 31)/2
Let a(t) be the second derivative of t**5/4 - 25*t**4/12 - 10*t**3/3 + 50*t**2 + 103*t - 3. Find x, given that a(x) = 0.
-2, 2, 5
Factor 86 + 106 - 1321*d + 82*d**2 + 1041*d - 30*d**3 + 2*d**4 + 62*d**2.
2*(d - 8)*(d - 3)*(d - 2)**2
Let u(v) = -v**3 + v**2. Let g(f) = -10*f**2 - 24*f - 20. Let r(h) = g(h) + u(h). Factor r(i).
-(i + 2)**2*(i + 5)
Let k(d) = -14*d + 31. Let h be k(2). Let n(t) be the third derivative of 0*t + 2*t**2 + 0*t**h + 1/360*t**6 - 1/36*t**4 + 0 - 1/180*t**5. Factor n(m).
m*(m - 2)*(m + 1)/3
Let w(z) = z**2 + 10*z - 261. Let n be w(-22). Suppose 1/5*p**2 - 2/5 + 1/5*p**4 + 3/5*p**n - 3/5*p = 0. What is p?
-2, -1, 1
Let q(i) be the third derivative of i**6/840 - i**5/210 - i**4/168 + i**3/21 - 9*i**2. What is k in q(k) = 0?
-1, 1, 2
Suppose -c = 2*w - 9, -c = 3*c + 20. Let n be (-27)/63 - (-31)/w. Factor -4*q**4 + 3*q**n - q + 0*q**2 - 3*q**3 + 0*q - 3*q**2.
-q*(q + 1)**3
Suppose 12*i - 9*i - 6 = 0. Let m(j) be the first derivative of 2 + 2/15*j**3 + 0*j**i - 2/5*j. Find v such that m(v) = 0.
-1, 1
Let n(t) be the first derivative of 7*t**7/60 - 7*t**6/360 - t**5/6 + t**4/6 + 3*t**3 + 7. Let w(z) be the third derivative of n(z). Solve w(q) = 0 for q.
-1/2, 2/7
Solve 30*t**3 + 103*t**4 - 73*t + 27*t**5 - 120*t**2 + 37 - 19 + 16*t - t**4 = 0 for t.
-3, -1, 2/9, 1
Suppose 0 = a - k, 5*k + 16 = 3*a + 10*k. Solve 18/5*g - 27/5 - 3/5*g**a = 0 for g.
3
Let t(u) = 2*u**4 + 2*u**3 - u**2 - 1. Let g(v) = -v**5 - 8*v**4 + v**3 + 22*v**2 - 4*v - 14. Let n(f) = g(f) + 2*t(f). Find h, given that n(h) = 0.
-4, -2, -1, 1, 2
Let w be 1 + (-1358)/(-98) + -14. Suppose 3/7*d**2 + w*d + 0 = 0. What is d?
-2, 0
Factor -1/4*x**2 + 1/2*x + 6.
-(x - 6)*(x + 4)/4
Suppose -136*w + 12 = -133*w. Let l(m) be the second derivative of 1/20*m**5 - 6*m + 0*m**3 + 1/6*m**w + 0 + 0*m**2. Determine n so that l(n) = 0.
-2, 0
Suppose -6*d + 4*d = 5*r + 10, 8 = -4*r. Let o = 10 + -5. Factor 2/7*p**o + 12/7*p**3 + 2/7*p - 8/7*p**2 + d - 8/7*p**4.
2*p*(p - 1)**4/7
Let c(o) be the third derivative of -o**7/7560 + o**6/270 - 2*o**5/45 + o**4 + 21*o**2. Let f(s) be the second derivative of c(s). Factor f(d).
-(d - 4)**2/3
Suppose -55*l - 42 + 42 = -8*l. Solve l + 0*m - 3/5*m**4 + 0*m**3 + 3/5*m**2 = 0 for m.
-1, 0, 1
Let b(o) be the second derivative of -o**6/630 + 2*o**4/21 - 2*o**3 + 10*o. Let j(s) be the second derivative of b(s). Factor j(g).
-4*(g - 2)*(g + 2)/7
Let i = 88 + -56. Factor 2 - i*d**2 - 2 - 84*d**3 - 15*d + 31*d.
-4*d*(3*d + 2)*(7*d - 2)
Let z(h) = -h**4 - 283*h**3 + 3627*h**2 + 8123*h + 4202. Let g(x) = 565*x**3 - 7255*x**2 - 16245*x - 8405. Let q(o) = -3*g(o) - 5*z(o). Factor q(a).
5*(a - 29)**2*(a + 1)**2
Let q = 71 - 111. Let r = q + 45. What is d in -r*d**2 + 4*d**2 - 2 + 39*d - 36*d = 0?
1, 2
Let d(h) be the second derivative of -h**7/3780 - h**6/1080 + h**5/90 - h**4/6 - 8*h. Let x(i) be the third derivative of d(i). Determine u so that x(u) = 0.
-2, 1
Solve 0 - 6*d**2 + 4*d + 3*d**3 - 1/2*d**4 = 0.
0, 2
Suppose 35*u = -10*u. Let y(c) be the third derivative of -1/180*c**5 + 0 + 0*c**3 + u*c - c**2 - 1/72*c**4. Factor y(o).
-o*(o + 1)/3
Suppose -4*u = -c - 1, -2*u + c + 2*c = -13. Let s be 5/(-10)*0 - u. Determine j, given that j + 4*j**2 + 11*j**2 + s - 16*j**2 - j**3 = 0.
-1, 1
Let q = -524 - -528. Let b(a) be the first derivative of 5 - 5/12*a**2 - 1/8*a**q + 1/6*a + 7/18*a**3. Determine v, given that b(v) = 0.
1/3, 1
Let a = -105 - -106. Let r(b) = -3*b**2 - 3*b - 6. Let w(m) = -m**2 + 2. Let y(j) = a*r(j) + 3*w(j). Factor y(c).
-3*c*(2*c + 1)
Find g, given that 16*g + 12*g**4 + 15*g - 24 + 45*g + 12*g**2 + 18*g - 76*g**3 - 18*g = 0.
-1, 1/3, 1, 6
Let f(o) = -o**5 - 9*o**4 - 13*o**3 - 15*o**2 - 10*o - 3. Let w(q) = q**5 + 8*q**4 + 13*q**3 + 14*q**2 + 8*q + 2. Let j(p) = -4*f(p) - 6*w(p). Factor j(r).
-2*r*(r + 1)**2*(r + 2)**2
Let t(u) = -8*u**2 - 13*u + 3. Let z(j) = 65*j**2 + 105*j - 25. Suppose 10*q + 1 - 31 = 0. Let w(b) = q*z(b) + 25*t(b). Determine p, given that w(p) = 0.
-2, 0
Let j(q) be the second derivative of 5*q**4/12 - 25*q**3/6 - q - 65. Factor j(f).
5*f*(f - 5)
Suppose 11*o = 34 - 12. Suppose c**3 + 10 + 5*c**o + 3 + 4*c - 13 = 0. What is c?
-4, -1, 0
Let m = 18 - 15. Factor -2*c - 136*c**3 + m*c**2 + 135*c**3 + 3*c**2 + 9*c.
-c*(c - 7)*(c + 1)
Let w be (-2 - -2)/((-6)/(-2)). Factor x + 3*x + w*x + x**2 - 2 - 3*x**2.
-2*(x - 1)**2
Let c(q) = 3*q**2 + 7*q - 8. Let a(r) = -10*r**2 - 22*r + 28. Let f(y) = 2*a(y) + 7*c(y). Determine j so that f(j) = 0.
-5, 0
Let v(s) be the third derivative of s**10/70560 + s**9/11760 - s**7/1470 + 5*s**4/24 + 42*s**2. Let j(b) be the second derivative of v(b). Factor j(c).
3*c**2*(c - 1)*(c + 2)**2/7
Let x = 2969/62 - -546/31. Let s = x + -65. Factor 0*d**3 + 1/4*d**5 - s*d**4 - 1/4*d + 1/2*d**2 + 0.
d*(d - 1)**3*(d + 1)/4
Let t be -1 + 2/(-4)*-10. Suppose t*c = -7*o + 3*o + 20, -17 = -4*o - 3*c. Solve -9*f**3 + f**2 - 9*f**2 - 3*f**4 + 0*f**3 + 9*f + 5*f**o + 6 = 0 for f.
-2, -1, 1
Suppose 48 - 54 = -4*b + 2*h, -2*b = h - 5. Let m(k) be the third derivative of -b*k**3 - 1/15*k**5 + 0 + 0*k + 2/3*k**4 - k**2. Factor m(o).
-4*(o - 3)*(o - 1)
Suppose 2*k - 31 - 1 = 0. Factor 18*b - 12*b**2 + 18*b - 15*b + 11*b - k.
-4*(b - 2)*(3*b - 2)
Let c = -10407 - -10410. Suppose 1/2*x**c - 3/4*x**2 + 0*x + 1/4*x**4 + 0 = 0. What is x?
-3, 0, 1
Suppose -4*l**5 - 40*l**4 + 4*l**2 - 4*l**5 + 36 + 12*l**5 - 72*l**3 + 78*l - 10*l**5 = 0. Calculate l.
-3, -1, -2/3, 1
Let q = 10647 - 42463/4. Factor q + 5/4*a**2 + 25/2*a.
5*(a + 5)**2/4
Let w(d) be the third derivative of -d**7/840 + d**6/96 - d**5/120 - 5*d**4/24 + d**3 - 23*d**2 + 6*d. Suppose w(y) = 0. What is y?
-2, 2, 3
Let s(d) be the first derivative of 11/4*d**4 + 8*d**3 + 2*d + 15/2*d**2 - 16. Find j, given that s(j) = 0.
-1, -2/11
Let i(j) = -j + 14. Let c be i(12). Solve 3 + 5*w - 4*w + w**c - 6 + 1 = 0.
-2, 1
Let s = 45 + -43. Factor 9*a**s + 5*a**2 - 2*a**3 - 2*a**2 - 2*a**3.
-4*a**2*(a - 3)
Suppose -36 = -132*r + 114*r. What is t in 2/5*t - 1/5*t**3 + 1/5*t**r + 0 = 0?
-1, 0, 2
Let r(u) be the second derivative of 0*u**3 + 0*u**5 + 0*u**2 - 8/147*u**7 + 0 + 2/105*u**6 + 0*u**4 + 2*u. Factor r(d).
-4*d**4*(4*d - 1)/7
Suppose -d = -1, d + 3*d + 55 = g. Suppose y = -57 + g. Factor -y*v**3 + 0 + 0*v - 6/5*v**4 - 4/5*v**2.
-2*v**2*(v + 1)*(3*v + 2)/5
Let m be (-2)/(-19) + 55/19. Let i(c) be the first derivative of -8/11*c + 7 - 4/11*c**2 - 2/33*c**m. Factor i(k).
-2*(k + 2)**2/11
Let q(y) = 2*y**2 - 9*y - 14. Let a(c) = -3*c**2 + 17*c + 26. Let s(n) = -3*a(n) - 5*q(n). Find j such that s(j) = 0.
-4, -2
Let l(z) be the first derivative of z**7/420 + 7*z**6/270 + 2*z**5/45 + 5*z**3 - 21. Let w(p) be the third derivative of l(p). What is m in w(m) = 0?
-4, -2/3, 0
Let v(t) be the second derivative of -t**5/20 - t**4/6 + 29*t**3/6 + 15*t**2 + t + 7. Factor v(o).
-(o - 5)*(o + 1)*(o + 6)
Let f(w) = 4*w**5 - 24*w**4 + 58*w**3 - 48*w**2 + 28*w - 6. Let l(g) = -g**3 - 2*g + 1. Let i(r) = -f(r) - 6*l(r). Factor i(h).
-4*h*(h - 2)**2*(h - 1)**2
Factor 1/3*k**2 - 1/3*k + 0.
k*(k - 1)/3
Let l = -4 - -11. Suppose 5 - l = -v. Determine w so that -w**2 + 4 - 17*w**v + 9*w + 2 + 9*w**3 - 6*w**2 = 0.
-1/3, 1, 2
Let y be (-4)/(-1) + 1*-2. Solve -i + 10*i + 3*i**y + 0*i + 6 = 0.
-2, -1
Let v(b) = b**2 + 2*b + 3. Suppose 3*f - 7*f = -j + 13, -15 = -3*j. Let r be v(f). Find n such that 3*n**r + 4*n**4 - n**2 + 0*n**4 - 6*n**3 = 0.
-1/4, 0, 1
Solve 37*j + 26*j**2 - 740 - 782*j - 23*j**2 - 8*j**2 = 0.
-148, -1
Let f = 31/280 - 3/35. Let b(n) be the third derivative of 0*n + 0 - 7/48*n**4 - 1/84*n**7 + 1/4*n**3 + 1/672*n**8 + 1/60*n**5 - 4*n**2 + f*n**6. Factor b(q).
(q - 3)*(q - 1)**3*(q + 1)/2
Factor 6/7*v**2 - 72/7*v - 78/7.
6*(v - 13)*(v + 1)/7
Suppose -s = -j + 11, 4*s - 12 = -4*j + 16. Let l(m) = -m**3 + 10*m**2 - 9*m. Let g be l(j). Factor -1/5*u**2 + 0*u + g.
-u**2/5
Let h be (-24)/88 - (-530)/330. Let l(z) be the first derivative of -1/3*z**2 - h*z + 2/9*z**3 + 2. Factor l(a).
2*(a - 2)*(a + 1)/3
Suppose 0 = w - 0*z - z + 1, 0 = 5*w + 3*z - 19. Suppose -2*j + j - 5*o = w, 3*o = -2*j + 10. Factor 6*c**4 + 12*c**2 + 4*c**3 - c**4 + j*c**3 - c**4 + 4*c.
4*c*(c + 1)**3
Solve -1661168/9*f**3 - 17672/3*f**2 - 188/3*f - 2/9 = 0 for f.
-1/94
Let s(d) be the first 