/11*m**3 + 8/11*m.
-2*(m - 2)*(m + 1)*(m + 2)/11
Let i(c) be the second derivative of c**6/105 + 3*c**5/70 - c**4/14 - 11*c**3/21 - 6*c**2/7 - 239*c. Factor i(z).
2*(z - 2)*(z + 1)**2*(z + 3)/7
Let c = 2161/12 - 180. Let j(u) be the second derivative of c*u**4 + 0 - 1/2*u**2 - 1/20*u**5 + 1/6*u**3 + 2*u. Let j(y) = 0. Calculate y.
-1, 1
Solve 19/4*v**2 + 23 - 22*v + 1/4*v**3 = 0.
-23, 2
Let r be (-3)/(-78)*104/78. Let x(y) be the first derivative of -6 + 2/13*y**2 - 2/13*y - r*y**3. Suppose x(w) = 0. What is w?
1
Suppose 92 = -11*z - 21 + 168. Determine c, given that -2/5*c - 9/5*c**z - 3*c**2 - 37/5*c**3 + 0 - 33/5*c**4 = 0.
-2, -1, -1/3, 0
Factor 3*m**3 - 52*m + 32*m**2 - 7*m**3 - 197 + 221.
-4*(m - 6)*(m - 1)**2
Let h(r) = -12*r**3 + 16*r**2 + 4. Let o(n) = n**4 - n**3 - 1. Let l(k) = -h(k) - 4*o(k). Factor l(t).
-4*t**2*(t - 2)**2
Let v be ((162/24)/9)/(2*24). Let h(d) be the third derivative of -8*d**2 - 1/80*d**6 + 0 + 1/32*d**5 + 0*d**3 - v*d**4 + 0*d. Factor h(j).
-3*j*(j - 1)*(4*j - 1)/8
Let b(h) be the first derivative of 0*h**2 - 13/3*h**3 - 1/2340*h**6 - 3/52*h**4 + 0*h - 8 + 1/130*h**5. Let f(u) be the third derivative of b(u). Factor f(c).
-2*(c - 3)**2/13
Let z(f) be the third derivative of -f**8/168 - 4*f**7/105 - f**6/15 + 137*f**2. Factor z(p).
-2*p**3*(p + 2)**2
Let s(d) be the first derivative of -6*d - 1/12*d**4 + 0*d**2 + 0*d**3 + 1 + 1/40*d**5. Let c(m) be the first derivative of s(m). Suppose c(k) = 0. What is k?
0, 2
Let o(f) = 15*f**3 - 42*f**2 - 6*f - 6. Let v(i) = -17*i**3 + 41*i**2 + 7*i + 7. Let d(s) = -7*o(s) - 6*v(s). What is r in d(r) = 0?
0, 16
Let k(n) be the second derivative of n**4/24 - 5*n**3/4 + 13*n**2/2 + 827*n. Factor k(p).
(p - 13)*(p - 2)/2
Let i = -292 - -292. Let b(w) be the second derivative of -1/60*w**5 + 1/126*w**7 + 0 - 2*w + 1/18*w**4 + 0*w**2 + i*w**3 - 1/45*w**6. Factor b(q).
q**2*(q - 2)*(q - 1)*(q + 1)/3
Let r be (43 + 0)*(1 - 0). Let g = -40 + r. Determine s, given that -2/5*s - 12/5*s**g - 8/5*s**4 + 0 - 8/5*s**2 - 2/5*s**5 = 0.
-1, 0
Let s(z) be the third derivative of z**8/1680 - z**7/840 - z**6/360 + z**5/120 - 11*z**3/6 - 3*z**2. Let g(k) be the first derivative of s(k). Factor g(c).
c*(c - 1)**2*(c + 1)
Let v(c) be the first derivative of -4*c**3/9 - 20*c**2 - 807. Factor v(d).
-4*d*(d + 30)/3
Factor 30*u - 12*u + u**2 + 16 - 10*u.
(u + 4)**2
Let t = 17 + -12. Suppose 0 = -2*l - 2 + 10. Factor 0*f**5 + 0*f**t - f**5 + 0*f**5 - 2*f**l.
-f**4*(f + 2)
Let t(k) be the first derivative of -k**5/120 - k**4/24 - 3*k**2/2 + 15. Let y(u) be the second derivative of t(u). Solve y(q) = 0.
-2, 0
Suppose 0 = 2*g + 4*j + 12, -g + 56 - 70 = 4*j. Find l such that g - 1/2*l**2 + 0*l = 0.
-2, 2
Suppose 1/3*j + 7/3*j**2 - 2 = 0. What is j?
-1, 6/7
Let b = 9813 + -19621/2. Solve -b*x + 1 + 2*x**2 - 1/2*x**3 = 0.
1, 2
What is k in -16/3 + 31/3*k**2 + 17/3*k - 2/3*k**3 = 0?
-1, 1/2, 16
Let z(g) be the first derivative of -6*g**5/5 + 3*g**4/2 + 116*g**3/9 - 4*g**2/3 - 16*g + 683. Suppose z(s) = 0. Calculate s.
-2, -2/3, 2/3, 3
Let d = 5/19 + 61/57. Let v = -220/3 + 74. Factor v*o**2 + 2/3 + d*o.
2*(o + 1)**2/3
Let c(s) = -3*s**3 - 801*s**2 - 32802*s - 32000. Let y(m) = 35*m**3 + 9610*m**2 + 393625*m + 384000. Let q(v) = 25*c(v) + 2*y(v). Factor q(o).
-5*(o + 1)*(o + 80)**2
Let l(u) be the first derivative of 4*u**5/25 - 6*u**4/5 + 52*u**3/15 - 24*u**2/5 + 16*u/5 - 91. Factor l(w).
4*(w - 2)**2*(w - 1)**2/5
Let w = 4618 - 32322/7. Factor 2/7*y**3 - 2/7*y - w + 4/7*y**2.
2*(y - 1)*(y + 1)*(y + 2)/7
Let -6*s**5 - 236/3*s**3 - 38*s**4 + 0 - 184/3*s**2 - 16*s = 0. What is s?
-3, -2, -2/3, 0
Let y(w) be the first derivative of 7*w**6/2 + 204*w**5/5 + 153*w**4 + 160*w**3 - 96*w**2 - 290. Let y(j) = 0. What is j?
-4, -2, 0, 2/7
Let d be 2/(-13) - (-26)/169. Let m(u) be the second derivative of 0*u**2 + 1/40*u**6 - 3*u + 0 - 9/80*u**5 + 1/8*u**4 + d*u**3. Let m(s) = 0. Calculate s.
0, 1, 2
Let m = 2698 + -13486/5. Let o(t) be the first derivative of 4*t**3 + 0*t + 0*t**4 + 2 - m*t**5 - 4*t**2. Factor o(f).
-4*f*(f - 1)**2*(f + 2)
Let z(h) be the third derivative of -h**7/105 - 3*h**6/10 - 56*h**5/15 - 45*h**4/2 - 175*h**3/3 + 4*h**2 - 56. Factor z(p).
-2*(p + 1)*(p + 5)**2*(p + 7)
Let b be 16/(-15)*(-2 + 132/72). Let m(d) be the first derivative of 0*d + 1/6*d**4 + 1/15*d**2 - b*d**3 - 4/75*d**5 - 5. What is x in m(x) = 0?
0, 1/2, 1
What is q in -202/7*q - 5000/7*q**3 + 5200/7*q**2 + 2/7 = 0?
1/50, 1
Let z(b) be the second derivative of -5*b**4/12 - 25*b**3/6 + 119*b. Find j, given that z(j) = 0.
-5, 0
Let h(i) be the first derivative of 0*i**3 - 1/12*i**4 + 1/60*i**5 + 3 + 0*i - 1/2*i**2. Let l(w) be the second derivative of h(w). Factor l(x).
x*(x - 2)
Let g = -42 - -22. Let i be 5/(-2)*4/g. Factor 0 + i*b - 1/2*b**2.
-b*(b - 1)/2
Let x(q) = -q**4 + 9*q**3 + 10*q**2. Let u(s) = 124*s**2 - 14*s**2 + 33*s**3 + 67*s**3 - 10*s**4. Let h(t) = 4*u(t) - 45*x(t). Factor h(b).
5*b**2*(b - 2)*(b + 1)
Let w = -42 - -102. Let x be ((-9)/(-27))/(2/w). Factor 12*s**4 + 11*s**3 - 3*s**2 - 10*s + x*s - 2*s**3.
3*s**2*(s + 1)*(4*s - 1)
Let j be 4/(-20) - 38/(-90). Let z be (-17)/((-306)/(-32)) - -1*2. Factor 0 - 2/9*i**2 + 2/9*i**4 - j*i + z*i**3.
2*i*(i - 1)*(i + 1)**2/9
Let x be (-10 - 273/(-26))/3. Let n(w) be the first derivative of -2/9*w**3 - x*w**2 + 1/6*w**4 + 1/15*w**5 - 1/18*w**6 + 1/3*w - 8. What is b in n(b) = 0?
-1, 1
Let o(i) be the first derivative of i**4/20 + 14*i**3/15 + 6*i**2 + 72*i/5 + 578. Factor o(c).
(c + 2)*(c + 6)**2/5
Let h(c) be the third derivative of -c**8/84 - 11*c**7/105 - 3*c**6/10 - 4*c**5/15 + c**4/3 + c**3 + 10*c**2 + 1. Solve h(f) = 0.
-3, -1, 1/2
Suppose -15 + 13 = -g. Determine t so that -4 + t**g - 5*t + 4*t**2 - 8 + 2 = 0.
-1, 2
Let g(l) be the second derivative of -l**4/6 + 5*l**3/3 - 4*l**2 + 120*l. Suppose g(m) = 0. Calculate m.
1, 4
Let u = -98/9 - -34/3. Let b be 14 - (12 - 22 - -24). Determine i, given that -u*i**3 - 2/9*i**4 + 0 + 0*i**2 + b*i = 0.
-2, 0
Factor 3993/2*j**3 + 16335*j**2 + 44550*j + 40500.
3*(11*j + 30)**3/2
Let 2/9*g**4 + 8/9*g**3 + 0 + 0*g + 8/9*g**2 = 0. What is g?
-2, 0
Let s = 11 + -7. Find h such that 63*h**2 - 34*h**s - 8*h**5 + 18*h - 12*h**2 - 7*h**5 - 3*h**3 - 17*h**4 = 0.
-3, -1, -2/5, 0, 1
Factor 18*m - m**2 + 10*m + 18*m - 954 + 425.
-(m - 23)**2
Let i(m) = 5486*m**2 + 306*m + 19. Let l(x) = 2742*x**2 + 152*x + 8. Let a(c) = 2*i(c) - 5*l(c). Factor a(w).
-2*(37*w + 1)**2
Let h(k) be the second derivative of 1/80*k**5 + 0 - 1/2*k**2 - 1/24*k**3 - 8*k + 1/12*k**4. Solve h(n) = 0 for n.
-4, -1, 1
Suppose 0 = i + 3*x - 4, -4*x + 3 = -2*i + 1. Let n be -2*i + 5/((-25)/(-12)). Determine l so that -4/5 + 2*l + n*l**3 - 8/5*l**2 = 0.
1, 2
Let c(q) = -9*q**4 + 40*q**3 + q**2 - 182*q + 112. Let h(d) = -d**3 - d**2 - d + 2. Let f(o) = c(o) - 2*h(o). Determine i so that f(i) = 0.
-2, 2/3, 3
Let i(u) be the second derivative of -u**7/105 + u**5/10 + u**4/6 + 19*u**2/2 - 24*u. Let s(j) be the first derivative of i(j). Factor s(l).
-2*l*(l - 2)*(l + 1)**2
Let z(s) be the first derivative of s**5/50 + 21*s**4/40 + 37*s**3/15 - 24*s**2/5 - 412. What is b in z(b) = 0?
-16, -6, 0, 1
Let t(p) be the first derivative of 10*p**3/27 - 22*p**2/3 + 26*p/9 + 21. Factor t(j).
2*(j - 13)*(5*j - 1)/9
Let q(x) be the third derivative of -2/245*x**7 + 0*x**5 - 1/294*x**8 - 1/210*x**6 + 0*x**4 + 0*x**3 + 0*x + 0 + 10*x**2. Factor q(n).
-4*n**3*(n + 1)*(2*n + 1)/7
Let d = 211 - 211. Let o(x) be the second derivative of -2*x - 2/3*x**3 + d + 3*x**2 + 1/18*x**4. Factor o(t).
2*(t - 3)**2/3
Let m(n) be the third derivative of -n**6/120 + 4*n**5/15 - 10*n**4/3 + 64*n**3/3 + 3*n**2 - 14. Factor m(r).
-(r - 8)*(r - 4)**2
Let n be (-1)/(4/12) + 4. Let a be (6/(-4))/((-1)/n). Solve 15/2*v**3 + 3*v**2 - a - 15/4*v - 3/2*v**4 - 15/4*v**5 = 0 for v.
-1, -2/5, 1
Let n = -851 - -76591/90. Let v(s) be the second derivative of 0*s**2 + 0 - 1/9*s**3 - 2/27*s**4 - n*s**5 + 5*s. Find b such that v(b) = 0.
-3, -1, 0
Let l(w) = -w**3 - 3*w**2 - 2*w. Let g be l(-2). Let h(b) be the third derivative of 3/40*b**5 + g + 1/80*b**6 + 0*b**4 + 0*b**3 + 7*b**2 + 0*b. Factor h(j).
3*j**2*(j + 3)/2
Let r(i) be the second derivative of 11*i + 3/80*i**5 - 1/8*i**3 + 0 + 0*i**2 - 1/40*i**6 + 1/16*i**4. Determine