(-7)/(105/6)*h. Suppose -g**2 - 2*g**2 + 4*g + 3 - 7*g + j*g**3 + g**3 = 0. What is g?
-1, 1
Let w(u) be the third derivative of 0*u - 1/420*u**6 + 1/84*u**4 + 0 - 1/21*u**3 + 1/210*u**5 - 10*u**2. Find b such that w(b) = 0.
-1, 1
Solve -81/5*u**2 + 30*u + 0 + 3/5*u**3 = 0 for u.
0, 2, 25
Let t(u) be the second derivative of 5*u**4/21 - 46*u**3/21 + 52*u**2/7 - 15*u + 3. Factor t(v).
4*(v - 2)*(5*v - 13)/7
Let d be 45/(1 - -8)*4/30. Suppose 3*n + 469 - 475 = 0. Determine t so that 2/3 + d*t**n + 4/3*t = 0.
-1
Let m(u) be the first derivative of -1/7*u**3 - 4*u**2 + 0*u + 1/42*u**4 - 6 + 1/210*u**5. Let h(t) be the second derivative of m(t). Factor h(k).
2*(k - 1)*(k + 3)/7
Suppose -2*q + 1 - 5 = -4*n, -n = -5*q + 17. Let c be n + -2 - 22/26. Factor 4/13*l + 2/13*l**2 + c.
2*(l + 1)**2/13
Suppose -3*r = -12*r + 18. Factor -2*f + f**2 - 2*f**r + 10*f**2 - 7*f**2.
2*f*(f - 1)
Suppose 0 = m + 5*m - 18. Factor -2*c**3 + 5*c**m + 9*c**2 + 27*c + 27 - c**3 - c**3.
(c + 3)**3
Let p(c) be the second derivative of -c**5/18 - 7*c**4/54 + 28*c**3/27 + 4*c**2/3 + 14*c - 1. Factor p(j).
-2*(j - 2)*(j + 3)*(5*j + 2)/9
Let q(a) be the third derivative of 20*a**2 + 0*a**3 + 0*a**5 + 0*a**4 + 0*a**7 + 1/2520*a**8 + 0*a + 0 - 1/900*a**6. Suppose q(k) = 0. What is k?
-1, 0, 1
Let f be 2037/399 - 4/38. Let s(i) be the first derivative of 0*i - 3*i**2 - i**3 - 6 + 3/5*i**f + 3/2*i**4. What is p in s(p) = 0?
-2, -1, 0, 1
Let k(q) = -q**2 - q - 1. Let s(m) = -4*m**3 - 28*m**2 - 68*m - 20. Let z(c) = -24*k(c) - s(c). Let z(o) = 0. Calculate o.
-11, -1
Let r(k) = -k**2 - 13*k - 32. Let b be r(-4). Factor -9/2*a**3 + 3/4*a**2 + 0*a + 27/4*a**b + 0 - 3*a**5.
-3*a**2*(a - 1)**2*(4*a - 1)/4
Factor -28/9*w**2 - 64/3 + 128/9*w + 2/9*w**3.
2*(w - 6)*(w - 4)**2/9
Let y be (-7*(-3)/4 + -3)*8. Let 0*f**2 + 4 + 7*f**3 + 2*f + 3*f**2 - y*f + 2*f**2 = 0. Calculate f.
-2, 2/7, 1
Suppose 21 - 4 = 2*w + 3*v, -2*v = -2*w + 12. Suppose -w = -2*y - 3. Factor 24*l**2 + 9*l**y + 9*l + 71*l - 20 + 12*l**2.
5*(l + 2)*(9*l - 2)
Let i(b) be the third derivative of b**2 + 0*b**4 + 0*b**3 - 1/1080*b**6 + 0*b - 1/180*b**5 + 0. Factor i(l).
-l**2*(l + 3)/9
Factor 2/13*l**3 + 18/13*l**2 - 20/13*l + 0.
2*l*(l - 1)*(l + 10)/13
Suppose 5*i = i - 56. Let p be 1/i*-36 - 1. Factor p*f + 2/7 + f**3 + 16/7*f**2.
(f + 1)**2*(7*f + 2)/7
Let j = -29/124 + 15/31. Let l(f) be the second derivative of -j*f**2 + 14*f + 0 - 1/24*f**4 - 1/6*f**3. Factor l(v).
-(v + 1)**2/2
Let g(y) be the second derivative of -y**7/1680 + y**6/720 + y**5/120 - 8*y**3/3 - 5*y. Let r(i) be the second derivative of g(i). Suppose r(x) = 0. What is x?
-1, 0, 2
Suppose -4*m + r = -2*m - 39, 0 = r - 3. What is n in 33 - m + 8*n - n**2 - 28 = 0?
4
Let v be (54/81)/((-1)/(-6)). Let w(x) be the first derivative of x - x**2 + 5/12*x**3 - 1/16*x**v - 1. Let w(c) = 0. What is c?
1, 2
Let f(a) be the second derivative of a**5/50 - a**4/30 - a**3/3 - 3*a**2/5 - a - 39. Factor f(j).
2*(j - 3)*(j + 1)**2/5
Factor a**2 + 2*a + a**4 - 2*a**5 + 4*a**2 - 6*a**2 + 3*a**5 - 3*a**3.
a*(a - 1)**2*(a + 1)*(a + 2)
Let r = 36 - 32. Solve w - 5*w - 21*w**2 - 24*w**3 - 2*w - 9*w**r = 0.
-1, -2/3, 0
Suppose 2*z - 4 = -3*i - 1, -5*z - 3 = 4*i. Let 0 + 9/4*x - 3/4*x**2 + 3/4*x**4 - 9/4*x**i = 0. What is x?
-1, 0, 1, 3
Let v(h) be the first derivative of -5*h**4/16 - 5*h**3/6 + 15*h**2/8 + 107. Factor v(n).
-5*n*(n - 1)*(n + 3)/4
Let m(l) = -7*l**4 - 3*l**3 + 17*l**2 + 43*l + 14. Let b(q) = 48*q**4 + 21*q**3 - 120*q**2 - 300*q - 99. Let k(z) = -4*b(z) - 27*m(z). Factor k(g).
-3*(g - 3)*(g + 1)**2*(g + 2)
Let b = -4 - -6. Factor -2*n**3 + 2 + 4*n + 6*n - n**3 + 8*n**b - 17*n.
-(n - 1)**2*(3*n - 2)
Let s(h) be the first derivative of h**4/21 - 4*h**3/21 + 2*h**2/7 - 18*h + 2. Let y(o) be the first derivative of s(o). Factor y(p).
4*(p - 1)**2/7
Let n(w) be the first derivative of 4*w**6/21 - 38*w**5/35 + 31*w**4/14 - 38*w**3/21 + w**2/7 + 4*w/7 - 61. Suppose n(q) = 0. Calculate q.
-1/4, 1, 2
Let t(b) be the first derivative of 2*b**5/25 + 3*b**4/10 + 2*b**3/5 + b**2/5 - 24. What is d in t(d) = 0?
-1, 0
Let t(r) = -r**2 + 31*r + 108. Let o be t(34). Let h be (12/14)/(o/21). Suppose 12/7*u**h - 12/7*u**4 + 0*u + 4/7*u**5 + 0 - 4/7*u**2 = 0. Calculate u.
0, 1
Let v be -1*(1 + -1)/3. Let l be 2 - (-1 - v) - -8. Factor 3*z**5 + l*z**5 + 2*z**3 - 2*z**5 - 3*z**2 + 21*z**4 + 4*z**3.
3*z**2*(z + 1)**2*(4*z - 1)
Let z(y) = -2*y + 3 - 6 + 2 + 6*y. Let n be z(1). Factor 5*o**3 - 10*o - 2*o**4 - 3 + 6*o**2 - 3*o**n + 3 + 4.
-2*(o - 1)**3*(o + 2)
Factor 424*t + 152*t**3 - 413*t**2 - 19*t**2 - 36*t**4 - 209 + 32*t**4 + 69.
-4*(t - 35)*(t - 1)**3
Suppose -21*q - 114 = -27*q. Suppose 6*n = -q + 31. Determine k so that -2/5*k**n + 0*k + 2/5 = 0.
-1, 1
Suppose -d + 2 = -7. Suppose 0*n = -3*i - n + d, 5*n + 19 = i. Suppose 6/7*o**i - 2/7*o + 0 - 2*o**3 + 10/7*o**2 = 0. What is o?
0, 1/3, 1
Suppose 0 = -h, -4*s + 4*h = -9*s + 25. Let k(l) be the third derivative of 0 - 1/40*l**s + l**2 - l**3 - 1/4*l**4 + 0*l. Determine b, given that k(b) = 0.
-2
Let d = 2797 + -2795. Factor -2/7*m - 4/7*m**d + 2/7*m**3 + 4/7.
2*(m - 2)*(m - 1)*(m + 1)/7
Let v = -153 + 154. Let t be v/(-3) - (-2 + 1). Suppose -4/3 - t*n + 2*n**2 = 0. What is n?
-2/3, 1
Let -2584 + 4*w + w**2 + 2589 - 2*w**2 = 0. Calculate w.
-1, 5
Factor 229*o + 0*o**3 + 1 + 2*o**3 - 1 - 247*o.
2*o*(o - 3)*(o + 3)
Let g be (-5)/(-35)*0 + (-26)/(-2). Suppose -3*p + b = -g, -4*p + 6*p + 5*b + 14 = 0. Let 0 - 3/5*t**p - 3/5*t**2 + 0*t = 0. Calculate t.
-1, 0
Let j(a) be the second derivative of a**7/1050 - a**6/600 - a**5/300 + a**4/120 + 7*a**2/2 + 16*a. Let c(s) be the first derivative of j(s). Factor c(x).
x*(x - 1)**2*(x + 1)/5
Let r(j) be the third derivative of j**6/120 - j**5/60 - j**4/12 - 78*j**2. Determine t so that r(t) = 0.
-1, 0, 2
Solve -4/5*o**3 - 12/5*o**2 + 336/5 + 32*o = 0.
-7, -2, 6
Suppose a - 26 = 3*c - 5, -c - 7 = -3*a. Let r(x) = -3*x - 21. Let g be r(c). Factor g + 2/3*l**2 + 2/3*l.
2*l*(l + 1)/3
Let -22/13*h**2 + 8/13*h**4 - 42/13*h**3 + 168/13*h - 40/13 = 0. Calculate h.
-2, 1/4, 2, 5
Let a = 8946651/235 - 38071. Let z = 12/47 - a. Solve -z*x**3 + 6/5*x + 4/5 + 0*x**2 = 0 for x.
-1, 2
Let w = -94 - -104. Suppose -12 = -2*u - 4*g, w + 2 = 3*u + 3*g. Factor 2*x - 8/3 + 2/3*x**u.
2*(x - 1)*(x + 4)/3
Suppose -65*w + 35 = -58*w. Let y(l) be the second derivative of 0 + 0*l**4 - 3/80*l**w + 0*l**2 - 8*l + 0*l**3 + 1/10*l**6. Find q such that y(q) = 0.
0, 1/4
Factor -14 + 11 + 4 - 2*y**2 + 10*y + 11.
-2*(y - 6)*(y + 1)
Let f(d) be the first derivative of -3*d**4/4 - 34*d**3 + 105*d**2/2 - 213. Solve f(w) = 0 for w.
-35, 0, 1
Suppose 0 = 2*i - n + 54, -6*i - 138 = -i - 4*n. Let u be (-316)/i + (90/65)/(-9). Solve u*m - 8/3 - 18*m**2 + 9*m**3 = 0.
2/3
Factor 1/4*x**4 + 3597/4*x**2 - 1711*x + 841 - 59/2*x**3.
(x - 58)**2*(x - 1)**2/4
Let h(q) be the first derivative of q**4/2 + 4*q**3/3 - 13*q**2 + 20*q + 420. Determine u, given that h(u) = 0.
-5, 1, 2
Let n be 0/(-9*((-32)/12 - -3)). Factor 0*l + 2/11*l**4 - 4/11*l**3 + 2/11*l**2 + n.
2*l**2*(l - 1)**2/11
Let l(h) = -2*h**5 - 39*h**4 - 127*h**3 - 173*h**2 - 108*h - 28. Let s(c) = c**4 + c**3 - c**2 - 2*c. Let p(o) = -2*l(o) - 6*s(o). Factor p(g).
4*(g + 1)**4*(g + 14)
Let n(a) be the second derivative of -6*a - 1/10*a**6 + 0 + 4/5*a**3 - 21/100*a**5 + 6/5*a**2 + 1/20*a**4 - 1/70*a**7. Find g, given that n(g) = 0.
-2, -1, 1
Let y(d) be the second derivative of -d**6/160 + d**5/240 - 9*d**2/2 - 14*d. Let v(p) be the first derivative of y(p). Solve v(r) = 0 for r.
0, 1/3
Let a be (-1508)/1914 + 3/((-9)/(-4)). Let -8/11 + a*r + 2/11*r**2 = 0. What is r?
-4, 1
Let b(j) be the second derivative of 2 - 23*j + 1/11*j**6 + 17/33*j**4 + 21/11*j**3 - 31/55*j**5 - 49/11*j**2 - 1/231*j**7. Find f, given that b(f) = 0.
-1, 1, 7
Let r(i) be the third derivative of -2*i**7/315 + i**6/45 - i**2 - 6. Find y, given that r(y) = 0.
0, 2
Let s = 981 - 10773/11. Let z = 3/1820 + 21807/20020. Let -8/11*r**4 - s*r**3 - 2/11*r - z*r**2 + 0 = 0. Calculate r.
-1, -1/4, 0
Let u = 6780 + -20332/3. Factor -2/3*b + 13/3*b**2 - u - b**3.
-(b - 4)*(b - 1)*(3*b + 2)/3
Let o = -120 + 1801/15. Let c(v) be the second derivative of 8*v + 0*v**3 - 1/12*v**4 + 0 - 1/20*v**5 + o*v**6 + 0*v**2. Factor c(i).
i*