16*i + 5*i**2 = 0.
-3, 2
Let n(z) be the second derivative of -z**4/90 + 134*z**3/45 - 4489*z**2/15 - 23*z - 2. Find v such that n(v) = 0.
67
Suppose -22/13 + 42/13*t - 18/13*t**2 - 2/13*t**3 = 0. What is t?
-11, 1
Suppose -3/2*y**3 - 7/6*y + 0 - 5/2*y**2 - 1/6*y**4 = 0. What is y?
-7, -1, 0
Let n = -780 - -783. Let y(f) be the third derivative of -1/52*f**4 - 2/39*f**n + 0*f + 0 - 1/390*f**5 + f**2. Suppose y(c) = 0. Calculate c.
-2, -1
Suppose 1 + 2 = r. Let z(h) = 2*h - 2. Let y be z(r). Let 2*d**3 + 4*d**y - 6*d**2 + 18*d**2 + 8*d**3 + 4*d + 2*d**3 = 0. What is d?
-1, 0
Let s = 26039 + -26037. Solve 1/4*i**5 - 1/4*i + 1/2*i**s - 1/2*i**4 + 0*i**3 + 0 = 0 for i.
-1, 0, 1
Let r(t) be the third derivative of t**8/1008 + 17*t**7/315 + 169*t**6/360 - 34*t**5/3 + 50*t**4 + 24*t**2 + 12*t. Factor r(k).
k*(k - 3)**2*(k + 20)**2/3
Let p(y) be the third derivative of -y**6/360 + y**4/24 + y**3/9 - 47*y**2. Find z, given that p(z) = 0.
-1, 2
Suppose 3*f = 4*i + 4 - 1, 5*f + 4*i - 37 = 0. Let p(t) be the third derivative of t**3 - 1/20*t**f + 0*t - 4*t**2 + 0 + 1/8*t**4. Factor p(r).
-3*(r - 2)*(r + 1)
Let c(m) = -m**2 - 5*m - 4. Suppose -5 = -3*s - 14. Let n be c(s). Let -35/2*x**3 + 2 - 14*x + 59/2*x**n = 0. What is x?
2/7, 2/5, 1
Factor 0*b**2 - 1/2*b**5 + 0*b + 0 + 1/2*b**4 + b**3.
-b**3*(b - 2)*(b + 1)/2
Suppose -3*c + 29 = -3*r + 80, -5*r = 3*c + 59. Let u be (2/(-6))/(3/c). Factor 22*t**u - 8*t + 17*t**4 + 2 - 5 - 4*t**5 - 28*t**3 + 4.
-(t - 1)**4*(4*t - 1)
Let p(q) = 85*q**3 + 880*q**2 + 1140*q - 610. Let k(d) = 28*d**3 + 293*d**2 + 380*d - 203. Let o(i) = 10*k(i) - 3*p(i). Factor o(f).
5*(f + 2)*(f + 10)*(5*f - 2)
Suppose -10*c + 50 + 40 = 0. Let d be (-254)/(-56) + c/(-36) + -4. Factor -2/7*l**5 + d*l**3 + 0 - 2/7*l**2 + 0*l + 2/7*l**4.
-2*l**2*(l - 1)**2*(l + 1)/7
Let m(y) be the first derivative of 0*y**2 + 0*y + 8/3*y**3 + 7*y**4 + 4*y**5 + 3. Find q, given that m(q) = 0.
-1, -2/5, 0
Let v be (-962)/52 + 19/1. Factor -1/4*h**4 + 1/4*h**3 - 5/4*h + v + 3/4*h**2.
-(h - 1)**3*(h + 2)/4
Let f(t) be the third derivative of t**7/420 + 7*t**6/120 + 11*t**5/30 + 5*t**4/6 - 2*t**2 + 10*t. Solve f(i) = 0.
-10, -2, 0
Let r(j) be the third derivative of 0*j + 0 + 7/24*j**4 - j**3 - 1/60*j**5 + 17*j**2. Determine q, given that r(q) = 0.
1, 6
Let g(t) = 10*t - 19. Let n be g(3). Suppose -2*f + a - 1 = -2*a, -n = -2*f - a. Find z, given that 0 - 1/7*z**5 + 2/7*z**3 - 1/7*z + 0*z**f + 0*z**2 = 0.
-1, 0, 1
Let b(n) be the first derivative of -3*n**4/4 + 4*n**3/3 - n**2/2 + 19. Let m(g) = 16*g**3 - 21*g**2 + 6*g - 1. Let t(k) = 22*b(k) + 4*m(k). Solve t(u) = 0.
-1, 1, 2
Let u(o) = o**2 - 20*o + 24. Let r be (-1242)/(-66) + 4/22. Let q be u(r). Suppose -c**q + 3*c**5 + 4*c**4 + 2*c**5 = 0. What is c?
-1, 0
Let k be (-48)/(-108) + 8/(-72). Factor 0 - 1/3*d**4 + d**3 - d + k*d**2.
-d*(d - 3)*(d - 1)*(d + 1)/3
Let y = 65 - 62. Suppose -u + y = z, -2*z = 2*u - 6*u. What is m in 8/7*m**z + 0 + 4/7*m**3 + 4/7*m = 0?
-1, 0
Let p(l) be the third derivative of l**7/70 - 51*l**6/40 + 228*l**5/5 - 800*l**4 + 6144*l**3 + 838*l**2. Factor p(u).
3*(u - 16)**3*(u - 3)
Let y(r) be the second derivative of -r**4/4 + 4*r**3 + 30*r**2 + 251*r. Let y(x) = 0. What is x?
-2, 10
Let x(z) = -z**3 + 7*z**2 + 2*z - 2. Let l be x(5). Suppose l*m = 61*m. Let 1/2*w - 1/2*w**4 + 3/2*w**3 + m - 3/2*w**2 = 0. Calculate w.
0, 1
Let v(b) be the third derivative of -1/24*b**6 + 0*b**5 + 0*b + 5/8*b**4 + 4*b**2 + 5/3*b**3 + 0. Solve v(a) = 0 for a.
-1, 2
Suppose -y - 4*q = -3*q - 6, 5*q - 12 = y. Find i such that 6*i**3 - 6*i**3 + 3 - 3*i**2 - 3*i + y*i**3 = 0.
-1, 1
Let m be 12/(-15)*(-30)/44. Factor -6/11*o**3 + m*o**4 + 0*o + 2/11*o**2 + 0 - 2/11*o**5.
-2*o**2*(o - 1)**3/11
Suppose -4*p - 3*l = -779, -2*p = -3*l - 168 - 235. Suppose -5*b - 187 = -p. Factor 0*o + 2/13*o**b - 2/13.
2*(o - 1)*(o + 1)/13
Let d(s) be the second derivative of s**4/3 + 34*s**3/3 - 36*s**2 + 152*s. Determine t so that d(t) = 0.
-18, 1
Let s be (-14)/5*(-3 + 91/14). Let d = s + 10. Suppose -2/5 - 1/5*k + d*k**3 + 3/5*k**2 - 1/5*k**4 = 0. Calculate k.
-1, 1, 2
Suppose 0 + 0*i + 9*i**2 + 29/2*i**3 + 6*i**4 + 1/2*i**5 = 0. What is i?
-9, -2, -1, 0
Determine p so that 0 + 121/4*p + 1/4*p**3 + 11/2*p**2 = 0.
-11, 0
Let o(n) be the second derivative of -n**6/120 - 3*n**5/16 - n**4/4 + 7*n**3/6 + 27*n + 4. Factor o(b).
-b*(b - 1)*(b + 2)*(b + 14)/4
Let d be (-6 - 3)*(-12)/54. Let l(j) be the third derivative of 0 + 0*j + 2/3*j**3 + 5/24*j**4 + 1/60*j**5 - 10*j**d. Factor l(w).
(w + 1)*(w + 4)
Factor 4*g**4 - 36*g + 50*g**2 - 29*g**2 + 55*g**2 - 44*g**3.
4*g*(g - 9)*(g - 1)**2
Factor -2/3*v**3 + 2/3*v**2 + 0 + 4*v.
-2*v*(v - 3)*(v + 2)/3
Suppose -398 - 22 = 2*k. Let u = k + 421/2. Factor u*d + 1/2*d**5 - d**3 + 0 + 0*d**2 + 0*d**4.
d*(d - 1)**2*(d + 1)**2/2
Let p be 2*(3/(-6) + 2). Suppose -c = -0 - 12. Suppose -p - 19*x**2 - 5*x**3 + x**2 - 7*x**3 - 3*x**4 - c*x = 0. What is x?
-1
Suppose 0 + 0 = -693*a - 0. Factor 0*k + a - 1/2*k**2.
-k**2/2
Let c(t) be the third derivative of -4/9*t**3 + 1/9*t**4 + 23*t**2 + 0 - 1/90*t**5 + 0*t. Factor c(q).
-2*(q - 2)**2/3
Let l(g) = -10*g**2 + 124*g - 294. Let n(x) = -9*x**2 + 122*x - 295. Let j(p) = 5*l(p) - 6*n(p). Factor j(r).
4*(r - 25)*(r - 3)
Let u(a) be the second derivative of -a**4/20 + 101*a**3/5 - 30603*a**2/10 + 70*a. Let u(m) = 0. Calculate m.
101
Let d(q) be the third derivative of -q**8/3780 + q**7/756 + q**6/540 + 2*q**3 - 20*q**2. Let w(r) be the first derivative of d(r). Find n, given that w(n) = 0.
-1/2, 0, 3
Factor -17*l**2 + 14*l - 8*l + 21*l**2 + 6*l.
4*l*(l + 3)
Let l(v) be the second derivative of 5*v + 13/4*v**4 + 24*v**3 + 0 + 3/20*v**5 + 54*v**2. Factor l(p).
3*(p + 1)*(p + 6)**2
Let v be (0 - 1)/(4/(-12)). Let q(h) be the second derivative of h + 3/5*h**2 - 2/15*h**v + 0 - 1/30*h**4. Determine p so that q(p) = 0.
-3, 1
Let p(y) be the first derivative of -50/7*y**2 + 12/7*y - 16/7*y**4 + 32/3*y**3 + 26. Find m, given that p(m) = 0.
1/4, 3
What is s in -303750*s + 562500 + 2/3*s**4 - 454/3*s**3 + 11550*s**2 = 0?
2, 75
Let t(s) = 198*s + 4953. Let b be t(-25). Let -1/2 - 1/6*i**2 + 1/6*i**b - 5/6*i = 0. Calculate i.
-1, 3
Let c(k) be the second derivative of 1/60*k**4 + 0*k**2 + 0 - 1/150*k**6 + 0*k**3 + 0*k**5 - 14*k. Suppose c(v) = 0. What is v?
-1, 0, 1
Let f(z) be the first derivative of 0*z + 27 - 2/17*z**3 + 1/34*z**4 + 0*z**2. Determine p, given that f(p) = 0.
0, 3
Let u = -3308 - -3310. Factor 2 + u*k + 1/2*k**2.
(k + 2)**2/2
Let x = 3556541/5 + -706642. Let n = x - 4642. Suppose -4/5 - 48/5*r - n*r**3 - 33*r**2 = 0. What is r?
-1, -2/11
Let t = -2005/112 + 291/16. Solve -18/7*s**2 + 8/7*s**3 + 12/7*s - t = 0 for s.
1/4, 1
Let k(t) = t**4 + 7*t**3 - 3*t**2 + t - 6. Let i(d) = d**4 + 8*d**3 - 4*d**2 + 2*d - 7. Let s(r) = 4*i(r) - 5*k(r). Determine y so that s(y) = 0.
-2, -1, 1
Let o(x) be the third derivative of x**5/30 - 23*x**4/12 - 26*x**3 + 130*x**2. Factor o(f).
2*(f - 26)*(f + 3)
Let x = -73 - -75. Find q, given that 2*q**2 + 2*q - 125 + x*q**2 - 3*q**2 + 126 = 0.
-1
Let z be (-3*(-10)/(-9))/((-2)/36). Let q be (0 + (-6)/(-20))/(72/z). What is f in -7/4*f**3 + 0 + 5/4*f**2 + 3/4*f**4 - q*f = 0?
0, 1/3, 1
Let c(j) be the second derivative of 0 - 1/6*j**3 - 1/8*j**2 - 1/8*j**4 - 31*j - 1/120*j**6 - 1/20*j**5. Factor c(d).
-(d + 1)**4/4
Let i(w) be the first derivative of w**6/9 + 8*w**5/15 + 2*w**4/3 - 4*w**3/9 - 5*w**2/3 - 4*w/3 - 6. Solve i(j) = 0.
-2, -1, 1
Let v(a) be the first derivative of 7*a**4/4 + 10*a**3/3 - 4*a**2 + 527. What is x in v(x) = 0?
-2, 0, 4/7
Suppose 0 = -2*u + 6 + 4. Factor -1 + 31*b + 24 + u*b - 131 - 3*b**2.
-3*(b - 6)**2
Let z = -54 + 49. Let l be (-5 - z)*(-1)/((-1)/(-1)). Factor -2/5*k**2 + l*k + 0.
-2*k**2/5
Let g = -2722 - -2725. What is a in -1 + 5/2*a**2 - 7/2*a + 2*a**g = 0?
-2, -1/4, 1
Let b(j) be the third derivative of j**6/360 + 7*j**5/180 + 11*j**4/72 + 5*j**3/18 - 8*j**2 - 4*j. What is k in b(k) = 0?
-5, -1
Let t(u) be the second derivative of u**4/4 + 22*u**3/3 - 15*u**2/2 + 11*u + 4. Let t(b) = 0. Calculate b.
-15, 1/3
Let m be (-14 + 278/20)/(2/(-30)). Solve 29/4*c - 15/2*c**2 + 7/4*c**3 - m = 0 for c.
2/7, 1, 3
Let a(s) be the second derivative of -17*s + 0*s**2 - 1/8*s**3 - 1/48*s**4 + 0. Factor a(m