et w(n) be the first derivative of -21/4*n**4 - 6*n + 21/2*n**a + 5 + 2*n**3. Solve w(b) = 0.
-1, 2/7, 1
Let n = -23 - -38. Suppose -4*m + 5 = -n. Factor 39*r**2 + 60*r**3 + m*r + r + 0*r.
3*r*(4*r + 1)*(5*r + 2)
Suppose 0 = 4*k + 6 + 6. Let m be (4 - 4 - -3) + k. Factor 0 + 1/2*w + m*w**2 - 1/2*w**3.
-w*(w - 1)*(w + 1)/2
Suppose 4*s - 7 = -39. Let v be -3 + 940/252 - s/(-28). Factor -8/9*j**2 - v - 10/9*j - 2/9*j**3.
-2*(j + 1)**2*(j + 2)/9
Let n = 59 + -10. Suppose 4*k - n = -1. Factor 36*v**2 + 3*v**3 + k*v + 3*v**3 + 9*v**3.
3*v*(v + 2)*(5*v + 2)
Let c(h) be the third derivative of h**7/210 + 7*h**6/120 + h**5/10 + 61*h**2. Suppose c(a) = 0. Calculate a.
-6, -1, 0
Let s = 1021 - 1019. Factor 2/17*q**s + 2/17 + 4/17*q.
2*(q + 1)**2/17
Suppose 7*a - 8*a = -6, a = -4*w + 18. Let 10/7*b**4 + 8/7*b - 22/7*b**2 - 8/7*b**w + 4/7*b**5 + 8/7 = 0. What is b?
-2, -1/2, 1
Suppose 4*d - 2*a = -0*a + 22, -2*a = -6*d + 30. Let f(p) be the second derivative of -3*p + 0 - 1/96*p**d + 0*p**2 - 1/48*p**3. Factor f(g).
-g*(g + 1)/8
Suppose 0 = -k + 4*r + 27, -2*k + 29 = 3*r - 6*r. Let h = k + -4. What is n in n - n**4 + 3*n**4 + 23*n + 13*n**h + 26*n**2 - n**3 + 8 = 0?
-2, -1
Let b(g) be the third derivative of -g**8/1512 - g**7/189 - g**6/540 + 13*g**5/270 + g**4/54 - 8*g**3/27 - 14*g**2 + 1. Determine y so that b(y) = 0.
-4, -2, -1, 1
Let v(x) be the third derivative of -x**8/336 + x**7/30 - x**6/15 - 4*x**5/15 - 3*x**2 + 2*x. Let v(m) = 0. Calculate m.
-1, 0, 4
Suppose -3*h = 2*h. Suppose h = -q + 5 - 2. Factor 2*x**4 - 9*x**2 + 3*x**q + 6*x**3 - 7*x**4 + 3*x + 2*x**4.
-3*x*(x - 1)**3
Factor 0 + 0*t + 58/7*t**3 - 2*t**2 - 8/7*t**4.
-2*t**2*(t - 7)*(4*t - 1)/7
Let o be (2/13)/((-3648)/(-156) + -23). Factor 24/5*y + o*y**3 + 16/5 + 12/5*y**2.
2*(y + 2)**3/5
Let a be 1414944/208 + (-1 + 0)*-4. Let c = a + -6802. Factor 40/13*g + 74/13*g**2 + c*g**3 + 18/13*g**4 + 8/13.
2*(g + 1)**2*(3*g + 2)**2/13
Let i = 42 + -40. Factor 2*o**3 - o**3 + 63*o**2 - 61*o**i.
o**2*(o + 2)
Determine u, given that 4/9*u**3 - 2/9*u**4 + 10/9*u**2 + 0 - 4/3*u = 0.
-2, 0, 1, 3
Let l(h) = -3*h + 9. Let o be l(1). Let w be 4/(-14)*(o - 7). Solve 0*t - 2/7 + w*t**2 = 0 for t.
-1, 1
Let v(h) = 6*h**3 + 8*h. Let t(b) be the third derivative of b**6/60 + b**4/8 - 14*b**2. Let y(f) = -14*t(f) + 5*v(f). Factor y(u).
2*u*(u - 1)*(u + 1)
What is n in 15/7*n**2 + 0 + 9/7*n**3 + n + 1/7*n**4 = 0?
-7, -1, 0
Let r be 5 - (0 + 3 - (13 - 10)). Suppose -4*l = 2*l - r*l. Let 0 + l*g**2 + 3/5*g**3 - 3/5*g = 0. What is g?
-1, 0, 1
Let b be -110*2/(-36) + 17/17 - 6. Let 0 + 4/3*p + 2/9*p**3 - b*p**2 = 0. Calculate p.
0, 2, 3
Suppose 3410 = 2*m + 8*m. Let u = m - 2383/7. Find s, given that -2/7*s**2 - 6/7*s**5 - u*s + 2/7*s**4 + 10/7*s**3 + 0 = 0.
-1, -2/3, 0, 1
Let y(n) = -1. Let q(c) = -1 - 5*c + 4 - 4*c + 0 - 3*c**2. Let p(r) = q(r) + 9*y(r). Factor p(d).
-3*(d + 1)*(d + 2)
Let d be 6/(-21) + (-6)/(-21). Suppose -3*v = -6 - d. Factor -93*i + 91*i - 5 + 5 + v*i**2.
2*i*(i - 1)
Let w(r) be the third derivative of 1/33*r**3 - 1/165*r**5 - 1/132*r**4 + 0 - 1/1848*r**8 + 12*r**2 + 1/330*r**6 + 1/1155*r**7 + 0*r. Factor w(v).
-2*(v - 1)**3*(v + 1)**2/11
Let h be (4/(-9))/((-42)/(-84)*1/(-3)). Determine c, given that 0 + 6*c**3 - 8*c**2 + h*c = 0.
0, 2/3
Let v(u) be the third derivative of u**6/30 - u**5/5 + 8*u**3/3 + 61*u**2. Determine q so that v(q) = 0.
-1, 2
Let s be (100/16)/(497/(-378) + (-8)/(-6)). Determine l, given that -90*l**2 + 0 + 6*l + s*l**3 = 0.
0, 2/15
Let d(q) = 11*q**3 + q**2 - 2*q. Let i(f) = -f**3. Let l(a) = -d(a) - 5*i(a). Factor l(p).
-p*(2*p - 1)*(3*p + 2)
Let d(k) be the third derivative of k**8/840 - k**6/180 + 7*k**3/2 - 7*k**2. Let i(m) be the first derivative of d(m). Factor i(a).
2*a**2*(a - 1)*(a + 1)
Let t be (-147)/98*(5 + -1). Let y be -2 + (-1)/(t/42). Factor -4/5*c**2 + 2*c**3 - 8/5*c**4 + 0 + 0*c + 2/5*c**y.
2*c**2*(c - 2)*(c - 1)**2/5
Find o such that -3/5*o**3 + 3/5*o - 6/5*o**2 + 6/5 = 0.
-2, -1, 1
Suppose 452*g - 8*g**4 - 54*g**3 + 2*g**5 + 92*g**2 + 48*g**2 - 52*g = 0. What is g?
-4, -2, 0, 5
Let x(t) be the first derivative of 1/300*t**5 + 0*t**3 + 1/60*t**4 + 1 + 3/2*t**2 + 0*t. Let u(b) be the second derivative of x(b). Factor u(c).
c*(c + 2)/5
Determine t, given that 0 + 7/8*t**4 + 7/2*t - 9*t**2 - 93/8*t**3 = 0.
-1, 0, 2/7, 14
Factor -88*r + 43*r - 8*r**2 - 29 - 19*r**2 - 25 - 204*r.
-3*(r + 9)*(9*r + 2)
Let y(m) = m**4 - 3*m**2 + m + 1. Let p(w) = 2*w**4 - 9*w**3 - 20*w**2 + 24*w + 3. Let l(v) = 2*p(v) - 6*y(v). Solve l(t) = 0.
-7, -3, 0, 1
Suppose -3*p - 14*p + 34 = 0. Let s(n) be the first derivative of -3 + 1/10*n**5 - 3/4*n**p + 3/8*n**4 + 1/6*n**3 - n. Find t such that s(t) = 0.
-2, -1, 1
Let o = 18 - 21. Let u(a) = -40*a**3 - 160*a**2 - 120*a + 25. Let r(v) = -5*v**3 - 20*v**2 - 15*v + 3. Let c(k) = o*u(k) + 25*r(k). Solve c(f) = 0.
-3, -1, 0
Factor 7/2*l**3 + 0 - 15/4*l**2 + l.
l*(2*l - 1)*(7*l - 4)/4
Let u(n) = 49*n**4 - 10*n**3 - 117*n**2 + 95*n - 17. Let r(l) = -16*l**4 + 3*l**3 + 39*l**2 - 32*l + 6. Let d(g) = 21*r(g) + 6*u(g). Solve d(y) = 0.
-2, 1/2, 4/7, 1
Find u, given that 92*u**3 + 78*u**3 - 140*u**2 - 36*u - 154*u**3 = 0.
-1/4, 0, 9
Let y(n) be the third derivative of -1/180*n**6 + 0 + 0*n**3 + 0*n + 0*n**5 - 4*n**2 - 1/504*n**8 + 2/315*n**7 + 0*n**4. Let y(d) = 0. What is d?
0, 1
Let m(a) = -a**3 + 3*a**2 - a. Let t be m(2). Let -15*o**t + 27*o - 2 + 24*o**3 + 21*o**4 - 3 - 51*o**3 - 1 = 0. What is o?
-1, 2/7, 1
Suppose 0 + 12 = 2*f + c, f + 5*c = 24. Solve 4 - 4 + 9*u**3 - 12*u + 3*u**f = 0 for u.
-2, 0, 1
Suppose -54 = -19*u + u. Let l(z) be the first derivative of 1/9*z**4 + 2/9*z - 2/9*z**u + 0*z**2 - 1. Factor l(n).
2*(n - 1)**2*(2*n + 1)/9
Let v(p) = 12*p**2 - 86*p + 104. Let o(k) = -k**2 - k - 1. Let r(i) = 10*o(i) + v(i). Suppose r(m) = 0. What is m?
1, 47
Let q = -12 - -14. Factor q*u**3 - 4*u**3 - 88*u**2 + 98*u**2 - 2*u**4 - 6*u.
-2*u*(u - 1)**2*(u + 3)
Let u = -25704 + 25704. Suppose 4/5*c**5 + 16/5*c**2 + u - 16/5*c**4 + 8/5*c**3 - 12/5*c = 0. What is c?
-1, 0, 1, 3
Let a(r) be the first derivative of -3*r + 9 + 6 - 3 - r**3 + 2*r**3. Factor a(j).
3*(j - 1)*(j + 1)
Let i(p) be the third derivative of -8*p**7/315 + 4*p**6/45 - p**5/10 + p**4/18 - p**3 + 26*p**2. Let u(j) be the first derivative of i(j). Factor u(k).
-4*(k - 1)*(4*k - 1)**2/3
Let y(s) = 5 + s - 10 + 5 - s**2. Let l(v) = -14*v + 26*v**2 - v - 8*v**2. Let r(g) = -l(g) - 15*y(g). Factor r(b).
-3*b**2
Let f = -21 + 26. Suppose 2*h - 18 = -2*q, -h + f*q - 23 = -8. Solve -2/3*s**4 + 2/3*s**2 + 1/3*s - 1/3*s**h + 0*s**3 + 0 = 0 for s.
-1, 0, 1
Let t(f) = -10*f**2 + 10. Let o be t(-1). Let x(v) be the first derivative of v**5 - 5*v**2 - 5*v + 2 + o*v**3 + 5/2*v**4. Solve x(r) = 0.
-1, 1
Let a(u) be the third derivative of u**6/600 - u**5/300 - u**4/12 - 4*u**3/15 - 54*u**2. Find r, given that a(r) = 0.
-2, -1, 4
Factor -51/2*q - 37*q**2 - 23*q**3 + 1/2*q**5 - 9/2*q**4 - 13/2.
(q - 13)*(q + 1)**4/2
Let n = 2 + -7. Let r = 8 + n. Factor 9*t**3 + 19*t + r*t**4 + 3*t**2 - 22*t - 6*t - 2 - 4.
3*(t - 1)*(t + 1)**2*(t + 2)
Let s be (4 + (1 - -15))*(-11)/(-286). Factor 2/13*v**2 - s + 8/13*v.
2*(v - 1)*(v + 5)/13
Let b(h) be the first derivative of -h**5/5 + 3*h**4/2 - 4*h**3 + 5*h**2 - 3*h + 201. Solve b(z) = 0 for z.
1, 3
Suppose -3*c + 30 = -5*d, 2*c + 2 = -d - 3*d. Solve -h**c + 0*h**4 - 597*h**2 + 598*h**2 - h**4 + h**3 = 0.
-1, 0, 1
Let b(q) be the third derivative of q**6/240 + q**5/40 - 5*q**2. Determine k so that b(k) = 0.
-3, 0
Let s(h) be the third derivative of -h**6/120 - 7*h**5/60 - h**4/12 + 20*h**3/3 + 255*h**2. Factor s(t).
-(t - 2)*(t + 4)*(t + 5)
Let n = -49 - -51. Let w**3 - 55 - n*w + 3*w**2 - 2*w**3 + 55 = 0. Calculate w.
0, 1, 2
Let n be ((-69)/5)/1*-5. Suppose -3*c + 0 = -9. Suppose 0*u + 3*u + n*u**2 - 3*u**3 - c*u**4 - 66*u**2 = 0. What is u?
-1, 0, 1
Let q be -3*10/255 - (-70)/306. Let y(z) be the first derivative of 1/15*z**5 + q*z**3 + 0*z**2 - 1/6*z**4 + 0*z - 1. Solve y(w) = 0 for w.
0, 1
Let l(s) = s**3 + 9*s**2 + s - 3. Let y be l(-8). Let a = y + -50. Suppose 0*m**4 + 16/11*m**2 - 12/11*m**a + 2/11*m**5 + 0 - 6/11*m = 0. Calculate m.
-3, 0, 1
Let u(m) be the first derivative of -m**3/7 + 51*m**2/14 - 48*m/7 + 283. Factor u(k).
-3*(k - 16)*(k