0 = -3*z - 14 + 14. Suppose -6*n = -z*n + 16*n. Factor -10/7*a**4 - 4/7*a**5 - 2/7*a**2 - 8/7*a**3 + n*a + 0.
-2*a**2*(a + 1)**2*(2*a + 1)/7
Suppose 268 = 43*j + 124*j - 33*j. Determine i, given that 12/7*i - 1/7*i**j - 36/7 = 0.
6
Let a = 4453 + -4450. What is r in -4/3*r**4 + 0 + 4/3*r**2 + 1/3*r**5 - 4/3*r + r**a = 0?
-1, 0, 1, 2
Factor 217*m**2 - 226*m + 255*m**2 + 66*m + 60*m**3 - 5*m**4 - 579*m**2 - 5*m**5 + 187*m**2 - 240.
-5*(m - 3)*(m - 2)*(m + 2)**3
Suppose 21*v - 26*v + 20 = 0. Suppose -l**3 - v*l**2 + l**4 - l**2 + l + 4*l**2 = 0. What is l?
-1, 0, 1
Factor -204*h - 3*h**2 - 4179 + 355 + 356.
-3*(h + 34)**2
Let z = 277/980 + -8/245. Factor 1/4*t**3 - 3/4 - 5/4*t - z*t**2.
(t - 3)*(t + 1)**2/4
Suppose -2*t + 16 = -4*z, 14*t - 11*t = -5*z - 9. Solve n**4 + 5*n**3 + 3 + 9*n**3 + n - 8*n**3 + 9*n + 12*n**t = 0.
-3, -1
Let h(c) be the third derivative of -c**9/60480 - c**8/10080 + c**7/1680 + 2*c**5/5 + 20*c**2. Let w(i) be the third derivative of h(i). What is j in w(j) = 0?
-3, 0, 1
Let w(z) = -5*z + 152. Let d be w(30). Factor -c**3 + 1/2*c**d + 0 - 1/2*c**4 + c.
-c*(c - 1)*(c + 1)*(c + 2)/2
Let h(n) be the third derivative of n**8/504 - 4*n**7/105 - n**6/180 + 2*n**5/15 + 34*n**2. Find o, given that h(o) = 0.
-1, 0, 1, 12
Let g = 554 + -550. Let u(h) be the first derivative of 0*h + 0*h**g - 6 + 2/3*h**3 + 0*h**2 - 2/5*h**5. Factor u(i).
-2*i**2*(i - 1)*(i + 1)
Let w(j) = -5*j**2 + 17*j - 20. Let x(l) = l**2 + 1. Let m(g) = w(g) + 4*x(g). Suppose m(i) = 0. What is i?
1, 16
Let a(l) = -3*l + 4*l + 14 - 13. Let g(p) be the second derivative of -p**4/12 - 5*p**3/6 - 2*p**2 - 15*p. Let w(z) = -3*a(z) - g(z). Factor w(f).
(f + 1)**2
Let t = -67 + 45. Let c = t + 24. Find d such that 7*d**3 - 2*d**3 + 3*d + 5*d - 3*d + 10*d**c = 0.
-1, 0
Let p(s) be the third derivative of 1/840*s**7 - 9*s**2 + 0*s**3 + 0*s**4 + 1/240*s**6 + 0 + 1/240*s**5 + 0*s. Suppose p(y) = 0. What is y?
-1, 0
Let t be (130/(-26))/(-3 + 2). Let z(u) be the first derivative of -3/14*u**4 + 2 + 1/7*u**3 + 0*u**2 + 0*u + 3/35*u**t. What is x in z(x) = 0?
0, 1
Let g(o) = o**2 + 21*o + 38. Let x be g(-19). Suppose x = -11*q + 6 + 16. What is c in 3/2*c**3 - 3 + 17/2*c - 7*c**q = 0?
2/3, 1, 3
Factor 0*j + 0 - 2/7*j**2 - 4/7*j**4 + 6/7*j**3.
-2*j**2*(j - 1)*(2*j - 1)/7
Let h be 3*(3 - (-15)/(-9)). Suppose -8 = -4*y + 8. What is p in 153*p**2 - p**5 - p**y - 151*p**2 + p - p**h = 0?
-1, 0, 1
Let k be 2/(-8) - 15/(-100)*3. Suppose -2/5*g + 0 + k*g**2 = 0. Calculate g.
0, 2
Let u(o) = 84*o**2 - 1372*o - 32. Let j(q) = 13*q**2 - 211*q - 5. Let z(k) = 32*j(k) - 5*u(k). Factor z(g).
-4*g*(g - 27)
Let v(k) = k**4 + k**2. Let l(q) = -q**5 + 6*q**4 + 7*q**3. Let j(m) = -5*l(m) + 30*v(m). Suppose j(w) = 0. Calculate w.
-3, 0, 1, 2
Let 3/2*h**2 + 5/4*h**3 - 8*h - 1/4*h**4 - 8 = 0. What is h?
-2, -1, 4
Let u(h) be the third derivative of h**8/1008 - h**7/315 + h**6/360 - 10*h**2. Factor u(j).
j**3*(j - 1)**2/3
Determine x, given that -20783*x**2 + 344605*x + 615*x**3 + 168*x**4 - 333*x**4 - 4432*x**2 + 160*x**4 = 0.
0, 41
Let b be (-31 - -42) + (0 - 4). Let i be -3 + 0 - (-23)/b. Factor -i*o**2 - 2/7 + 4/7*o.
-2*(o - 1)**2/7
Let u(b) be the first derivative of -25*b**4/102 + 10*b**3/51 - b**2/17 - 5*b + 17. Let n(o) be the first derivative of u(o). Factor n(t).
-2*(5*t - 1)**2/17
Let l(h) = 15*h**2 - 90*h + 135. Let a(s) = -5*s**2 + 30*s - 45. Let w be 3*2/8*-4*-1. Let c(x) = w*l(x) + 8*a(x). Suppose c(n) = 0. What is n?
3
Let w(h) be the first derivative of h**4/8 - 2*h**3 + 9*h**2/4 + 11*h - 70. Factor w(a).
(a - 11)*(a - 2)*(a + 1)/2
Let 3*u**2 - 5*u**2 + 4 + 5800*u - 5798*u = 0. Calculate u.
-1, 2
Let a = -422 - -425. Let i(j) be the first derivative of 0*j**2 + 2/11*j - 2/33*j**a - 2. Factor i(z).
-2*(z - 1)*(z + 1)/11
Solve 30*r**3 + 117/2*r**4 - 147/4*r - 105/2*r**2 + 27/4*r**5 - 6 = 0.
-8, -1, -1/3, 1
Let x be 3/(-2) + (-28)/(-8) - 2. Suppose -5*z + x*z = -20. Factor 1/6*n**3 - 1/6*n**z + 1/6*n**2 - 1/6*n + 0.
-n*(n - 1)**2*(n + 1)/6
Let i(t) be the second derivative of 0*t**2 + 1/42*t**7 + 24*t + 9/20*t**5 + 1/3*t**3 + 7/12*t**4 + 0 + 1/6*t**6. Factor i(x).
x*(x + 1)**3*(x + 2)
Let m(k) be the second derivative of k**4/48 + 5*k**3/8 + 7*k**2 + 45*k. Factor m(g).
(g + 7)*(g + 8)/4
Let f(x) be the first derivative of 1/9*x**3 - 2/3*x**2 - 14 + x. Factor f(d).
(d - 3)*(d - 1)/3
Suppose -8 = n - 4*q, 0*q - 14 = 3*n - 2*q. Let s be 11/n + 66/22. Suppose -1/2*a**3 + s + 1/2*a + 0*a**2 - 1/4*a**4 = 0. What is a?
-1, 1
Let c be (-3 - 758/(-54))/((-3)/(-18)). Let o = -66 + c. Factor 0 + 2/9*p - o*p**2.
-2*p*(p - 1)/9
Determine a so that -7/3*a**2 - 44/3 - 1/3*a**3 + 40/3*a = 0.
-11, 2
Let o(h) be the third derivative of -h**8/420 - h**7/35 - h**6/12 + h**5/30 + 9*h**4/20 + 2*h**3/3 + 97*h**2. Solve o(t) = 0 for t.
-5, -2, -1, -1/2, 1
Let s be (0 + 12/(-10))/(4/(-10)). Let p(k) be the second derivative of -11*k - 8/75*k**5 + 7/45*k**s + 1/15*k**2 + 0 + 4/45*k**4. Factor p(o).
-2*(o - 1)*(4*o + 1)**2/15
Let h(z) = z**2 + 6*z - 2. Let o be h(-7). Factor 186*a**o - 182*a**5 - a**4 + 7*a**4 + 2*a**3.
2*a**3*(a + 1)*(2*a + 1)
Let f(m) be the first derivative of m**5/20 - m**4 - m**3/12 + 2*m**2 + 93. Let f(v) = 0. Calculate v.
-1, 0, 1, 16
Let m(g) be the first derivative of g**4 + 12*g**3 - 2*g**2 - 36*g + 21. Factor m(w).
4*(w - 1)*(w + 1)*(w + 9)
Suppose 5*n = 2*a - 25, 3*n = a + a - 19. Suppose 2*z**4 - 4*z**2 - 325*z**3 + 2 - z**a + 327*z**3 - z + 0*z**2 = 0. Calculate z.
-1, 1, 2
Let c(o) be the third derivative of 97*o**5/75 - 193*o**4/60 - o**3/15 + 420*o**2. Determine d, given that c(d) = 0.
-1/194, 1
Let o(f) = f**2 + 5. Suppose 3*x = 8*x. Let a be o(x). Suppose -5*u**5 + 3*u**5 + 4*u**2 + 18*u**a + 36*u**4 + 24*u**3 = 0. What is u?
-1, -1/4, 0
Factor 2*r**4 + 11/2*r**3 - 1/2*r**5 + 0 + 0*r + 3*r**2.
-r**2*(r - 6)*(r + 1)**2/2
Suppose 3*h + 7 = -4*u, 4*h - 16 = -3*u + 6*h. Suppose 4*x + 4*n = -20, -4*x + n + 2094 = 2074. Factor 1/4*y**x + 0 + 0*y - 1/4*y**u.
y**2*(y - 1)/4
Let v = 42 - 42. Let a(w) be the first derivative of -2 - 3/4*w**4 + v*w**2 + 3/20*w**5 + w**3 + 0*w. Find q, given that a(q) = 0.
0, 2
Let q = -48 - -4321/90. Let b(h) be the third derivative of 0*h - 1/24*h**4 + 0 + 0*h**7 - 1/1008*h**8 - 1/9*h**3 + 1/90*h**5 + 5*h**2 + q*h**6. Factor b(x).
-(x - 2)*(x - 1)*(x + 1)**3/3
Let t(w) be the second derivative of w**4/4 + 19*w**3/10 + 21*w**2/5 + 3*w + 29. Factor t(i).
3*(i + 1)*(5*i + 14)/5
Let v(y) = -y**3 - 28*y**2 + y + 30. Let o be v(-28). Let a(m) be the first derivative of 1/3*m**6 + 4 + o*m + m**2 - 4/3*m**3 + 2/5*m**5 - m**4. Factor a(r).
2*(r - 1)**2*(r + 1)**3
Let u(s) = 6 + 11*s**3 + 5*s - 24*s**3 + 14*s**3 + 5*s**2. Let b be u(-4). Factor 4*c**3 - 32*c**2 - c - 4*c - b*c**3 + 8*c**4 - 3*c.
2*c*(c - 2)*(c + 2)*(4*c + 1)
Determine v, given that -12/5 + 2/5*v**2 + 2/5*v = 0.
-3, 2
Let m = 1390 + -244639/176. Let d = m + 877/528. Factor 0 - 1/3*g - g**4 - d*g**2 - 7/3*g**3.
-g*(g + 1)**2*(3*g + 1)/3
Let d(t) be the first derivative of -14*t**5 + 435*t**4/4 + 125*t**3 + 35*t**2 - 505. Find a, given that d(a) = 0.
-1/2, -2/7, 0, 7
Let u(m) be the second derivative of m**5/210 - m**4/42 - m**3/7 - 9*m**2 - 35*m. Let t(p) be the first derivative of u(p). Find s such that t(s) = 0.
-1, 3
Let p = -4796 + 23986/5. Suppose 0 + 3/5*h**5 + p*h + 3/5*h**4 - 9/5*h**3 - 3/5*h**2 = 0. What is h?
-2, -1, 0, 1
Let f(c) be the second derivative of -1/80*c**5 + 1/48*c**4 + 0 - 1/8*c**2 + 6*c + 1/24*c**3. Factor f(m).
-(m - 1)**2*(m + 1)/4
Let m = -2 + 7. Let n(h) = -10*h**2 - 2*h - 1. Let w(o) = -12*o**2 - o**3 - 5 + 3 - 5*o - 7*o**2. Let s(d) = m*n(d) - 3*w(d). Determine c, given that s(c) = 0.
-1, -1/3
Factor -2/9 - 2/9*r**2 - 4/9*r.
-2*(r + 1)**2/9
Factor -9*s**3 - 174*s + 158 - 64*s**2 - 324 - 203*s**2 + 166.
-3*s*(s + 29)*(3*s + 2)
Suppose 3*i - 33 = -i - h, 5*h = -4*i + 37. Let g(q) be the first derivative of -2/3*q + i - 2/3*q**2 - 2/9*q**3. Factor g(p).
-2*(p + 1)**2/3
Suppose 5*h + 15 = 8*h. Factor 6 - 26*p - h*p**2 - 16 + 11*p.
-5*(p + 1)*(p + 2)
Let h(j) = -18*j**2 - 54*j + 48. Let g(d) = -67*d**2 - 216*d + 193. Let y(f) = -4*g(f) + 15*h(f). Factor y(u).
-2*(u - 26)*(u - 1)
Let f = -149 + 155. Let u(d) be the first derivative of 1/48*d**f - 1/16*d**4 + 0*d**5 + 