 - 251 - 225 + 766 + 4*i**2 + 24*i.
4*(i + 2)*(i + 4)
What is o in -780*o + 277*o**2 - 106 + 2*o**3 + o**4 - 32*o**3 + 0*o**4 + 245 + 537 = 0?
2, 13
Suppose -5*d = 4*d - 18. Let x be 0*((-26)/6 - (d - 6)). Factor -1/2*q**2 + x - q.
-q*(q + 2)/2
Let f = -654 + 1964/3. Factor a + f + 1/3*a**2.
(a + 1)*(a + 2)/3
Suppose 3*o = 4 + 2. Factor 15*w**3 - 10*w - 7 + 5*w**4 + o - 5*w**3.
5*(w - 1)*(w + 1)**3
Suppose -5*o = -4*o - 5*j, 4*o = -j. Determine m so that o*m**2 - 2*m**2 + 2*m - 3*m**2 + 5*m**4 + 3*m - 5*m**3 = 0.
-1, 0, 1
Let v(r) be the thir