 2)**2*(b + 1)**2/3
Let j(d) be the first derivative of 1/14*d**4 - 6/7*d + 7 - 5/7*d**2 - 2/21*d**3. Factor j(a).
2*(a - 3)*(a + 1)**2/7
Find q, given that 24*q**2 - 39*q**4 + 12 + 31*q**3 - 18*q - 24*q + 3*q**2 + 26*q - 24*q + 9*q**5 = 0.
-1, 2/3, 1, 3
Suppose 2 = -5*d + 5*x - 3, -5*x + 15 = 0. Suppose -2*g**2 + 0*g**d + 74 + g**3 - 74 = 0. What is g?
0, 2
Suppose -5*i + 1 - 6 = -5*g, -2*i = -g + 2. Let z = -89/2 + 45. Factor z*s**2 + s + g.
s*(s + 2)/2
Let t = 9 + -7. Find b such that 0*b**2 - 5*b**3 - 121*b + 126*b + 0*b**t = 0.
-1, 0, 1
Let 915*u**5 - 236*u**3 - 112*u**4 - 60*u**2 + 919*u**5 - 1830*u**5 - 60*u**2 = 0. What is u?
-1, 0, 30
Suppose -12*q + 10*q = 20, -3*n = -2*q - 20. Let n + 2/3*r**2 + 0*r = 0. Calculate r.
0
Suppose -2*u + 12 = 0, -3*u - 2 = -s - 16. What is v in 4*v**2 - 2/5*v**s - 6/5*v**3 - 19/5*v + 1/5*v**5 + 6/5 = 0?
-3, 1, 2
Let j be ((680/(-24))/17)/(5/(-16)). Suppose -j - 4/3*u**3 - 32/3*u - 20/3*u**2 = 0. What is u?
-2, -1
Factor -6*o**2 - 24*o**2 - 6*o + 13*o + 3*o**3 + 68*o.
3*o*(o - 5)**2
Let d(c) be the first derivative of 2*c**3/57 + 3*c**2/19 - 20*c/19 + 55. Find q such that d(q) = 0.
-5, 2
Let z(d) = -13*d**2 - 11*d - 4. Let u(r) = -2*r**2 - r - 1 + 10*r**2 - 10*r**2. Let s(h) = 35*u(h) - 5*z(h). Let s(b) = 0. What is b?
1, 3
Suppose 258*b - 268*b + 40 = 0. Let k(s) be the third derivative of 0*s**6 + 0*s**5 + 0*s - 7*s**2 + 0 - 1/210*s**7 + 0*s**3 + 0*s**b. Factor k(f).
-f**4
Let 0 - 73/10*l**3 - 1/10*l**5 + 87/10*l**2 + 21/10*l**4 - 17/5*l = 0. What is l?
0, 1, 2, 17
Let b be 5/(-33) + (6 + -8)*(-3)/18. Solve b*p**2 - 2/11 - 2/11*p + 2/11*p**3 = 0.
-1, 1
Find y, given that -9*y - 3/4*y**2 + 135/4 = 0.
-15, 3
Let q = 399 - 13964/35. Let l(g) be the third derivative of 0*g**3 + q*g**7 - 1/30*g**5 + 0*g - 1/30*g**6 + 0 - g**2 + 0*g**4. Factor l(u).
2*u**2*(u - 1)*(3*u + 1)
Let a(o) = 2*o**2 + 2*o. Let w(y) = -y**2. Let t(f) = -f**3 + 3*f**2 - 1. Let h be t(3). Let p(i) = h*a(i) - 4*w(i). Suppose p(r) = 0. Calculate r.
0, 1
Let o be 3/3*(7 - 7). Suppose 4*h + 0 - 20 = o. Factor 2*l**2 + 3*l**3 - 2*l**4 - l**3 - 6*l**h + 0*l**3 + 4*l**5.
-2*l**2*(l - 1)*(l + 1)**2
Let t be ((-16)/132)/2*(-187)/51. Solve -4/9*o**2 + 0 - t*o + 4/9*o**4 + 2/9*o**3 = 0.
-1, -1/2, 0, 1
Let h(y) be the first derivative of y**7/840 - y**6/180 + y**5/120 + 2*y**3/3 - 7. Let c(s) be the third derivative of h(s). Suppose c(f) = 0. Calculate f.
0, 1
Let b(u) = -u**3 - 10*u**2 + 3*u + 34. Let z be b(-10). Solve -10*c**z + 2*c + 24*c**2 - 3 - 17 + 8 - 4*c**3 - 2*c**4 + 2*c**5 = 0.
-1, 1, 6
Let x(u) = 322*u**2 + 1154*u + 1028. Let h(d) = -d**2 + d + 2. Let f(k) = -2*h(k) + x(k). Let f(r) = 0. Calculate r.
-16/9
Let k(s) be the first derivative of 3/2*s**4 + 0*s - 4/3*s**3 + 6 + 0*s**2 - 2/5*s**5. Factor k(z).
-2*z**2*(z - 2)*(z - 1)
Let c(w) be the second derivative of -w**3/6 + 4*w**2 + 4*w. Let y be c(6). Factor -3*n**4 - 3*n**2 + 9*n**3 + 3*n - n**y - 5*n**2.
-3*n*(n - 1)**3
Let a(c) be the third derivative of 0*c + 1/108*c**4 - 2/135*c**5 + 1/180*c**6 + 10*c**2 + 0*c**3 + 0. Find p, given that a(p) = 0.
0, 1/3, 1
Let z = 1/275 + 2191/2475. Factor z*a - 8/9 - 2/9*a**2.
-2*(a - 2)**2/9
Suppose 3/5*j**5 + 12/5*j**3 - 6/5 + 12/5*j**4 - 6/5*j**2 - 3*j = 0. What is j?
-2, -1, 1
Let x be 10/30 + 4/(-12). Let t(c) be the second derivative of 1/6*c**4 + c + 1/6*c**3 + 0 + x*c**2 + 1/20*c**5. Factor t(a).
a*(a + 1)**2
Suppose 0 = 13*u - 10*u - 6. Let w(t) be the second derivative of 0 - 1/6*t**4 + 1/3*t**3 + 2*t**u + 2*t. Determine y, given that w(y) = 0.
-1, 2
Factor 144/7*n**2 - 1863/7*n + 3174/7 - 3/7*n**3.
-3*(n - 23)**2*(n - 2)/7
Let q(a) be the third derivative of -a**7/42 + a**6/4 - 2*a**5/3 - 5*a**4/4 + 15*a**3/2 + 57*a**2. Factor q(b).
-5*(b - 3)**2*(b - 1)*(b + 1)
Suppose 0 = -s + 5, 4*z - 2*s = 7*z - 94. Factor -2*f - 12*f**2 + 47*f**3 - z*f**3 - 2*f + 12*f**4.
f*(f + 2)*(3*f - 2)*(4*f + 1)
Let r be ((-119)/21 - -5)/(-12). Let q(o) be the third derivative of r*o**4 + 11*o**2 + 1/90*o**5 + 1/9*o**3 + 0*o + 0. Factor q(i).
2*(i + 1)**2/3
Let n be 3 + 9/((-18)/(-4)). Determine y so that -4*y - 4*y**3 - 9*y**2 - n*y - 3*y**2 - 4 - 3*y = 0.
-1
Let v = 3493 + -3490. Let 0*x + 8/7*x**v + 0 - 2/7*x**2 = 0. Calculate x.
0, 1/4
Suppose -7*r + 2 = -110. Factor 13*v + 5 - r*v + 18*v**2 + 12*v**4 - 27*v**3 - 5.
3*v*(v - 1)**2*(4*v - 1)
Let g(v) be the first derivative of -v**3 + 87*v**2/2 - 162*v - 121. Find s such that g(s) = 0.
2, 27
Let i(g) be the first derivative of -g**7/21 + g**5/10 + 8*g + 15. Let w(o) be the first derivative of i(o). Suppose w(c) = 0. Calculate c.
-1, 0, 1
Let f be (-4)/(-10) + (-48)/(-30). Suppose f*j = -2*j + 20. Find q, given that 3*q**2 - 4*q - j*q**2 + 3*q**2 - 78 + 82 = 0.
2
Let l(p) be the second derivative of p**6/900 - p**5/75 + p**4/15 - 4*p**3 - 21*p. Let y(m) be the second derivative of l(m). Determine r, given that y(r) = 0.
2
Let j be (-54)/(-10) + (1 - 7/5). Suppose 0 = j*d - 13 + 3. Factor -1/2 + 7/4*i + 1/2*i**3 - 2*i**d + 1/2*i**4 - 1/4*i**5.
-(i - 1)**4*(i + 2)/4
Let a be (7/(-2) + -1)/((-117)/273). Let k(d) be the first derivative of 27/2*d**2 + 6*d - a*d**4 + 8 + 3*d**3. Factor k(r).
-3*(r - 1)*(2*r + 1)*(7*r + 2)
Factor 132*t + 106*t - 69*t - 4*t**3 - t**3 + 56*t - 115 - 105*t**2.
-5*(t - 1)**2*(t + 23)
Let l = 100 - 96. Let u(v) be the first derivative of v**2 + 4/3*v - 4/9*v**3 + l. Factor u(c).
-2*(c - 2)*(2*c + 1)/3
Let b = -62 + 131. Let 3*j**2 + 4*j - 4*j**3 + 5*j**2 - 77 + b = 0. Calculate j.
-1, 1, 2
Let i(h) be the third derivative of 0 - 2/45*h**5 + 4/9*h**3 - 2/45*h**6 + 0*h + 0*h**7 + 1/252*h**8 + 1/6*h**4 + 13*h**2. Factor i(c).
4*(c - 2)*(c - 1)*(c + 1)**3/3
Let l(p) = 4*p**2 + 41*p + 105. Let r be l(-6). Suppose -1/3*u**r + 0 + u**2 + 4/3*u = 0. What is u?
-1, 0, 4
Let l(o) = o**2 + 4*o + 19. Let i be l(-3). Suppose 0 = i*a - 14*a - 12. Factor a*h - 3/4*h**2 - 12.
-3*(h - 4)**2/4
Let r = -74 + 68. Let v be 8 - ((8 - -4) + r). Let 2/9 - 4/9*u + 2/9*u**v = 0. Calculate u.
1
Let d(s) be the third derivative of -1/24*s**3 + 1/48*s**4 + 0*s + 0 - 1/240*s**5 - 3*s**2. Factor d(j).
-(j - 1)**2/4
Determine g, given that 5*g + 5*g**2 + 450 + 90*g - 210 = 0.
-16, -3
Let m(z) be the first derivative of -1/24*z**6 + 0*z + 16 + 0*z**4 + 0*z**2 + 3/20*z**5 - 1/3*z**3. Factor m(h).
-h**2*(h - 2)**2*(h + 1)/4
Let i(f) be the third derivative of -f**10/756000 + f**8/100800 + 11*f**5/60 - 6*f**2. Let o(r) be the third derivative of i(r). Factor o(n).
-n**2*(n - 1)*(n + 1)/5
Let a(o) be the second derivative of -1/4*o**3 + 3/40*o**5 + 1/20*o**6 + 14*o - 1/8*o**4 + 0 + 0*o**2. Factor a(y).
3*y*(y - 1)*(y + 1)**2/2
Factor 60/7*f**3 + 0*f**2 + 0*f - 1/7*f**5 + 0 - 4*f**4.
-f**3*(f - 2)*(f + 30)/7
Let 0 + 16/5*l + 2/5*l**2 = 0. Calculate l.
-8, 0
Factor 61*m**2 + 5*m**3 + 320 - 265*m**2 + 85*m**2 + 240*m + 44*m**2.
5*(m - 8)**2*(m + 1)
Let v = -96 + 101. What is c in c**3 + 12 + 5 - v - 5*c**2 + 2*c - 4 = 0?
-1, 2, 4
Let h(i) be the first derivative of -i**4/6 + 16*i**3/9 - i**2/3 - 28*i - 256. Factor h(x).
-2*(x - 7)*(x - 3)*(x + 2)/3
Let l(f) = 28*f**4 + 43*f**3 - 5*f**2 + 7. Let k(z) = 9*z**4 + 14*z**3 - 2*z**2 + 2. Let o(w) = -7*k(w) + 2*l(w). Factor o(a).
-a**2*(a + 2)*(7*a - 2)
Factor 0 + 1/3*v**2 + 1/3*v.
v*(v + 1)/3
Solve -11907/2 - 3/2*u**2 - 189*u = 0 for u.
-63
Suppose t - 72 + 254 = 0. Let f = -108 - t. Solve 7*s - 19*s + 10 - 2 + 78*s**2 - f*s**2 = 0 for s.
1, 2
Let a = -28 - -30. Suppose -a*n + 24 = -4*j, 3*n - j - 26 = 3*j. Determine k, given that -1/4*k**n + 0 - 3/4*k = 0.
-3, 0
Let y = 217/15 + -212/15. Factor 2/3*o - y*o**2 - 1/3.
-(o - 1)**2/3
Suppose 5*g = 64 - 54. Let l(k) = k**3 + 8*k**2 + 7*k + 3. Let n be l(-7). Let -2 + 1 + b**n + b**g - 7*b + 6*b = 0. What is b?
-1, 1
Let u(h) be the second derivative of h**6/2 + 9*h**5/20 - 15*h**4/4 - 19*h**3/2 - 9*h**2 - 4*h - 19. Factor u(c).
3*(c - 2)*(c + 1)**2*(5*c + 3)
Let g(c) be the second derivative of c**8/36960 - c**6/1320 - c**5/330 + c**4 + 20*c. Let t(f) be the third derivative of g(f). Solve t(j) = 0.
-1, 2
Let c(z) be the third derivative of 1/36*z**4 - 1/180*z**5 + 0*z - 16*z**2 + 0*z**3 + 0. Factor c(o).
-o*(o - 2)/3
Let h = -2176/3 - -728. Find p, given that 8/3*p**4 + 4*p**3 + 2/3*p + 0 + 2/3*p**5 + h*p**2 = 0.
-1, 0
Let z