(b - 1)*(3*b - 1)/5
Let n(d) = d**3 - 12*d**2 - 13*d + 3. Let k be n(13). Determine j so that -2*j - 4*j**2 - j**k - 3*j**3 + 9*j**3 + j**3 = 0.
-1/3, 0, 1
Let o be -3 - (5 + -5 + (-12 - -1)). Factor -4*h + o*h**2 + 0*h + 7*h**3 - 9*h**4 + 8*h**3 + 0*h**2.
-h*(h - 2)*(3*h - 1)*(3*h + 2)
Suppose 30 = 5*q + 2*k, -7 = 2*q - k - 10. Let z(r) be the second derivative of 0 + 1/18*r**q - 4/9*r**3 - 6*r + r**2. Suppose z(b) = 0. Calculate b.
1, 3
Solve 82*r**2 - r**3 - 37*r**2 - 31*r**2 = 0.
0, 14
Let g(a) be the second derivative of -a**5/5 - 4*a**4/3 + 10*a**3 + 36*a**2 + 201*a. Factor g(x).
-4*(x - 3)*(x + 1)*(x + 6)
Let o(v) be the second derivative of 53*v**4/18 - 55*v**3/9 + 2*v**2/3 + 15*v - 4. Factor o(z).
2*(z - 1)*(53*z - 2)/3
Let u(z) be the first derivative of -z**3/30 - 3*z**2/10 + 7*z/10 + 108. Factor u(a).
-(a - 1)*(a + 7)/10
Let 392/3 + 92/3*c**4 - 8/3*c**5 - 308/3*c - 116/3*c**3 - 916/3*c**2 = 0. Calculate c.
-2, -1, 1/2, 7
Let a = 4726 - 4724. Solve -16/9 - 4/3*w**a + 2/9*w**3 + 8/3*w = 0 for w.
2
Suppose -4*q - q = 0. Let t be 42/98 - 1*(-1)/14. Find g such that 1/2*g**2 - t + q*g = 0.
-1, 1
Let q(m) be the third derivative of 0*m**5 - 1/30*m**6 + 11*m**2 + 0 + 0*m**3 + 0*m - 4/105*m**7 + 0*m**4 + 5/336*m**8. Factor q(j).
j**3*(j - 2)*(5*j + 2)
Let z(w) be the second derivative of 63/4*w**5 - 25/6*w**3 + 0 - 22*w + 10*w**4 - 5*w**2. Find y such that z(y) = 0.
-1/3, 2/7
Let a(r) be the second derivative of r**7/168 - r**6/4 - 241*r**5/80 - 323*r**4/24 - 61*r**3/2 - 37*r**2 + 625*r. Factor a(g).
(g - 37)*(g + 1)*(g + 2)**3/4
Let g(b) be the first derivative of -5*b**4/12 + 5*b**3/6 - 28*b - 41. Let y(m) be the first derivative of g(m). Let y(j) = 0. Calculate j.
0, 1
Let w = 8634 + -8632. Determine f, given that -27/2*f**w - 9*f**3 - 3/2*f**4 + 0*f + 0 = 0.
-3, 0
Let d(q) = q**4 + 36*q**3 + 67*q**2 + 60*q + 23. Let a(y) = -y**4 - 54*y**3 - 100*y**2 - 90*y - 35. Let u(s) = 5*a(s) + 8*d(s). Factor u(v).
3*(v + 1)**3*(v + 3)
Let h be -39 + (-1)/((2/(-4))/(-1)). Let u = h - -45. Find o, given that 2/13*o**5 + 0*o**2 + 0*o**3 + 0*o - 4/13*o**u + 0 = 0.
0, 2
Let c(n) be the second derivative of -n**7/70 - n**6/20 + n**5/20 + n**4/4 - 19*n**2/2 - 14*n. Let y(h) be the first derivative of c(h). Solve y(k) = 0.
-2, -1, 0, 1
Solve -1/2*o**3 + 13/2*o**2 + 0 + 15*o = 0.
-2, 0, 15
Let g(x) be the first derivative of 3*x**3 - 33*x**2 + 21*x + 16. What is h in g(h) = 0?
1/3, 7
Let q(x) be the first derivative of 1/2*x**4 - 2*x**3 - x**2 + 13 + 4*x + 2/5*x**5. Factor q(m).
2*(m - 1)**2*(m + 1)*(m + 2)
Let l(d) be the first derivative of d**6/60 + 3*d**5/40 + d**4/8 + d**3/12 + d + 7. Let m(k) be the first derivative of l(k). Let m(g) = 0. Calculate g.
-1, 0
Let q(r) = 3*r**2 - 8*r + 18. Let i = 2 - 5. Let a(b) = -4*b**2 + 8*b - 19. Let x(c) = i*q(c) - 2*a(c). Factor x(g).
-(g - 4)**2
Let f(q) be the second derivative of -q**4/6 + 14*q**3/3 - 49*q**2 + 2*q + 118. Find x such that f(x) = 0.
7
Suppose 3*w = 5*d, 226*w - 5*d = 225*w. What is m in 0 + w*m + 8/11*m**5 + 4/11*m**2 + 6/11*m**4 - 18/11*m**3 = 0?
-2, 0, 1/4, 1
Let b(w) be the first derivative of 4/7*w + 11/28*w**4 - 31/21*w**3 + 8 + 8/7*w**2. Determine k so that b(k) = 0.
-2/11, 1, 2
Let j be 611/1692 + 2/(-6). Let u(n) be the second derivative of -1/72*n**4 - j*n**3 + 0 + 1/6*n**2 - 2*n. Factor u(p).
-(p - 1)*(p + 2)/6
Let z be (5 - (-10)/(-36)*21)*(1 + -16). Solve -10*p - 2 - z*p**2 = 0 for p.
-2/5
Let z = 19/51 + 5/17. Let u(h) be the first derivative of -6 + 7/6*h**2 + z*h - 4/9*h**3. Factor u(n).
-(n - 2)*(4*n + 1)/3
Let i = 229/396 + -23/44. Let w(p) be the second derivative of -i*p**4 + 2*p + 0*p**3 + 0 + 0*p**2. Factor w(d).
-2*d**2/3
Let b(v) be the first derivative of -4/39*v**3 - 2/13*v + 1 + 3/13*v**2. Suppose b(m) = 0. What is m?
1/2, 1
Let p(h) be the third derivative of -h**8/1120 - h**7/280 + h**5/40 + h**4/16 - 11*h**3/6 + 6*h**2. Let t(i) be the first derivative of p(i). Factor t(z).
-3*(z - 1)*(z + 1)**3/2
Factor 0*s - 33/8*s**3 - 3/2*s**4 - 9/4*s**2 + 0 + 3/8*s**5.
3*s**2*(s - 6)*(s + 1)**2/8
Let z be -2*(2 - 42/12). Suppose 2*y - 5*o = 11, 3*y - 3*o - 15 = -z. Solve y*h**3 - 9/2*h**2 + 3 - 9/2*h = 0 for h.
-1, 1/2, 2
Let p(x) be the third derivative of -x**8/84 + 634*x**7/105 - 12797*x**6/15 + 14978*x**5/3 - 74261*x**4/6 + 49298*x**3/3 + x**2 - 829*x. Factor p(t).
-4*(t - 157)**2*(t - 1)**3
Let l(d) be the second derivative of 0 + 10/3*d**3 + 10*d + 5/2*d**2 + 1/2*d**5 + 25/12*d**4. Factor l(a).
5*(a + 1)**2*(2*a + 1)
Let k(b) = -b**2 - 96*b - 453. Let t be k(-5). Suppose -w + 15 = -3*l + 4*w, -l = 2*w - 6. Suppose l + 2/3*u**t + 2/3*u = 0. What is u?
-1, 0
Let k(c) be the first derivative of -5*c**3/9 + 35*c**2 - 400*c/3 - 310. Factor k(v).
-5*(v - 40)*(v - 2)/3
Suppose -8*c + 3*c**2 - 264*c**4 + 3*c**2 + 258*c**4 + 10*c**3 - 2*c**5 = 0. Calculate c.
-4, -1, 0, 1
Factor 1728/5 + 36/5*f**2 - 432/5*f - 1/5*f**3.
-(f - 12)**3/5
Let y = 2739 + -2735. Factor 6/11*c**3 + 0 + 4/11*c - 2/11*c**5 - 2/11*c**y + 10/11*c**2.
-2*c*(c - 2)*(c + 1)**3/11
Let x be 366/(-610) + 1*3. Factor 12/5*s + x + 3/5*s**2.
3*(s + 2)**2/5
Let w = -583/6 - -3920/39. Let g = -24/13 + w. Find x such that 3/2*x**2 - 9/2*x**3 + 9/2*x + g - 3*x**4 = 0.
-1, -1/2, 1
Let w(t) = 13*t + 8. Let k be w(4). Let q be (-8)/k + 15/(-9) + 2. Determine m, given that 0*m + q*m**5 + 1/5*m**2 - 1/5*m**3 + 0 - 1/5*m**4 = 0.
-1, 0, 1
Let n(j) = -4*j**3 + 38*j**2 + 94*j + 58. Let i(d) = -4*d**3 + 39*d**2 + 95*d + 57. Let g(v) = 6*i(v) - 5*n(v). Factor g(y).
-4*(y - 13)*(y + 1)**2
Let l = 58 - 55. Let a be (-87)/(-153) + l/(-9). Suppose -a*r**3 - 2/17*r**4 - 8/17*r + 0 + 14/17*r**2 = 0. What is r?
-4, 0, 1
Factor -8*q**2 + 3*q**5 - q**2 - 3*q**4 - 3*q**3 + q**2 + 11*q**2.
3*q**2*(q - 1)**2*(q + 1)
Let g(s) be the second derivative of 2*s**6/3 + 126*s**5/5 + 3289*s**4/15 - 5712*s**3/5 + 9248*s**2/5 - 15*s + 1. Factor g(i).
4*(i - 1)**2*(5*i + 68)**2/5
Let p(r) be the first derivative of -r**3/27 - r**2/9 + 8*r/9 + 62. Find m such that p(m) = 0.
-4, 2
Let -7/4*q**4 + 0*q**2 + 0 + 0*q + 1/2*q**3 = 0. What is q?
0, 2/7
Let j(i) = 2*i - 3. Let k be j(2). Suppose 4*g + k = 9. Determine d, given that -2 - d**g + 4*d**2 - 5*d**2 + 4*d = 0.
1
Let g(t) = -6*t**5 + 3*t**3 - 3*t**2 + 3. Let a(i) = 0 - i**4 - 64*i**5 - 4 - 3*i**3 - i**3 + 4*i**2 + 71*i**5. Let l(q) = -3*a(q) - 4*g(q). Factor l(d).
3*d**4*(d + 1)
Let q(u) be the second derivative of u**5/90 - 2*u**4/27 + 5*u**3/27 - 2*u**2/9 + 123*u + 2. Find r such that q(r) = 0.
1, 2
Let u(i) = i**3 + 4*i**2 - i - 1. Let n be u(-4). Let g(y) be the first derivative of 24*y**2 - y**n - 3*y**3 - 6 - 30*y**2 - 3*y. Factor g(d).
-3*(2*d + 1)**2
Let k(j) be the first derivative of -3*j**5/20 - 33*j**4/16 - 19*j**3/4 - 27*j**2/8 - 57. Determine q, given that k(q) = 0.
-9, -1, 0
Suppose v = 2*r - 3 - 0, 5*v - 18 = -r. Suppose 10 = -v*a + 8*a. Factor -i + 4*i**2 - a*i**5 + 3*i**5 - 4*i**2 - 2*i**4 + 2*i**2.
i*(i - 1)**3*(i + 1)
Let o be ((-3)/6)/(2/16). Let r = o + 6. Factor u**r + u**2 + 4*u - u**2 - 3*u.
u*(u + 1)
Let l = -977/7 + 140. Let n be 4/22 - 12/66. Find i, given that 0 + n*i - l*i**2 = 0.
0
Suppose -14*u + 29*u = -15. Let v be (((-8)/10)/u)/((-4)/(-6)). Let v - 12*c**3 + 99/5*c**2 - 9*c = 0. Calculate c.
1/4, 2/5, 1
Suppose 14*i = 129 - 87. Let r(q) be the second derivative of 10*q**2 - 12*q + 0 - 5/12*q**4 + 5/2*q**i. Determine v, given that r(v) = 0.
-1, 4
Let h(p) be the third derivative of -p**8/1512 - 2*p**7/945 + p**5/135 + p**4/108 - p**2 + 91*p. Suppose h(r) = 0. What is r?
-1, 0, 1
Let u be (429/(-77) - -9)*(-21)/(-30). Factor -12/5 - 3/5*n**2 + u*n.
-3*(n - 2)**2/5
Let n(l) be the third derivative of l**6/120 + 2*l**5/15 + 391*l**2. Factor n(i).
i**2*(i + 8)
Let g(n) be the first derivative of -5*n**3/3 + 20*n**2 - 80*n - 59. Factor g(i).
-5*(i - 4)**2
Let t = -926/33 + 15427/264. Factor 3/8*h**4 + 0 + 297/8*h**2 + t*h + 57/8*h**3.
3*h*(h + 1)*(h + 9)**2/8
Suppose -5*o + 70 = 2*v, 5*o = 2*v + v + 70. Suppose 3*b + 4*s + o = 0, -5*b - 2*s + 3*s = -15. Solve -4*l - 3*l**b - 4/3 = 0 for l.
-2/3
Let f be (-1)/8 + 82/656. Let c(h) be the third derivative of 1/60*h**4 + 1/300*h**6 + f*h**3 + 0 + 0*h + 1/75*h**5 - 7*h**2. Suppose c(x) = 0. Calculate x.
-1, 0
Let s be (-10)/20