39, 0 = -m - 5. Let z = -8 + f. Solve -h**2 + 5*h**z - h**3 + 3*h**3 = 0 for h.
-2, 0
Factor 0 + 2/9*w**2 + 0*w - 2/9*w**3.
-2*w**2*(w - 1)/9
Let p(h) = h - 6. Let w be p(8). Suppose -9 = -2*d + 5*l, 4*d + 2*l - w = 2*d. Solve 2*i**2 + 6 - i**4 - 6 - d*i**3 - 3*i**2 = 0.
-1, 0
Let c(x) be the second derivative of -x**6/30 + x**5/10 + x**4/12 - x**3/3 + 46*x. Determine n so that c(n) = 0.
-1, 0, 1, 2
Suppose -4*k = 2*t - 30, -3*k + 5 = 4*t - 6*t. Suppose 3*z + 6 + 5 = 5*i, 3 = -3*i + k*z. Factor 11 + 3*o**3 - i*o**2 - o**2 + 1 - 4*o**2.
3*(o - 2)**2*(o + 1)
Let o(f) be the second derivative of f**5/80 - 7*f**4/48 - 7*f**3/8 + 27*f**2/8 - 209*f. Find k, given that o(k) = 0.
-3, 1, 9
Let q = -56327/13 + 4333. Solve -4/13 - q*o**2 - 6/13*o = 0 for o.
-2, -1
Let b(f) be the first derivative of -f**5/105 + f**4/21 - 2*f**3/21 - 9*f**2/2 - 7. Let w(k) be the second derivative of b(k). Factor w(h).
-4*(h - 1)**2/7
Let w(h) be the third derivative of h**6/24 - 5*h**5/12 - 5*h**4/24 + 25*h**3/6 - 345*h**2. Factor w(m).
5*(m - 5)*(m - 1)*(m + 1)
Suppose 4*h - 1 = 3*h. Let j be (h/(-9))/(4 - (-50)/(-12)). Determine k, given that 0 - k**2 - j*k + 1/3*k**4 + 0*k**3 = 0.
-1, 0, 2
Determine k, given that -23 - 3*k**2 - 2*k**2 + 4 + 39 = 0.
-2, 2
Suppose 0 = -m + 4*c + 15, 527*c - 528*c = -4*m + 15. Determine d, given that 1/3*d**m + 0*d**2 - 2/3 - d = 0.
-1, 2
Let d(u) = -u**3 - 62*u**2 + 408*u + 4. Let o be d(6). Factor -594/7*g**3 + 243/7*g**o + 12/7 + 471/7*g**2 - 132/7*g.
3*(g - 1)**2*(9*g - 2)**2/7
Suppose 17 + 1 = 9*q. Let x(s) be the second derivative of 0 + s**3 + 4*s - 3/10*s**5 + 0*s**q + 1/4*s**4 - 1/10*s**6. Factor x(m).
-3*m*(m - 1)*(m + 1)*(m + 2)
Let l(u) = -u**2 - 1. Let f(m) = m**4 + m**3 - 2*m**2 - 2. Let r(d) = 3*f(d) - 6*l(d). Determine h so that r(h) = 0.
-1, 0
Let u(v) be the second derivative of 3*v**5/40 - v**4 + 3*v**3 + 72*v. Factor u(c).
3*c*(c - 6)*(c - 2)/2
Let v(h) be the first derivative of 6*h**5/115 + h**4/46 - 6*h**3/23 + 3*h**2/23 + 4*h/23 + 19. Suppose v(x) = 0. What is x?
-2, -1/3, 1
Let b(g) be the first derivative of 0*g - 5/6*g**6 + 5/2*g**2 - 11 + 10/3*g**3 - 2*g**5 + 0*g**4. Find z such that b(z) = 0.
-1, 0, 1
Let v = 22151/2 + -11074. Factor v*b**2 - 6*b + 6.
3*(b - 2)**2/2
Let q(d) be the second derivative of 0 + 9/13*d**2 - 2/13*d**3 + 3*d + 1/78*d**4. Factor q(h).
2*(h - 3)**2/13
Let b(g) be the first derivative of g**7/70 - 3*g**6/40 + g**5/10 + 13*g**2/2 + 12. Let j(z) be the second derivative of b(z). Find n, given that j(n) = 0.
0, 1, 2
Let d(m) be the first derivative of -1/5*m**5 - 1/2*m**4 + 11/3*m**3 + 6*m**2 - 36*m + 19. What is v in d(v) = 0?
-3, 2
Factor -5492*f - 1350*f + 1702*f + 28 + 46947*f**2 + 283298*f**2 - 8.
5*(257*f - 2)**2
Suppose 0 = 2*t + 4*k - 22, 0 = 8*t - 11*t - 5*k + 29. Find y, given that 4/5*y - 2/5*y**4 + 8/5*y**t + 0 - 2*y**2 = 0.
0, 1, 2
Let y(m) be the second derivative of -10/3*m**3 - 11*m + 5/12*m**4 + 10*m**2 + 0. Factor y(w).
5*(w - 2)**2
Let l = 13345 + -4257051/319. Let f = 2532/1595 + l. What is r in 8/5*r + 4/5*r**2 - f*r**3 + 2/5 - 6/5*r**4 = 0?
-1, -1/3, 1
Suppose 846 = 204*j - 49*j + 268*j. Find g, given that -4/3*g - 1/3*g**j + 1/3*g**3 + 4/3 = 0.
-2, 1, 2
Let a(o) = 3*o + 4 - 2*o - 4*o. Let g be a(0). Determine x so that 0 + 4/3*x**2 + 5/3*x**4 - g*x**3 + 0*x = 0.
0, 2/5, 2
Suppose -3*o + 43 = -4*t - 4*o, -2*t = 2*o + 14. Let u be 322/392 - -1*t/21. Find v such that u*v**2 + 0 + 3/4*v = 0.
-3, 0
Solve 1/7*o**2 - 40/7 + 39/7*o = 0 for o.
-40, 1
Let b(y) = -y**3 - 5*y**2 + 5*y - 1. Suppose 3*q + 6 = 0, -3*q = 3*m + q + 26. Let h be b(m). Let 2*w**2 - 4*w + 6 - h*w**2 + 4*w + 3*w = 0. What is w?
-1, 2
Factor -237/5*p**2 + 1/5*p**3 + 18723/5*p - 493039/5.
(p - 79)**3/5
Suppose b - 3*m = -15, -5 = -3*b + 3*m - 4*m. Let o = 6 + -1. Let 2*u - o*u**2 + b*u**3 + u**2 + 2*u**3 = 0. Calculate u.
0, 1
Let q = -16 - -31. Let s be (-2 + 40/q)/(20/18). Find k such that -s*k**2 - 2/5 + k = 0.
2/3, 1
Let k(u) = -u**4 - 20*u**3 + 62*u**2 + 2. Let j(i) = -4*i**4 - 62*i**3 + 185*i**2 + 7. Let l(b) = -2*j(b) + 7*k(b). What is r in l(r) = 0?
0, 8
Factor -52/5*t + 18/5 - 8/5*t**3 - 78/5*t**2.
-2*(t + 1)*(t + 9)*(4*t - 1)/5
Suppose -3*p - 13 = k, 3*p + 19 = -2*p + k. Let h be 1 + (-9)/((-54)/p). Factor -h*t**2 + 1/3*t + 0.
-t*(t - 1)/3
Let p(g) = -g**2 + 6. Let k be p(0). Suppose -d + k = d. Factor 2*n**5 + n**4 - n**5 + n**5 - d*n**4.
2*n**4*(n - 1)
Solve -1/7*o**3 + 0*o**2 - 16/7 + 12/7*o = 0 for o.
-4, 2
Let y = -52545/4 - -13152. Find f such that -3 + y*f**3 - 111/4*f**2 + 18*f - 3*f**4 = 0.
1/4, 1, 2
Let n(m) be the third derivative of -m**5/30 - 8*m**4/3 - 31*m**3/3 - 2*m**2 + 13*m. Factor n(z).
-2*(z + 1)*(z + 31)
Let i = -25/9 + 3. Let z(b) be the first derivative of 4 - 2/27*b**3 + 1/9*b**2 - 1/18*b**4 + i*b. Factor z(s).
-2*(s - 1)*(s + 1)**2/9
Let w be 18/3 - (-3 + 0). Let x = w - 6. Factor -s**3 - 4*s - 2*s**x - 6 + 13*s.
-3*(s - 1)**2*(s + 2)
Let s = 40835 + -122503/3. Find r such that -1/2*r - 1/6*r**3 - s*r**2 + 0 = 0.
-3, -1, 0
Solve -16/9*s + 20/9*s**2 + 0 + 2/3*s**3 = 0 for s.
-4, 0, 2/3
Let j(r) be the first derivative of 3*r**4/4 + r**3 - 15*r**2 + 24*r - 100. Let j(o) = 0. What is o?
-4, 1, 2
Factor 4/7*u**2 - 32/7 - 4*u.
4*(u - 8)*(u + 1)/7
Let g(u) = -u. Let i be g(-4). Let r = -1907 - -1911. Factor 20*a + 24*a**2 + 16*a**3 + r - 4*a - 19*a**4 + 23*a**i.
4*(a + 1)**4
Let i(k) be the third derivative of -5*k**7/42 + k**6/2 + 3*k**5 - 10*k**4/3 + 196*k**2. Let i(y) = 0. Calculate y.
-2, 0, 2/5, 4
Factor -c - 6 - 6*c**2 + 12 + 8*c**3 + 5*c - 12*c.
2*(c - 1)*(c + 1)*(4*c - 3)
Let d(o) be the first derivative of -o**6/2160 + o**4/36 + 2*o**3/3 + 7. Let f(m) be the third derivative of d(m). Suppose f(i) = 0. What is i?
-2, 2
Factor 18/7 + 38/7*c + 22/7*c**2 + 2/7*c**3.
2*(c + 1)**2*(c + 9)/7
Factor 32/3 - 16/3*y**2 + 32/3*y - 32/3*y**3 - 2/3*y**5 - 14/3*y**4.
-2*(y - 1)*(y + 2)**4/3
Let l(m) be the third derivative of -m**6/60 + 3*m**5/10 - 2*m**4/3 - 254*m**2 - 1. Factor l(c).
-2*c*(c - 8)*(c - 1)
Let q(g) = 12*g + 3. Let z be q(0). Let t(o) be the third derivative of 0*o - 1/21*o**4 + 0 - 8/21*o**z - 1/420*o**5 + 4*o**2. Factor t(d).
-(d + 4)**2/7
Let i(q) be the third derivative of -3*q**2 - 1/30*q**6 + 1/8*q**4 + 0*q + 1/3*q**3 - 1/30*q**5 + 0*q**7 + 1/336*q**8 + 0. Factor i(v).
(v - 2)*(v - 1)*(v + 1)**3
What is t in -16/3*t**4 - 2/3*t**5 + 16/3*t**2 + 32/3*t + 0 - 10*t**3 = 0?
-4, -1, 0, 1
Let q(c) be the third derivative of c**6/60 + 2*c**5/15 + c**4/4 + 3*c**2 - 2. Factor q(v).
2*v*(v + 1)*(v + 3)
Let i(c) be the second derivative of c**5/110 - 2*c**4/33 - c**3/3 + 30*c**2/11 - 323*c. Factor i(y).
2*(y - 5)*(y - 2)*(y + 3)/11
Let i be 15/(-20) - 253/(-92). Factor 9/4*l**i + 1/4*l**4 + 1/2 + 7/4*l + 5/4*l**3.
(l + 1)**3*(l + 2)/4
Let y(j) be the second derivative of 3*j + 0 + 1/5*j**5 - 2/3*j**3 + 1/3*j**6 + 0*j**2 - 5/6*j**4. Factor y(z).
2*z*(z - 1)*(z + 1)*(5*z + 2)
Let h(n) be the first derivative of 3*n**5/10 + 15*n**4/8 - n**3/2 - 15*n**2/4 - 136. Let h(d) = 0. Calculate d.
-5, -1, 0, 1
Let h be ((-104)/80 + 17 + -16)*2*-1. Factor 17/10*t - h - 3/2*t**2 + 1/10*t**4 + 3/10*t**3.
(t - 1)**3*(t + 6)/10
Let m = 7954/4965 + -2/993. Solve 2/5*x**2 + m*x + 8/5 = 0.
-2
Factor -7/2*r**3 + 15/2*r**2 - 13/2*r + 1/2*r**4 + 2.
(r - 4)*(r - 1)**3/2
Suppose 0 = -c + 2*d + 12, 2*d = -4*c - 2*d + 24. Let o be (-6 - -1)*(-8)/c. Factor 4*j**3 - 10 - 4*j**o + 10 + 2*j**5 - 2*j.
-2*j*(j - 1)**2*(j + 1)**2
Factor -229 + 277 + i**2 - 6*i**2 + 2*i**2 - 45*i.
-3*(i - 1)*(i + 16)
Factor 3/7*v**5 + 6/7*v**3 - 9/7*v**4 + 0*v**2 + 0 + 0*v.
3*v**3*(v - 2)*(v - 1)/7
Let c(g) be the first derivative of -g**6/12 + g**5/4 - 5*g**4/24 - 14*g - 26. Let w(p) be the first derivative of c(p). Factor w(s).
-5*s**2*(s - 1)**2/2
Let v = -2 - 21. Let c = -21 - v. Factor s**3 - s**3 + c*s**2 - 8*s**5 + 2*s**3 - 6*s**3 - 14*s**4.
-2*s**2*(s + 1)**2*(4*s - 1)
Let h(k) be the third derivative of -k**7/105 + 29*k**6/60 - 9*k**5/10 - 29*k**4/12 + 28*k**3/3 + 21*k**2. Find j, given that h(j) = 0.
-1, 1, 28
Let r = -2433 - -2433. Let w(o) be the second derivative of r - 3/2*o**3 - 3/20*o**5 + 0*o**2 + o**4 + 9*o. Factor w(x).
-3*x*(x - 3)*(x - 1)
Let f(k) be the third derivative of 0 - 1/6*k**4 - 1/30*k**5 +