+ 3)**2
Let y(j) be the second derivative of -j**6/180 + j**5/15 - j**4/3 - 5*j**3/6 + 9*j. Let o(q) be the second derivative of y(q). Let o(z) = 0. What is z?
2
Let x(t) = t**3 - 1. Let z(g) = 7*g**3 - 7. Let i(n) = 6*x(n) - z(n). Let w(q) be the first derivative of i(q). Let w(c) = 0. What is c?
0
Let x = -31/12 - -11/4. Let i(k) be the first derivative of 0*k**2 - 1/4*k**4 + 0*k**5 - 1 + x*k**6 + 0*k**3 + 0*k. Factor i(u).
u**3*(u - 1)*(u + 1)
Suppose 2 = -5*j + 22. Let u = -50 - -152/3. Determine k so that 0*k - 4/3*k**j - 2/3*k**5 + 0 - u*k**3 + 0*k**2 = 0.
-1, 0
Let y(c) be the second derivative of c**9/3780 + c**8/840 + c**7/630 - c**4/12 - 6*c. Let d(i) be the third derivative of y(i). Let d(w) = 0. Calculate w.
-1, 0
Let y(s) be the second derivative of -s**6/120 + s**5/5 - 2*s**4 + 32*s**3/3 - 32*s**2 + 29*s. Factor y(b).
-(b - 4)**4/4
Let f(x) be the second derivative of 5*x**4/12 - x**3/9 - x**2/6 + 4*x. Solve f(t) = 0.
-1/5, 1/3
Let h be 3 - 2/(-3)*(-18)/(-12). Find y such that -2/5*y + 2/5*y**3 + 0 + 2/5*y**h - 2/5*y**2 = 0.
-1, 0, 1
Suppose 0 = -d - 1 + 7. Let q be -8*((-3)/d + 0). Let 22*g**q + 2*g**5 - 22*g**4 - 4*g**3 + 2*g = 0. What is g?
-1, 0, 1
Factor 9*r - 3*r**5 - 6*r**3 - 5*r**4 + 0*r**4 - 4*r**4 + 6*r**2 + 3 + 0*r**2.
-3*(r - 1)*(r + 1)**4
Let t = -161 + 91. Let d be (-9)/21 - 58/t. Factor -2/5*j + d*j**2 + 0.
2*j*(j - 1)/5
Let o(q) be the second derivative of q**6/780 - q**4/156 - 4*q**2 - 10*q. Let z(y) be the first derivative of o(y). Factor z(k).
2*k*(k - 1)*(k + 1)/13
Let i(g) be the first derivative of g**4/4 - 4*g**3/3 - g**2/2 + 4*g + 39. Let i(j) = 0. What is j?
-1, 1, 4
Let j(a) be the first derivative of 2 - 2/3*a**3 + 0*a - 2/5*a**5 + 0*a**2 + a**4. Let j(g) = 0. What is g?
0, 1
Let l = 18901/70 + -270. Let a(m) be the second derivative of -l*m**5 + 0*m**2 + m + 1/21*m**4 - 1/21*m**3 + 0. Factor a(f).
-2*f*(f - 1)**2/7
Let b(k) be the third derivative of 0 + 1/140*k**7 - 1/16*k**4 - 4*k**2 + 0*k**3 + 0*k + 3/40*k**5 - 3/80*k**6. Factor b(s).
3*s*(s - 1)**3/2
Suppose 0 = -5*r + 5, -o + 0*o = 3*r - 5. Let k be -1*((-24)/10 + o). Let 0 + 6/5*f**3 + k*f**2 + 0*f + 2/5*f**5 + 6/5*f**4 = 0. Calculate f.
-1, 0
Suppose 20*m**4 + 23/3*m**3 - 12*m**5 + 0*m + 0 + 2/3*m**2 = 0. What is m?
-1/6, 0, 2
Let s be 2964/(-880) + 4/(-22). Let w = s + 19/5. Find h, given that w*h**2 + 1/2 + 3/4*h = 0.
-2, -1
Let w = 1402/5 + -280. Factor -w + 0*u + 2/5*u**2.
2*(u - 1)*(u + 1)/5
Let n(a) be the third derivative of a**8/84 + 2*a**7/105 + 19*a**2. Suppose n(g) = 0. Calculate g.
-1, 0
Let v(m) be the second derivative of 2*m**7/21 - 4*m**6/15 - m**5/5 + 2*m**4/3 + 3*m. Factor v(g).
4*g**2*(g - 2)*(g - 1)*(g + 1)
Let s be -1 + (222/(-15))/(-2). Determine i so that 0 + s*i**4 - 48/5*i**3 - 6*i**2 - 4/5*i = 0.
-1/4, 0, 2
Let k be (-1)/(-3) + (-4)/(-12). Determine i so that 2/3 - 2/3*i - k*i**2 + 2/3*i**3 = 0.
-1, 1
Suppose 0*c = -3*c. Suppose -a + 0*a = c. Factor 3 + 2*q**2 + a*q**2 - 3 - 2*q.
2*q*(q - 1)
Let -85/4*u + 60*u**2 - 45/4*u**5 + 95/2*u**4 - 155/2*u**3 + 5/2 = 0. Calculate u.
2/9, 1
Let p be 0/((-22)/99 + (-40)/(-18)). Factor -2/11*j**2 + 2/11*j + p + 2/11*j**4 - 2/11*j**3.
2*j*(j - 1)**2*(j + 1)/11
Suppose -17*t = 56*t - 146. Factor 0 - 8/7*a - 2/7*a**t.
-2*a*(a + 4)/7
Let w = -3 - -7. Let x = -4 + 6. Find j such that x*j**3 - j**w - j - 3*j**3 + j**2 + 2*j**3 = 0.
-1, 0, 1
Factor 5*m - 6 - 17*m + 3*m - 3*m**2 + 0*m.
-3*(m + 1)*(m + 2)
Let l be 2/10 + (-14)/84. Let x(k) be the second derivative of 0 + 1/50*k**5 - 1/15*k**3 - l*k**4 + k + 1/5*k**2. Factor x(m).
2*(m - 1)**2*(m + 1)/5
Let r = -158 - -160. Solve 0 + 2/9*g - 2/9*g**3 + 2/9*g**4 - 2/9*g**r = 0 for g.
-1, 0, 1
Let r(v) = -v**3 + 4*v**2 + 2*v - 6. Suppose -4*w + 22 = -y - 2*y, -5*w - 4*y = -12. Let k be r(w). Factor -2 - c**3 + 2*c**k - c + 3*c - c**3.
-2*(c - 1)**2*(c + 1)
Factor 0*i**3 + 4/7*i**2 - 3/7*i**4 - 1/7*i**5 + 0*i + 0.
-i**2*(i - 1)*(i + 2)**2/7
Let g(a) = a**5 + a**3 - a**2 + a. Let l(y) = 4*y**5 - 5*y**4 + 11*y**3 - 7*y**2 + 3*y. Let d(p) = 3*g(p) - l(p). Factor d(i).
-i**2*(i - 2)**2*(i - 1)
Let u(y) = 10*y**4 - 8*y**3 + 10*y**2 - 14*y - 9. Let p(n) = -n**4 + n**3 - n**2 + n + 1. Let o(d) = 44*p(d) + 4*u(d). Suppose o(v) = 0. Calculate v.
-1, 1, 2
Let q(a) be the second derivative of -3*a + 0 + 5/4*a**4 + 3/2*a**3 - 3*a**2. Find m, given that q(m) = 0.
-1, 2/5
Let v be (8/10)/((-6)/(-15)). Suppose 0 = 2*q - 6 + v. Determine g so that q*g**3 + 3*g + 0*g - 5*g = 0.
-1, 0, 1
Find d such that -3*d + 1/3*d**4 + 0 + 5/3*d**3 + d**2 = 0.
-3, 0, 1
Let c(i) = -5*i + 16. Let m be c(9). Let t = -259/9 - m. Determine k, given that -2/9*k**2 - t + 4/9*k = 0.
1
Let g(r) = -2*r - 6. Let l be g(-6). Suppose -8 = -5*y - 2*f, -f = 4*y - l*f - 13. Factor 2*j**2 + j**2 - j**2 - y.
2*(j - 1)*(j + 1)
Let u(m) = -2*m + 32. Let c be u(15). Let a(w) be the first derivative of -2 - 4*w - 1/3*w**3 - 2*w**c. Factor a(z).
-(z + 2)**2
Let s(m) = -m**3 + 6*m**2 - 6*m + 7. Let k be s(5). Let x be 0 - -1 - (k - 4). Solve -1 + 10*w**5 + 57/2*w**4 + 5/2*w**2 - 9/2*w + 49/2*w**x = 0 for w.
-1, -1/4, 2/5
Factor 5*f**5 - 2*f**3 - 19*f**3 - 10*f**4 + 40*f**2 + f**3.
5*f**2*(f - 2)**2*(f + 2)
Let q = 49 - 47. Factor 0 + 0*f**3 + 1/2*f**4 + 0*f + 0*f**q.
f**4/2
Determine w so that -12/13*w**2 + 0 - 10/13*w - 2/13*w**3 = 0.
-5, -1, 0
Let i(f) = 3*f**5 + 6*f**2 + 3*f. Let t(l) = l**4 + l**3 + l**2 + l. Let x(r) = -i(r) + 3*t(r). Find s such that x(s) = 0.
-1, 0, 1
Let l(g) = -4*g**5 - 2*g**4 - 2. Let j(k) = -5*k**5 - k**4 + k**3 - 3. Let t(n) = -4*j(n) + 6*l(n). Solve t(a) = 0 for a.
-1, 0
What is j in 68*j**3 - 68*j**3 - 3*j**4 + 0*j**4 = 0?
0
Let d(w) = -20*w**4 - 15*w**3 + 15*w - 5. Let s(l) = -l**4 - l**3 + l. Let y(o) = -d(o) + 25*s(o). Factor y(u).
-5*(u - 1)*(u + 1)**3
Let a(r) be the second derivative of -r**7/189 + r**5/30 - r**4/27 - 22*r. Factor a(l).
-2*l**2*(l - 1)**2*(l + 2)/9
Let q(l) be the third derivative of l**2 - 7/360*l**6 + 0 + 0*l**3 + 1/36*l**5 + 0*l + 1/36*l**4. Factor q(p).
-p*(p - 1)*(7*p + 2)/3
Let n(r) be the third derivative of -r**6/480 + r**5/60 - 5*r**4/96 + r**3/12 - 20*r**2. Let n(w) = 0. What is w?
1, 2
Let y be (3/6)/((-1)/(-4)). Factor -3 + 0*s + s - 1 + s + 2*s**y.
2*(s - 1)*(s + 2)
Let d(n) be the third derivative of -n**6/33 + 23*n**5/330 - n**4/132 - 2*n**3/33 - 10*n**2. Determine z so that d(z) = 0.
-1/4, 2/5, 1
Let s = 197 - 2557/13. Suppose -2/13*p**2 - 2/13*p + s = 0. What is p?
-2, 1
Suppose 0 + 0*i - 1/3*i**3 - 2/3*i**2 = 0. Calculate i.
-2, 0
Suppose 0 = 4*j, 2*v - 4*v + 5*j + 2 = 0. Let a be (2 - 7)/(v/(-1)). Solve 2*w + w + a*w + w**2 - 6*w = 0 for w.
-2, 0
Let i be 122/60 + -8 + 6. Let l(y) be the third derivative of 0*y - 1/80*y**6 - 1/48*y**4 + 0*y**3 + 0 - i*y**5 + y**2. Find r such that l(r) = 0.
-1, -1/3, 0
Let a(c) be the third derivative of c**6/480 - c**5/240 + 2*c**2 + 4*c. Solve a(s) = 0 for s.
0, 1
Let b(y) be the second derivative of y**5/80 + y**4/12 + y. Let b(j) = 0. What is j?
-4, 0
Let o(u) be the second derivative of 0 - 9/2*u**3 - 3/4*u**4 + 4*u + 3/5*u**5 - 3*u**2. Factor o(t).
3*(t - 2)*(t + 1)*(4*t + 1)
Let k = 36 + -30. Let g be 2/6*k/9. Determine l, given that -4/9*l - 2/9 - g*l**2 = 0.
-1
Factor 6/11*h**3 + 2/11 - 10/11*h**2 + 2/11*h.
2*(h - 1)**2*(3*h + 1)/11
Let l(t) = t**2 - t. Let h be l(2). Suppose 2*x - x - h = 0. Factor 8*y**3 + 4*y**2 - 17*y**2 - y**2 + 4*y + x.
2*(y - 1)**2*(4*y + 1)
Suppose 0 = 53*k - 60*k + 140. Let 138/7*r**2 - k*r**3 + 50/7*r**4 + 8/7 - 8*r = 0. Calculate r.
2/5, 1
Suppose u + 23 = 2*p + 4*u, 4*p - 3*u = 1. Factor 2/3*b**p - 1/3*b**5 + 0*b**3 + 0 + 1/3*b - 2/3*b**2.
-b*(b - 1)**3*(b + 1)/3
Let d be (6 + -2 + -4)/2. Solve d - 2/5*i - 4/5*i**2 = 0.
-1/2, 0
Let x be (-5 + 4)/(-1 + 2) + 2. Factor -1/4*p**4 - p + 3/4*p**2 - x + 1/2*p**3.
-(p - 2)**2*(p + 1)**2/4
Factor -5/6*a**5 - 5/6*a + 5/3*a**3 + 5/6*a**4 - 5/3*a**2 + 5/6.
-5*(a - 1)**3*(a + 1)**2/6
Let r(b) be the first derivative of b**5 - 5*b**4/4 - 5*b**3/3 + 5*b**2/2 - 1. Factor r(u).
5*u*(u - 1)**2*(u + 1)
Let u(p) = -p**4 - p**3 - p**2 + p. Let s(t) = 6*t**4 + 6*t**3 + 3*t**2 - 3*t. Let r(v) = s(v) + 3*u(v). Suppose r(z) = 0. Calculate z.
-1, 0
Let z(g) be the second derivative of -g**7/105 + g**6/75 + g**5/50 - g**4/30 - 33