(p - 1)*(p + 3)/3
Let v(j) be the second derivative of j**9/22680 - j**7/1890 + j**5/180 - j**4/2 + 2*j. Let g(s) be the third derivative of v(s). Solve g(o) = 0 for o.
-1, 1
Let g(q) = 4*q**3 + 10*q**2 - 6*q + 6. Let o(h) = h**2 - h + 1. Let i(r) = g(r) - 6*o(r). Find n, given that i(n) = 0.
-1, 0
Let k(g) be the first derivative of -g**3/3 - g**2/2 - 4. Let k(h) = 0. What is h?
-1, 0
Let q(y) be the second derivative of -y**4/66 + 2*y**3/33 - 7*y. Find z, given that q(z) = 0.
0, 2
Let h(l) be the first derivative of -7*l**6/18 + 2*l**5/15 + 4. What is p in h(p) = 0?
0, 2/7
Let l be (-1)/1*1*0/(-36). Let z(p) be the third derivative of -1/4*p**4 + l*p - 1/30*p**5 - 2/3*p**3 + 0 - 4*p**2. Factor z(m).
-2*(m + 1)*(m + 2)
Factor -54*p - 13*p**2 - 54 - 4*p**2 - p**2 - 2*p**3.
-2*(p + 3)**3
Let c(a) = -3*a**2 + 6*a - 10. Let p(b) = -b**2 + 2*b - 3. Let t be 1 + 0 + -1 - -2. Let n(r) = t*c(r) - 7*p(r). Factor n(o).
(o - 1)**2
Let u(d) be the first derivative of -2*d**7/21 + 2*d**5/5 - 2*d**3/3 - 4*d + 10. Let r(b) be the first derivative of u(b). Find a such that r(a) = 0.
-1, 0, 1
Let i be (-2)/17 + (-28)/(-238). Factor 2*w**4 - 8/3*w**2 + 0*w - 2/3*w**5 + i + 0*w**3.
-2*w**2*(w - 2)**2*(w + 1)/3
Let g(k) be the third derivative of -k**7/1995 + 7*k**6/1140 + 34*k**2. Factor g(y).
-2*y**3*(y - 7)/19
Let h(s) = s**2 - s + 1. Let u(q) be the second derivative of q**5/20 - q**3/6 + q**2/2 + 2*q. Let p(i) = h(i) - u(i). Factor p(a).
-a**2*(a - 1)
Let o(q) be the second derivative of q**4/6 + 4*q**3/3 - 52*q. Factor o(x).
2*x*(x + 4)
Let p(y) be the second derivative of y**6/15 - y**5/5 - y**4/6 + 2*y**3/3 - 21*y. Let p(s) = 0. Calculate s.
-1, 0, 1, 2
Let o(n) = n**3 + 5*n**2. Let v(f) = 2*f**3 + 4*f**2 + 3*f + 1. Let y be v(-2). Let m be o(y). Determine r so that 2/3*r**2 + m + 0*r**3 + 0*r - 2/3*r**4 = 0.
-1, 0, 1
Suppose -1/3*w**2 - 1/3*w + 0 = 0. Calculate w.
-1, 0
Let o(t) = -t**3 + t**2 + 2*t. Let j be o(2). Let h(v) be the second derivative of 0 - 1/40*v**5 + 1/60*v**6 + 0*v**3 + 2*v + j*v**2 - 1/12*v**4. Factor h(x).
x**2*(x - 2)*(x + 1)/2
Factor -4/7*z**3 + 2/7*z**4 + 4/7*z - 2/7 + 0*z**2.
2*(z - 1)**3*(z + 1)/7
Factor 0*o**2 + 4/7*o**3 - 2/7*o**4 - 4/7*o + 2/7.
-2*(o - 1)**3*(o + 1)/7
Let p(k) be the first derivative of -5/2*k**4 + 1 + 8/5*k**5 + 2/3*k**3 + 0*k**2 + 0*k. Factor p(g).
2*g**2*(g - 1)*(4*g - 1)
Let m(h) be the first derivative of -3*h**4/16 + h**3/3 + h**2/8 - h/2 - 6. Factor m(b).
-(b - 1)**2*(3*b + 2)/4
Let v = 4 + 0. Factor 1 + 3*k**2 - 5*k + v*k - 4*k**2 + k**3.
(k - 1)**2*(k + 1)
Let l(i) be the third derivative of i**7/1260 - i**5/120 + i**4/72 + 6*i**2. Factor l(v).
v*(v - 1)**2*(v + 2)/6
Let j = 3099/4 - 771. Let h = 4 - j. Factor h*y**2 - 3/4*y + 1/2.
(y - 2)*(y - 1)/4
Let u(j) = 2*j**5 - 6*j**4 - 12*j**3 + 4*j**2 + 6*j + 2. Let x(l) = -l**5 + 7*l**4 + 12*l**3 - 4*l**2 - 5*l - 3. Let g(k) = 3*u(k) + 2*x(k). Solve g(h) = 0.
-1, 0, 1, 2
Let y(b) be the third derivative of b**8/2184 - b**7/455 - b**6/780 + 7*b**5/390 - 4*b**3/39 + 31*b**2. Solve y(n) = 0.
-1, 1, 2
Let j = -7 + 11. Let f(b) be the second derivative of 1/6*b**3 + 1/6*b**2 + 1/12*b**j + 1/60*b**5 + 0 + 2*b. Factor f(k).
(k + 1)**3/3
Let m be 6/((-2100)/(-707)) + (-2 - 0). Let n(q) be the second derivative of -1/5*q**3 + m*q**5 + 0 - 2*q + 0*q**4 - 2/5*q**2. Suppose n(k) = 0. Calculate k.
-1, 2
Determine i, given that 5/2*i**4 - 5/2*i**2 - 5*i**3 + 5*i + 0 = 0.
-1, 0, 1, 2
Find g such that 6*g**2 - 6*g + 4*g - g + 3*g**3 - 6 = 0.
-2, -1, 1
Let y(q) be the third derivative of q**5/20 - 2*q**4 + 32*q**3 - 39*q**2. Factor y(b).
3*(b - 8)**2
Let m(r) be the third derivative of r**7/8820 - r**5/420 + r**4/6 + r**2. Let h(u) be the second derivative of m(u). Factor h(g).
2*(g - 1)*(g + 1)/7
Let a be (3/(-6) - 0)*-4. Suppose 0*l + 2*l - 23 = -3*o, -3*l + a = -2*o. Factor 17*q**3 + 12*q**l + 6*q**2 + 7*q**3 - 3*q**3 - 3*q.
3*q*(q + 1)**2*(4*q - 1)
Factor -95 + 15 + 5*y**2 + 20 + 5*y.
5*(y - 3)*(y + 4)
Suppose 10 + 9 = n - 4*o, 4*n - o = 16. What is l in 10/9*l + 4/9 - 2/3*l**n - 8/9*l**2 = 0?
-2, -1/3, 1
Let x = -106 - -30. Let t = x + 382/5. Factor -2/5*l**4 + 2/5*l**2 + t*l**3 - 2/5*l + 0.
-2*l*(l - 1)**2*(l + 1)/5
Let -40*y**2 - 10*y**5 - 36*y**3 - 2*y - 14*y**4 - 6*y + 8*y**5 - 8*y = 0. Calculate y.
-2, -1, 0
Let p be 104/(-5)*102/(-17). Let g = 126 - p. What is t in g*t + 2/5*t**3 + 2/5 + 6/5*t**2 = 0?
-1
Let -3/8*x**2 - 9/8*x + 3/2 = 0. Calculate x.
-4, 1
Let u(y) be the first derivative of y**6/40 - y**5/10 + y**4/8 - y**2/2 - 5. Let j(b) be the second derivative of u(b). Let j(s) = 0. What is s?
0, 1
Factor -16*i**4 - 6*i**4 + 10*i**4 + 15*i**2 + 4*i**5 + i**2.
4*i**2*(i - 2)**2*(i + 1)
Let b(h) = -4*h - 1. Let l be b(-1). Let g(w) be the first derivative of 1/2*w - 3/8*w**2 - 3 + 1/12*w**l. Factor g(m).
(m - 2)*(m - 1)/4
What is h in 10/3*h**2 + 5/3*h**3 + 0 + 0*h = 0?
-2, 0
Let r = 11 - 59. Let q be (2/3)/(r/(-90)). Solve 1/2*n + 7/4*n**2 - 7/4*n**4 + 0 - q*n**5 + 3/4*n**3 = 0.
-1, -2/5, 0, 1
Factor 2/3*p**2 - 4/3 - 2/3*p.
2*(p - 2)*(p + 1)/3
Let f = 8/3 + -31/15. Factor f*n**2 + 0*n**3 - 3/5*n**4 + 0 + 0*n.
-3*n**2*(n - 1)*(n + 1)/5
Let m(b) be the third derivative of -b**5/100 + b**3/10 - 3*b**2. Determine c, given that m(c) = 0.
-1, 1
Suppose i - 5*i - 2*a = 16, 0 = -3*i + 5*a + 1. Let b(t) = 4*t**3 - 9*t**2 + 12*t - 11. Let c(u) = u**3 - u**2 - 1. Let h(p) = i*c(p) + b(p). Factor h(q).
(q - 2)**3
Let o be (3/9)/((-82)/(-24) + -3). Find q such that 2*q**2 + 0 - 8/5*q**3 - o*q + 2/5*q**4 = 0.
0, 1, 2
Suppose -b - 5*n = -24, 0 = n + 6 - 2. Suppose -i = 4*u - 144, -3*u - 4*i + 139 = b. Factor -u*c**2 - 4 - 13*c**2 - 4 + 5*c + 35*c.
-2*(5*c - 2)**2
Let q(n) be the first derivative of -4*n**5/15 - 2*n**4/3 + 4*n**3/3 + 8*n**2/3 - 16*n/3 - 3. Factor q(h).
-4*(h - 1)**2*(h + 2)**2/3
Let b be (-2)/10*104 - -4. Let f = -16 - b. Let -2/5*n**3 - 2/5*n + 0 + f*n**2 = 0. Calculate n.
0, 1
Let y(b) = -5*b**4 - 13*b**3 + 2*b**2 + 2. Let o(r) = -60*r**4 - 155*r**3 + 25*r**2 + 25. Let c(x) = -2*o(x) + 25*y(x). Factor c(f).
-5*f**3*(f + 3)
Let y = -61/2 - -31. Let u be 17/26 + (-6)/39. Factor u*s + 0 + y*s**2.
s*(s + 1)/2
Let j(g) = 14*g**2 + 8*g - 6. Let l(o) = -5*o**2 - 3*o + 2. Let b be 8/(-3) - (-2)/(-6). Let w(h) = b*j(h) - 8*l(h). Find x such that w(x) = 0.
-1, 1
Let k(r) be the second derivative of -2*r**6/15 + 4*r**5/5 - 2*r**4 + 8*r**3/3 - 2*r**2 + 20*r. Factor k(h).
-4*(h - 1)**4
Let q(v) = -v. Let m be q(-2). Suppose -1 = -u + 1. Suppose 2*r**2 - u*r - 2*r**m - 2*r**2 = 0. What is r?
-1, 0
Let v = -7 + 11. Suppose 0 = -2*y + 3*f - 6, 0 = -4*y - 5*f + 14 + 18. Factor 4*z**v - 2*z**4 + 8*z**2 - 9*z**y + z**3.
2*z**2*(z - 2)**2
Let x be (4/(-10))/(1/(-5)). Factor -3*y - y**x - 9 + 0*y**2 + 7.
-(y + 1)*(y + 2)
Factor -2/3 + 2/3*z**2 + 0*z.
2*(z - 1)*(z + 1)/3
What is p in 0*p + 2/7*p**5 + 4/7*p**4 + 0*p**2 + 2/7*p**3 + 0 = 0?
-1, 0
Let p be 3/(((-8)/2)/(-4)). Let n be p/(-6)*(-1 + 1). Factor n*t - 1/3*t**3 + 0 + 2/3*t**2.
-t**2*(t - 2)/3
Let s = -15 + 27. Let z = s + -9. Factor 2*h**z - 4/3*h**2 - 2/3*h + 0.
2*h*(h - 1)*(3*h + 1)/3
Let t(a) = a**3 + 1. Let r(q) = 4*q**4 + 13*q**3 + 12*q**2 + 4*q + 1. Let z(v) = -r(v) + t(v). Factor z(x).
-4*x*(x + 1)**3
Suppose 2*h - 4*v + 80 = 0, -3*v + 59 = -h + 17. Let c be -2 + (-3)/(h/32). Factor 0 + c*n**2 + 2*n**4 + 0*n + 2*n**3 + 2/3*n**5.
2*n**2*(n + 1)**3/3
Let g = -27 + 22. Let l = g - -7. Factor -3/5*y**l + 1/5*y + 2/5 + 1/5*y**4 - 1/5*y**3.
(y - 2)*(y - 1)*(y + 1)**2/5
Suppose q + 6 = 2*n, -5*q = n - 0*n + 8. Let y be (-3)/n - (-12)/8. Factor y*o**2 + 0*o**4 + 1/3*o**5 + 0 + 1/3*o - 2/3*o**3.
o*(o - 1)**2*(o + 1)**2/3
Let u be 4/(-14) - 37/(-7). Let -3*p**5 + 6*p**u + 12*p**4 - 3*p**3 - 12*p**4 = 0. What is p?
-1, 0, 1
Let x(p) = 7*p**2 + p - 8. Let w(j) = 8*j**2 + j - 9. Let m(u) = 6*w(u) - 7*x(u). Suppose m(i) = 0. What is i?
-2, 1
Suppose -3 = -v - 0*v. Find t, given that -3*t**2 + t - t + v*t = 0.
0, 1
Let i(r) be the second derivative of -2*r**7/21 + 4*r**6/5 - 13*r**5/5 + 4*r**4 - 8*r**3/3 - 5*r. Determine s so that i(s) = 0.
0, 1, 2
Let t(o) = 12*o**2 - o - 2. Let w be t(-2). Find m, given that 21*m**3 + w*m**2 + 85 - 85 + 12*m = 0.
-2, -2/7, 0
Let x be 23637/345 + 4/46. Factor x*l**4 + 76/5*l - 42*l**2 - 8/