(38 + -36)*6/20. Factor 0*j**2 + 0 - t*j**3 + 6*j.
-3*j*(j - 2)*(j + 2)/2
Suppose 0 = -5*t + 14 + 6. Let o(p) = -p**2 - 1. Let b(q) = -4*q**3 - 12*q**2 - 20*q - 4. Let n(i) = t*o(i) + b(i). Factor n(w).
-4*(w + 1)**2*(w + 2)
Suppose 6*p + 11 = k + 3*p, -5*p = 10. Determine m, given that 9 + 3*m**2 - k*m + 11*m - 6*m**2 = 0.
-1, 3
Let m = 924 + -8314/9. Let a(t) be the third derivative of t**2 + 1/90*t**5 + 0 - 1/12*t**4 + m*t**3 + 0*t. Factor a(n).
2*(n - 2)*(n - 1)/3
Let p(r) be the second derivative of -9/10*r**6 + 24*r**3 - 14*r + 0 - 14*r**4 + 24/5*r**5 - 24*r**2 + 1/14*r**7. Factor p(d).
3*(d - 2)**4*(d - 1)
Factor -238*a**3 + 208*a**3 + 5*a**4 + 30*a**2 + 30*a**2 - 40*a.
5*a*(a - 2)**3
Let r be (2/6)/(10/15)*-10. Let b be (-4)/20 - 11/r. Let -4/7*n**4 + 0 + 0*n**b - 2/7*n**3 + 0*n - 2/7*n**5 = 0. What is n?
-1, 0
Let z(t) be the third derivative of t**7/42 + 5*t**6/24 + 5*t**5/12 - 25*t**4/24 - 5*t**3 - 182*t**2. Determine l so that z(l) = 0.
-3, -2, -1, 1
Factor -11*d**3 + d**4 + 64*d**3 + 23*d**2 - 11*d**3 - 29*d**3 + 11*d.
d*(d + 1)**2*(d + 11)
Suppose -123 = -3*q - 108. Let n(l) be the first derivative of 0*l + 3/2*l**2 - 3/2*l**4 + 9 + 0*l**q + 1/2*l**6 + 0*l**3. Find m such that n(m) = 0.
-1, 0, 1
Suppose 3*t + 8*y - 12*y - 13 = 0, t = 3*y + 6. Suppose 3*d = -0*d + 9. Let 0*m**3 - 3*m**2 + t*m**5 + 3*m**2 + d*m**3 + 6*m**4 = 0. Calculate m.
-1, 0
Let u(f) be the third derivative of f**8/504 - 2*f**7/63 + 7*f**6/180 + f**5/5 - 485*f**2. Let u(h) = 0. Calculate h.
-1, 0, 2, 9
Let v(y) = y**3 - 7*y**2 - y + 54. Let a be v(4). Factor 2/3*g**2 + 4/3 + a*g.
2*(g + 1)*(g + 2)/3
Solve 0*p + 0*p**2 + 0 - 2/17*p**4 + 2/17*p**3 = 0 for p.
0, 1
Let i(w) be the third derivative of w**8/56 + 3*w**7/70 - w**5/20 + 150*w**2. Determine x, given that i(x) = 0.
-1, 0, 1/2
Factor 2*k - 36/7 + 2/7*k**2.
2*(k - 2)*(k + 9)/7
Let u(g) be the third derivative of 5*g**6/8 + 31*g**5/12 - 215*g**4/24 - 5*g**3/2 - 10*g**2 - 13*g. Let u(n) = 0. Calculate n.
-3, -1/15, 1
Factor 7*u**2 - 5/2*u**3 - 3/2*u + 1/4*u**4 - 45/4.
(u - 5)*(u - 3)**2*(u + 1)/4
Determine c, given that -488601/2*c**2 + 699*c**3 - 3/4*c**4 - 8841886563/4 + 37948011*c = 0.
233
Let p be 2*(-2)/3*-24. Let l = -24 + p. Find a such that -6 - 6 + l + 11*a - 3*a - 4*a**2 = 0.
1
Let p = 44 - 42. Let -12*w - 3*w**p - 2*w**2 + w**2 - 8 = 0. Calculate w.
-2, -1
Suppose -4*t + 16 = -4. Let c(l) be the second derivative of 1/5*l**3 - 1/10*l**2 + 5*l - 3/20*l**4 + 0 + 1/25*l**t. Factor c(n).
(n - 1)**2*(4*n - 1)/5
Let w(f) = -f**3 + 16*f**2 - 12*f - 41. Let o be w(15). Suppose -2*x - 2*x + 2*k = 2, -3*k = o*x - 23. Factor 0 + 1/5*y**x + 1/5*y**3 - 1/5*y - 1/5*y**4.
-y*(y - 1)**2*(y + 1)/5
Factor -31*u - 37*u**3 + 11*u - 7*u**4 + 9*u**3 - 44*u**2 + 3*u**4.
-4*u*(u + 1)**2*(u + 5)
Suppose 13*c - 12*c - 5*t = -21, 3*c - 3*t = -3. Let w = 815/9 - 90. Suppose 0*r - 4/9*r**c + 0 - 2/9*r**2 - 1/9*r**5 - w*r**3 = 0. What is r?
-2, -1, 0
Let n(d) be the first derivative of 8/5*d**5 - 5 + d**6 + 4*d - 4*d**3 + d**2 - 2*d**4. Find f, given that n(f) = 0.
-1, 2/3, 1
Factor -250*o**3 + 506*o**3 - 258*o**3 + 100*o**2.
-2*o**2*(o - 50)
Let j(b) be the second derivative of 0 - 5/6*b**4 + 1/30*b**5 + 16*b + 64/3*b**2 + 16/3*b**3. Suppose j(k) = 0. What is k?
-1, 8
Let c(s) = 219*s + 1973. Let a be c(-9). Suppose 2*n + 0*n = 0. Determine g so that n*g**3 - 1/2*g**a + 1/2*g**4 + 0 + 0*g = 0.
-1, 0, 1
Suppose -n = -3*n + 8. Factor 16*s**2 - 8*s**2 + 3*s**3 - s**n + s - 11*s**2 + 0*s**3.
-s*(s - 1)**3
Let l(b) be the third derivative of 0 - 2/15*b**5 + 0*b + 0*b**3 - 13*b**2 - 1/2*b**4 + 1/30*b**6. Find s such that l(s) = 0.
-1, 0, 3
Suppose 4*y = -18 - 30. Let x be 3/y + (-8)/(-16). Factor -1/2*g**2 + 0 - x*g**3 - 1/4*g.
-g*(g + 1)**2/4
Let r be 8/(-3)*((-375)/(-12) + -32). Solve -6/5 - 2/5*a**r - 8/5*a = 0.
-3, -1
Let d = 37295/34 + -1097. Let z = d + 293/238. Solve -z - 4/7*o**2 - 12/7*o = 0 for o.
-2, -1
Factor 2/5*p**3 - 126/5 - 26/5*p**2 + 102/5*p.
2*(p - 7)*(p - 3)**2/5
Let q(z) be the first derivative of -2*z**7/63 + 8*z**6/45 - 2*z**5/5 + 4*z**4/9 - 2*z**3/9 - 6*z - 1. Let b(d) be the first derivative of q(d). Factor b(t).
-4*t*(t - 1)**4/3
Let f(n) = n + 1. Let s be (-2 - (-2)/(-2)) + 8. Let z(r) = -r**2 + 4*r - 20. Let c(w) = s*z(w) + 20*f(w). Solve c(q) = 0 for q.
4
Factor 0 - 3/2*d**3 + 3*d**2 + 0*d.
-3*d**2*(d - 2)/2
Suppose -5*y - 25 = -4*g, 34*y - 33*y = 4*g - 21. Let x = 27 + -27. Factor -2/3*l**3 + 2/3*l**4 - 2/3*l**2 + 0*l + 2/3*l**g + x.
2*l**2*(l - 1)*(l + 1)**2/3
Let f = 1587 - 1577. Let h(j) be the first derivative of 1 - 5/4*j**4 + 10/3*j**3 + 5/2*j**2 - f*j. Factor h(o).
-5*(o - 2)*(o - 1)*(o + 1)
Factor -67/4*v**3 - 1/8*v**4 + 0 + 0*v - 4489/8*v**2.
-v**2*(v + 67)**2/8
Suppose -3*g - 17 = -b, -3*b = -b - g - 9. Let k(f) be the first derivative of 4*f**2 + 16/3*f**3 + 2/5*f**5 + 5/2*f**4 + 0*f + b. What is w in k(w) = 0?
-2, -1, 0
Let b = 23 + -4. Solve 3*h**3 + b*h**2 - 21*h**2 - 4*h**3 = 0.
-2, 0
Factor -2/5*b**2 - 102/5*b + 0.
-2*b*(b + 51)/5
Let q(r) = r + 4. Let j be q(0). Suppose j*o + 6 - 22 = 0. Factor 5*v**4 + 4*v**4 + 3*v**2 + 3*v**5 + o*v**3 + 5*v**3.
3*v**2*(v + 1)**3
Let s(v) be the second derivative of -v**4/12 + 22*v**3/3 - 43*v**2/2 - 168*v - 1. Determine c so that s(c) = 0.
1, 43
Let l(c) be the second derivative of c**10/10080 - c**9/2520 + c**7/420 - c**6/240 + 15*c**4/4 + 38*c. Let j(t) be the third derivative of l(t). Solve j(z) = 0.
-1, 0, 1
Let a(n) be the second derivative of n**7/420 - 11*n**6/540 + n**5/15 - n**4/9 - 7*n**3/6 - 18*n. Let l(r) be the second derivative of a(r). Solve l(w) = 0.
2/3, 1, 2
Let b(o) be the third derivative of o**6/1440 - o**5/240 - 13*o**4/288 + 5*o**3/24 + 8*o**2 - 4. Factor b(r).
(r - 5)*(r - 1)*(r + 3)/12
Let s(o) = 9*o + 3. Let l(j) = j**2 + 8*j + 3. Let a(d) = 3*d - 2. Let y be a(4). Suppose m - y = 6*m. Let i(f) = m*s(f) + 3*l(f). Factor i(r).
3*(r + 1)**2
Suppose -16*i - 9 = -9. Let c(y) be the third derivative of 13*y**2 - 1/105*y**5 + i - 1/14*y**4 + 0*y + 0*y**3. Determine m so that c(m) = 0.
-3, 0
Let x = -9765 - -9767. Let -9/8*q**3 + 3/8*q + 0 + 3/4*q**x = 0. Calculate q.
-1/3, 0, 1
Find l, given that 4/7 + 1/7*l**2 + 1/7*l**5 - 5/7*l**4 + l**3 - 8/7*l = 0.
-1, 1, 2
Let o(j) be the third derivative of -j**7/70 + 3*j**6/20 - 2*j**5/5 - 226*j**2 - j. Let o(f) = 0. Calculate f.
0, 2, 4
Suppose -5*v + 6*t = t - 60, -12 = -v + 5*t. Factor -2*d - 7*d - 21*d**2 - 3 + v*d**2 - 3*d**3.
-3*(d + 1)**3
Factor -3*c**3 - 17/5*c + 0 + 1/5*c**4 - 33/5*c**2.
c*(c - 17)*(c + 1)**2/5
Factor -3/5*v**2 + 0 + 24/5*v.
-3*v*(v - 8)/5
Let l(r) = 1949*r - 3896. Let d be l(2). Factor 1/2*o**5 - 1 - 2*o**3 + 3/2*o + o**d + 0*o**4.
(o - 1)**3*(o + 1)*(o + 2)/2
Factor -12/5*j + 15*j**2 + 0.
3*j*(25*j - 4)/5
Suppose 4 + 32 = 9*g. Let z(i) be the first derivative of 10/3*i**3 + 0*i - 2*i**5 - 2*i**2 + i**g + 3. Determine a so that z(a) = 0.
-1, 0, 2/5, 1
Let b(l) be the second derivative of -l**4/12 - 11*l**3/36 - 5*l**2/12 + 91*l. Factor b(m).
-(m + 1)*(6*m + 5)/6
Suppose -26*t - 43*t = -11*t. Factor t - 4/11*i + 2/11*i**2.
2*i*(i - 2)/11
Let c(m) be the second derivative of -3*m**5/20 + 61*m**4/4 + 125*m**3/2 + 189*m**2/2 + 125*m. Solve c(f) = 0.
-1, 63
Let n = 407 - 269. Let x = n + -134. Factor -3*t**2 - 2/3*t + 0 - t**5 - 11/3*t**x - 5*t**3.
-t*(t + 1)**3*(3*t + 2)/3
Suppose -r = -q - 1, 257*q = 260*q + 5*r - 5. Suppose 0 + q*h**2 + 0*h - 1/3*h**4 - 2/3*h**3 = 0. What is h?
-2, 0
Factor -5*a**2 - 190 + 865/3*a.
-5*(a - 57)*(3*a - 2)/3
Let k = 7535/2 + -3767. Factor 1/2*z**2 + k*z**3 + 0 - 1/2*z - 1/2*z**4.
-z*(z - 1)**2*(z + 1)/2
Factor 48/7*n**3 + 8*n**2 + 19/7*n + 2/7.
(3*n + 2)*(4*n + 1)**2/7
Let j(f) be the first derivative of 4*f**5/5 + 2*f**4 - 4*f**3 - 8*f**2 + 16*f + 99. Solve j(t) = 0 for t.
-2, 1
Let g(m) be the third derivative of m**8/2856 + m**7/1785 - 3*m**6/170 + 7*m**5/255 + m**4/12 - 5*m**3/17 - 389*m**2. Let g(r) = 0. Calculate r.
-5, -1, 1, 3
Let i(k) = 11*k**4 + 5*k**3 - 9*k**2 - 19*k - 4. Let n = 6 + 0. Let u(h) = 32*h**4 + 15*h**3 - 28*h**2 - 58*h - 13. Let a(v) = n*u(v) - 17*i(v). Factor a(r).
5*(r - 2)*(r + 1)**3
Let j(k) be the third derivative of -1/735*k**7 + 1/210*k**6 + 0*k**3 + 0*k**5 + 17*k**2 + 0 + 0*k + 0*k**4. Factor j(w).
