
Let y be (-2 - (-2)/4)/((-4)/24). Suppose -8*s = -y*s + 18. Factor -21/2*x**3 - 3 + s*x**2 - 9/2*x.
-3*(x - 1)**2*(7*x + 2)/2
Let a be 2/7*(-427)/(-183). Factor 1/3*x**2 - x + a.
(x - 2)*(x - 1)/3
Let j(r) be the first derivative of -1/9*r**2 - 9 + 0*r - 4/27*r**3 - 1/18*r**4. Find v, given that j(v) = 0.
-1, 0
Let p = -211756/7 + 30251. Determine g so that -p*g**3 + 1/7*g + 2/7 + 1/7*g**4 - 3/7*g**2 = 0.
-1, 1, 2
Let n(h) be the first derivative of h**7/168 - h**6/18 + h**5/6 - 8*h**3/3 + 34. Let j(b) be the third derivative of n(b). Suppose j(f) = 0. What is f?
0, 2
Suppose z = -4*o - 29, -5*z + 68 = 7*o + 109. Factor 0 - 2/17*y**z - 2/17*y - 4/17*y**2.
-2*y*(y + 1)**2/17
Let f(h) be the first derivative of -2/15*h**3 + 8*h + 1/30*h**4 + 0*h**2 - 9. Let j(g) be the first derivative of f(g). Determine m so that j(m) = 0.
0, 2
Let i(g) be the second derivative of -2*g**6/75 + 8*g**5/25 - g**4/15 - 28*g**3/5 - g - 114. Determine f, given that i(f) = 0.
-2, 0, 3, 7
Let h(w) be the third derivative of w**8/14 + 6*w**7/35 - 7*w**6/20 - 7*w**5/20 + 9*w**4/8 - w**3 - 18*w**2 + 4. Factor h(f).
3*(f + 1)*(f + 2)*(2*f - 1)**3
Let v = 3084 - 3082. Factor 1/2*n**v + 0 - 1/2*n.
n*(n - 1)/2
Let w = -20255/3 - -6753. What is p in 4/9*p**3 + 0*p - w*p**2 + 16/9 = 0?
-1, 2
Let b(l) = -7*l + 25. Let v be b(3). Let j be ((-6)/27)/(74/(-18) + v). Factor 1/3*x + 0 + 1/3*x**4 + x**3 + x**j.
x*(x + 1)**3/3
Let s(z) be the second derivative of 0 + 1/20*z**5 + 0*z**3 + 1/12*z**4 - 9*z + 0*z**2. Determine d, given that s(d) = 0.
-1, 0
Let j be (3 - (-4 + 8)) + (4 - 0). Factor -6 + 11 + 3*z**2 - j*z**4 + 6*z**3 - 5 - 6*z.
-3*z*(z - 2)*(z - 1)*(z + 1)
Let t(y) be the first derivative of y**5/300 - y**4/12 + 3*y**3/10 + 27*y**2/2 - 26. Let o(l) be the second derivative of t(l). Factor o(c).
(c - 9)*(c - 1)/5
Let x(f) be the first derivative of 5/12*f**3 + f + 10 - 3/2*f**2. Let x(t) = 0. What is t?
2/5, 2
Let a(f) be the second derivative of -5*f**4/12 + 10*f**3 + 65*f**2/2 + 90*f. What is x in a(x) = 0?
-1, 13
Let j = -3928 + 19652/5. Factor 4/5*p**3 - 4/5 + j*p - 12/5*p**2.
4*(p - 1)**3/5
Let c(h) be the second derivative of h**5/110 + 4*h**4/33 + 13*h**3/33 + 6*h**2/11 - 19*h + 3. Factor c(f).
2*(f + 1)**2*(f + 6)/11
Let x(c) = -c**2 + 3*c + 1. Let a be x(5). Let m be (a/(-5))/((-6)/(-40)). Solve -32*f**3 - 9*f**2 + 30*f**4 + 6*f - 75*f**4 - 12*f**3 - m*f**5 - 4*f**3 = 0.
-2, -1, 0, 1/4
Let s(q) be the first derivative of q**8/672 - q**7/210 + q**6/240 + 17*q**2/2 + 14. Let i(o) be the second derivative of s(o). Find m such that i(m) = 0.
0, 1
Find l such that 38071*l + 3*l**2 - 22500 - 38671*l - 7*l**2 = 0.
-75
Suppose -4 - 30 = 2*k + 5*x, 0 = 3*k - 2*x - 25. Let -21/2*a**2 + 12*a - 2 + 5/2*a**k = 0. Calculate a.
1/5, 2
Suppose 0 = 3*s - 319 + 295. Factor 16/3*t**2 - s*t**3 + 0*t + 0 - 10/3*t**5 - 12*t**4.
-2*t**2*(t + 2)**2*(5*t - 2)/3
Determine b so that 3*b**3 - 39/2*b**5 + 0*b + 0*b**2 + 0 + 33/2*b**4 = 0.
-2/13, 0, 1
Let n(o) be the third derivative of 0*o**3 + 1/840*o**7 + 0 + 0*o**4 + 0*o + 1/96*o**6 + 1/40*o**5 - 7*o**2. Determine c so that n(c) = 0.
-3, -2, 0
Let p be (-47)/((-235)/12)*5/3. Let d(b) be the second derivative of 0*b**2 + 5/4*b**p + 3*b - b**3 - 3/5*b**5 + 0 + 1/10*b**6. What is w in d(w) = 0?
0, 1, 2
Suppose 223 = -33*g + 322. Factor -2/17*k**g + 16/17 - 24/17*k + 12/17*k**2.
-2*(k - 2)**3/17
Let i(m) be the first derivative of -m**4/6 - 136*m**3/3 - 4624*m**2 - 628864*m/3 - 106. Factor i(l).
-2*(l + 68)**3/3
Let p be (-5193)/(-2308) + (6/16)/(3/(-2)). Solve 0*c + 0 - 3/2*c**4 - 1/2*c**5 - 3/2*c**3 - 1/2*c**p = 0.
-1, 0
Let h be ((-2)/40)/(18/(-12)). Let g(a) be the third derivative of 0*a**3 + 1/12*a**4 + 0*a - 1/60*a**6 - 3*a**2 + 1/105*a**7 - h*a**5 + 0. Factor g(n).
2*n*(n - 1)**2*(n + 1)
Let w(x) be the first derivative of 1/35*x**5 - 16/7*x + 16 - 1/28*x**4 - 4/7*x**3 + 2*x**2. Suppose w(s) = 0. Calculate s.
-4, 1, 2
Let b(i) = -2*i**2 - 12*i - 5. Let c(z) = -9*z**2 - 63*z - 24. Let a(h) = 24*b(h) - 5*c(h). Suppose a(f) = 0. Calculate f.
0, 9
Let m(j) = j**3 + 17*j**2 - 18*j + 5. Let v be m(-18). Factor -v*x**2 - 10*x + 1 + 3 + 10*x**2 - 2*x**3 + 3*x**2.
-2*(x - 2)*(x - 1)**2
Suppose -2*j + 5 = 3*d - 18, -3*j = -d + 15. Let a(z) = -z**2 + 7*z + 22. Let w be a(d). Factor h**w + 37/4*h**2 + 6*h + 21/4*h**3 + 1.
(h + 1)*(h + 2)**2*(4*h + 1)/4
Let u(j) be the first derivative of j**4/14 + 16*j**3/21 + 20*j**2/7 + 32*j/7 + 209. Factor u(g).
2*(g + 2)**2*(g + 4)/7
Factor 2/5*x + 1/2*x**3 - 13/10*x**2 + 2/5.
(x - 2)*(x - 1)*(5*x + 2)/10
Let o(a) = a**2 + 34*a + 266. Let c be o(-12). What is s in 28/3*s**c + 32/3*s + 0 - 4/3*s**3 = 0?
-1, 0, 8
Let y(n) = 3*n - 3. Let b be y(2). Determine c so that 4*c**4 + 0*c**4 + 34*c**2 - 10*c - 20*c**b + c**4 - 9*c**2 = 0.
0, 1, 2
Suppose -48*u - 56 = -52*u. Suppose -n - 4 = 0, -4*a = -3*n - 14 - u. Factor 0 + 2/5*k**a + 2/5*k - 2/5*k**3 - 2/5*k**2.
2*k*(k - 1)**2*(k + 1)/5
Let i = 284 + -293. Let k be (-4)/(-14)*(i - 427/(-42)). Determine s, given that 5/3*s - 4/3 - k*s**2 = 0.
1, 4
Let w = 1552 + -1549. Factor 0 + 0*y**2 + 2/3*y**w - 2/3*y.
2*y*(y - 1)*(y + 1)/3
Let c(z) be the first derivative of -z**4/2 + 52*z**3/3 - 192*z**2 + 576*z - 89. Factor c(h).
-2*(h - 12)**2*(h - 2)
Let d(v) be the second derivative of v**4/48 + v**3/4 - 7*v**2/8 - 6*v - 11. Factor d(m).
(m - 1)*(m + 7)/4
Factor -68*r**2 - 30*r**2 + 1440*r + 576 + 1024 + 4*r**3 - 58*r**2.
4*(r - 20)**2*(r + 1)
Let x = -2/2271 + 1520/6813. Factor 2/9*i - 4/9*i**2 + x*i**3 + 0.
2*i*(i - 1)**2/9
Let u(n) be the first derivative of -n**5/10 - 6*n**4 - 263*n**3/3 + 300*n**2 - 625*n/2 - 465. Solve u(x) = 0 for x.
-25, 1
Let 5*n**3 - 9*n + 3*n - 24*n**3 + n**4 + 80*n**2 + 97*n + 9*n = 0. What is n?
-1, 0, 10
Let v be ((-20)/(-36))/((-16)/(-120) + 1/5). What is c in 5/6*c**2 + 5/6*c - v = 0?
-2, 1
Let m(y) be the first derivative of -2*y**3/3 - 30*y**2 - 450*y + 61. Factor m(x).
-2*(x + 15)**2
Let d(f) = -7*f**5 + 3*f**4 + 9*f**3 - 11*f**2 + 6*f - 6. Let k(u) = u**5 - u**4 + u**2 - u + 1. Let h(g) = -5*d(g) - 30*k(g). Find z, given that h(z) = 0.
-5, 0, 1
Determine a so that 3/4*a**2 - 81/2*a + 2187/4 = 0.
27
Let g(k) be the first derivative of 0*k - 4 - 5/6*k**4 + 0*k**2 + 0*k**3 + 2/15*k**5. Solve g(z) = 0.
0, 5
Let j(h) be the first derivative of -14/25*h**5 + 8/5*h + 26/15*h**3 + 7/5*h**4 + 3 - 4*h**2 - 4/15*h**6. Find w such that j(w) = 0.
-2, 1/4, 1
Let n(b) be the first derivative of 8*b**5/85 + 10*b**4/17 + 22*b**3/17 + 20*b**2/17 + 8*b/17 + 207. Find l such that n(l) = 0.
-2, -1/2
Determine r so that 2/3*r**3 + 20/3 + 2*r - 4*r**2 = 0.
-1, 2, 5
Let p(v) be the first derivative of -40*v + 25 + 25*v**2 - 5/4*v**4 - 5/3*v**3. Let p(h) = 0. Calculate h.
-4, 1, 2
Let c(b) be the second derivative of -b**7/42 + b**6/3 - 11*b**5/6 + 5*b**4 - 15*b**3/2 - 6*b**2 + 20*b. Let m(d) be the first derivative of c(d). Factor m(n).
-5*(n - 3)**2*(n - 1)**2
Let g(w) be the second derivative of 13*w - w**5 + 0 - 5*w**2 - 2*w**6 + 35/6*w**4 - 5/2*w**3 + 5/6*w**7. Factor g(v).
5*(v - 1)**3*(v + 1)*(7*v + 2)
Let m = 3168 + -3165. Factor 0*h + 0 - 3/8*h**2 - 3/8*h**m.
-3*h**2*(h + 1)/8
Suppose 0 = -3*r + 17 + 19. Suppose 0*m + m - r = -4*d, 2*m = -2*d + 6. Determine y so that 3/7*y**3 + m - 3/7*y**2 - 3/7*y + 3/7*y**4 = 0.
-1, 0, 1
Let w be (-1)/((-4)/1512*2). Let o = 124 - w. Let m(y) = -55*y**2 + 10*y - 65. Let k(x) = -5*x**2 + x - 6. Let i(s) = o*k(s) + 6*m(s). Factor i(l).
-5*l*(l + 1)
Let z be 9838/(-30) - 14/35. Let i = -322 - z. What is j in 0 - 7/3*j**5 - i*j**4 - 8/3*j**3 + 4/3*j**2 + 0*j = 0?
-2, -1, 0, 2/7
Let o(t) = t**3 + 53*t**2 - 135*t + 25. Let j(n) = -n**3 - 27*n**2 + 67*n - 15. Let h(b) = 5*j(b) + 3*o(b). Factor h(s).
-2*s*(s - 7)*(s - 5)
Solve 51/7*n**3 - 9/7*n**4 + 0 + 5/7*n - 31/7*n**2 = 0.
0, 1/3, 5
Let u = 22 - 16. Factor -14*m**2 + 26*m + 5*m**3 - 10 - u*m**2 - m.
5*(m - 2)*(m - 1)**2
Let x(i) = 4*i**5 + 28*i**4 - 36*i**3 - 44*i**2 - 8*i - 24. Let y(p) = -p**4 + p**3 + p**2 + 1. Let h(k) = x(k) + 24*y(k). Factor h(s).
4*s*(s - 2)*(s + 1)**3
Let z(u) be the first derivative of 0*u**2 + 0*u - 4/3*u**3 - 16 + u**4. Find p, given that z(p) = 0.
0, 1
Let b(d) = 7*d**4 + 17*d**3 + 12*d**2 - 2*d + 2. Let l(t) = -120*t**4 - 290*t**3 - 205*t**2 +