k**3 - 1/2*k**2 + 0.
k*(k - 3)*(k - 2)/10
Let r(q) be the first derivative of -3*q**5/25 - 9*q**4/20 + 6*q**2/5 + 3. Find n, given that r(n) = 0.
-2, 0, 1
Let z(p) be the third derivative of p**7/189 + p**6/45 + p**5/45 - p**4/27 - p**3/9 - 13*p**2 - 3*p. Find v such that z(v) = 0.
-1, 3/5
Let c(a) be the first derivative of 21*a**5/5 - 3*a**4/2 - 7*a**3 + 3*a**2 + 23. Factor c(r).
3*r*(r - 1)*(r + 1)*(7*r - 2)
Factor -7 + 1 - 6 + 4 + 4*t**2 - 4*t + 0*t.
4*(t - 2)*(t + 1)
Let h(q) be the third derivative of -q**5/15 + 2*q**4 + 6*q**2 - 4. Factor h(k).
-4*k*(k - 12)
Let o(l) = -4*l**5 + 18*l**4 + 12*l**3 - 5*l**2 - 5. Let g(u) = 5*u**5 - 19*u**4 - 12*u**3 + 6*u**2 + 6. Let b(r) = 5*g(r) + 6*o(r). Factor b(m).
m**3*(m + 1)*(m + 12)
Let a(y) be the second derivative of y**6/30 - 44*y**5/5 + 1711*y**4/2 - 97468*y**3/3 - 205379*y**2/2 - 91*y. Suppose a(d) = 0. What is d?
-1, 59
Let u(g) be the first derivative of g**7/315 - g**6/90 - g**2 - 14. Let m(d) be the second derivative of u(d). Find y such that m(y) = 0.
0, 2
Suppose -106/13*a + 270/13*a**2 - 32/13*a**4 - 144/13*a**3 + 12/13 = 0. What is a?
-6, 1/4, 1
Let m be ((-9)/(-495))/(79/(-10) - -8). Factor 8/11 + m*d**3 - 6/11*d**2 + 0*d.
2*(d - 2)**2*(d + 1)/11
Let s(q) be the third derivative of q**6/24 + 5*q**5/12 - 95*q**2. Determine g so that s(g) = 0.
-5, 0
Let d = -26 - -30. Suppose 0*c**5 - c**d + c**5 - 2*c**5 + 3*c**3 - 2*c + c**2 = 0. Calculate c.
-2, -1, 0, 1
Let s(f) be the second derivative of -f**5/110 + 3*f**3/11 + f - 5. Factor s(u).
-2*u*(u - 3)*(u + 3)/11
Let c(p) be the third derivative of -1/720*p**6 + 0 + 0*p + 1/240*p**5 + 0*p**4 + 1/2*p**3 - 5*p**2. Let d(y) be the first derivative of c(y). Factor d(r).
-r*(r - 1)/2
Let u(b) be the first derivative of 3*b**4/28 - 23*b**3/21 + 16*b**2/7 - 12*b/7 - 116. Factor u(w).
(w - 6)*(w - 1)*(3*w - 2)/7
Suppose 10 = -3*x + 5*x. Suppose -4*k = -4*p + p - 24, x*k - 30 = 4*p. Factor 6*u**2 + 4 - 4*u**2 + 2*u - k*u - 10.
2*(u - 3)*(u + 1)
Let m(k) be the second derivative of -k**7/42 + k**6/3 - 7*k**5/20 - 3*k**4/2 - k - 261. Factor m(v).
-v**2*(v - 9)*(v - 2)*(v + 1)
Suppose 4*v**3 + 3*v - 13*v + 0*v**2 + 16*v**2 + 0*v**3 - 10*v = 0. Calculate v.
-5, 0, 1
Solve 0*a + 3*a**4 + 0 + 0*a**2 + 3/7*a**5 + 30/7*a**3 = 0.
-5, -2, 0
Determine x so that -6561 + 729*x - 27*x**2 + 1/3*x**3 = 0.
27
Suppose -1/2*f**3 - 10 - 11/2*f + 4*f**2 = 0. What is f?
-1, 4, 5
Let g(z) = -z**3 + 14*z**2 - 17*z + 54. Let k be g(13). Let x(t) be the first derivative of -4/5*t**k + 8/5*t - 9 + 2/15*t**3. Find o, given that x(o) = 0.
2
Let k(s) = s**2 - s - 2. Let c(w) = -2*w**2 + w + 4. Let a(f) = -2*c(f) - 3*k(f). Factor a(y).
(y - 1)*(y + 2)
Suppose 4*s + 3*f = 38, -4*s + 32*f = 37*f - 42. Let v(p) be the second derivative of -1/3*p**4 + 0 - s*p**2 + 9*p - 8/3*p**3. Factor v(r).
-4*(r + 2)**2
Let j = -3524/3 - -1176. Factor -1/6*s**2 - 8/3 - j*s.
-(s + 4)**2/6
Let v be ((-2)/4)/((-15)/30). Suppose 0 = -s + 1 + v. Determine y so that -4*y + y**4 - 5*y**4 - 3*y**3 + 7*y**3 + 4*y**s = 0.
-1, 0, 1
Let k(d) = d**4 - 4*d**3 + 3*d**2 - 4*d. Let v(u) = -3*u**4 + 9*u**3 - 6*u**2 + 9*u. Suppose -4*b - 174 = -158. Let h(l) = b*v(l) - 9*k(l). Factor h(r).
3*r**2*(r - 1)*(r + 1)
Let v(r) = r**3 - 2*r**2 + 5*r - 5. Let q be v(2). Suppose 2*f**3 + 4*f**4 - 4*f**5 + 14*f**q - 8*f**5 = 0. Calculate f.
-1, 0
Let c(b) = 28*b**3 + 152*b**2 - 28*b - 136. Let u(v) = 9*v**3 + 50*v**2 - 9*v - 45. Let m(j) = 5*c(j) - 16*u(j). Let m(y) = 0. What is y?
-10, -1, 1
Let o(r) = -80*r**4 - 620*r**3 + 1485*r**2 + 4510*r + 2760. Let a(l) = 3*l**4 + 23*l**3 - 55*l**2 - 167*l - 102. Let q(k) = -55*a(k) - 2*o(k). Factor q(n).
-5*(n - 3)*(n + 1)**2*(n + 6)
Suppose 50/9*j - 2/9*j**2 - 16/3 = 0. What is j?
1, 24
Let t(o) be the first derivative of -5*o**3/3 - 20*o**2 + 165*o + 451. Determine l so that t(l) = 0.
-11, 3
Let y(i) = -2*i**2 - 492*i + 12990. Let f(s) = s**2 + 6*s + 1. Let t(h) = -6*f(h) - y(h). Let t(w) = 0. What is w?
57
Let d = -670 + 3351/5. Let z(b) be the first derivative of -1/3*b**3 + 0*b + 1/2*b**2 - 5 - 1/4*b**4 + d*b**5. Factor z(n).
n*(n - 1)**2*(n + 1)
Suppose 2*m + 3*m = 10. Let w be (2560/(-30) - 6)*(-3)/2. Factor -f**3 + 137 - 2*f - 3*f**m - w.
-f*(f + 1)*(f + 2)
Let b(r) be the third derivative of r**8/1680 + 2*r**7/175 - 29*r**6/600 - r**5/25 + 7*r**4/30 + 430*r**2. Determine a so that b(a) = 0.
-14, -1, 0, 1, 2
Let y(a) = 58*a**2 - 1392*a + 2. Let n be y(24). Factor 4/3*z**n - 2/3*z - 4/3 + 2/3*z**3.
2*(z - 1)*(z + 1)*(z + 2)/3
Let p(l) be the first derivative of l**4/8 + 7*l**3 + 513*l**2/4 + 722*l - 710. Factor p(i).
(i + 4)*(i + 19)**2/2
Factor 30*v**3 + 0 - 53/6*v**2 + 1/3*v.
v*(4*v - 1)*(45*v - 2)/6
Factor -1/3*a**3 - a**2 + 12*a - 32/3.
-(a - 4)*(a - 1)*(a + 8)/3
Let l(v) = 2*v**2 + 28*v + 92. Let h be l(-5). Determine o, given that -4/5*o - 3/5*o**h - 1/5*o**4 + 4/5 + 4/5*o**3 = 0.
-1, 1, 2
Let m(y) be the second derivative of y**4/12 + 17*y**3/27 - 4*y**2/9 + 3*y + 6. Factor m(l).
(l + 4)*(9*l - 2)/9
Let n(d) be the second derivative of -3/13*d**2 + 2/65*d**5 + 0 - 4/39*d**4 - 5*d - 11/39*d**3. Factor n(p).
2*(p - 3)*(2*p + 1)**2/13
Let a(i) be the second derivative of -i**6/360 - i**5/40 + 5*i**4/12 - 3*i**3 - 32*i. Let c(t) be the second derivative of a(t). Let c(p) = 0. Calculate p.
-5, 2
Factor 15 + 25/2*g - 5/2*g**2.
-5*(g - 6)*(g + 1)/2
Let b be (-2*4/960)/(6 + -7). Let l(t) be the second derivative of 0*t**2 + b*t**4 + 10*t - 1/30*t**3 + 0. Factor l(m).
m*(m - 2)/10
Factor 0 - 28/9*s**3 + 26/9*s**2 + 2/9*s**4 + 0*s.
2*s**2*(s - 13)*(s - 1)/9
Let o(s) be the first derivative of -s**5/15 - 13*s**4/6 - 193*s**3/9 - 52*s**2 - 48*s - 191. Factor o(f).
-(f + 1)**2*(f + 12)**2/3
Let p(q) be the second derivative of -q**6/6 + 19*q**5/4 - 85*q**4/4 + 245*q**3/6 - 40*q**2 - 16*q - 1. Find v, given that p(v) = 0.
1, 16
Let t(u) be the third derivative of -1/108*u**4 - 1/90*u**5 - 1/945*u**7 + 0 + 0*u**3 + 5*u**2 - 1/180*u**6 + 0*u. Find c such that t(c) = 0.
-1, 0
Let m = -53 + 58. Suppose 0 = 2*a + 4*q - 22, 31 = 5*a + m*q - q. Factor -2/11*c**2 - 2/11*c + 2/11*c**a + 2/11.
2*(c - 1)**2*(c + 1)/11
Let v(n) be the third derivative of -n**7/70 - n**6/10 + 4*n**5/5 + 2*n**4 - 24*n**3 + 74*n**2 - 1. What is h in v(h) = 0?
-6, -2, 2
Factor 80*w - 40*w + 295*w**2 - 299*w**2.
-4*w*(w - 10)
Let l be ((-1 + 1)/2)/(-2). Suppose 2*x = c + 1, -c - 1 = 24*x - 23*x. Find r such that x*r**2 + l + 3/5*r**3 + 3/5*r**4 + 0*r = 0.
-1, 0
Let c(y) be the third derivative of -y**6/120 - 17*y**5/20 - 289*y**4/8 + 11*y**3/6 + 23*y**2 + 2. Let f(u) be the first derivative of c(u). Factor f(r).
-3*(r + 17)**2
Let o(v) be the second derivative of v**4/30 - 7*v**3/15 - 8*v**2/5 - 178*v. Suppose o(d) = 0. Calculate d.
-1, 8
Let r = 3290/7543 - 6/397. Solve -r*b + 2/19*b**2 + 0 = 0 for b.
0, 4
Let t be (0/2)/(23 - 21). Suppose 2*y = -t*y + 6. Factor 0 - 1/2*i**y - i - 3/2*i**2.
-i*(i + 1)*(i + 2)/2
Let r = 18 - 14. Let v(a) be the second derivative of r*a + 1/6*a**4 + 0 - 4/3*a**3 - 4*a**2 + 1/10*a**5. What is c in v(c) = 0?
-2, -1, 2
Suppose -x + 25 = 21. Let t(p) be the second derivative of 4*p - 1/8*p**2 + 0*p**3 + 0 + 1/48*p**x. Factor t(o).
(o - 1)*(o + 1)/4
Let a(r) be the second derivative of -r**4/20 + 297*r**3/5 - 264627*r**2/10 + 5*r + 123. Factor a(k).
-3*(k - 297)**2/5
Let o(f) be the third derivative of -f**8/96 + 11*f**7/840 + 11*f**6/160 + f**5/60 - f**4/24 + 99*f**2. Let o(t) = 0. What is t?
-1, -1/2, 0, 2/7, 2
Let k(i) be the third derivative of -i**7/140 - 37*i**6/120 - 47*i**5/120 + i**4/2 + 15*i**2 - i. What is n in k(n) = 0?
-24, -1, 0, 1/3
Factor 4/5*r - 4/5*r**3 - 8/5*r**2 + 6/5 + 2/5*r**4.
2*(r - 3)*(r - 1)*(r + 1)**2/5
What is a in -25*a**3 - 15*a**2 + a**4 + 14*a**4 + 25*a - 5*a**4 - 15*a**4 + 20 = 0?
-4, -1, 1
Let q(y) = y**2 - 12*y. Let g be q(12). Let c be g + ((-112)/(-52) - 2). Factor -2/13*a**2 + 4/13 + c*a.
-2*(a - 2)*(a + 1)/13
Suppose 3*c + 5 = 3*g + 5*c, -5*g + 5*c = -50. Suppose -3*o = -4*u + u, -4*u + 18 = g*o. Factor -o*a - a - 5*a + 3*a**2 + 6 - a.
3*(a - 2)*(a - 1)
Let q(i) be the third derivative of 1/57*i**3 + 0*i + 0*i**5 + 0 - 1/1995*i**7 + 1/570*i**6 + 17*i**2 - 1/114*i**4. Factor q(z).
-2*(z - 1)**3*(z + 1)/19
Let k(f) be the third derivative of f**7