 = 3*y - 8, -20*i - 5 = -17*i + 5*y. Factor -2*x + 2*x**3 + 156*x**2 - i*x**3 - 152*x**2 + x**3.
-2*x*(x - 1)**2
Let v(g) be the third derivative of -g**6/40 + g**5/5 - 3*g**4/8 - 139*g**2. Suppose v(o) = 0. What is o?
0, 1, 3
Let m(q) be the second derivative of -q**6/360 + 2*q**5/15 - 8*q**4/3 + 4*q**3 - 17*q. Let z(b) be the second derivative of m(b). Factor z(w).
-(w - 8)**2
Suppose -5*o + g + 10 + 8 = 0, o + 4*g = -9. Let h(m) be the first derivative of 27/4*m**4 + 3*m**3 - 15/2*m**2 + o*m - 3. What is i in h(i) = 0?
-1, 1/3
Let s = -8402 - -8402. Determine t, given that 2/3*t**2 + 0 + s*t + 2/3*t**3 = 0.
-1, 0
Let b(o) = -2*o**3 + 2*o**2 - o - 1. Let j be b(-1). Suppose 4*v**j + v**3 + 280*v - 5*v**3 - 20*v**2 - 292*v = 0. Calculate v.
-1, 0, 3
Determine r so that -3/2*r**4 - 19683/2 + 4374*r + 54*r**3 - 729*r**2 = 0.
9
Let x(k) be the second derivative of -5*k**4/12 - 10*k**3/3 - 10*k**2 - 39*k - 1. Suppose x(t) = 0. Calculate t.
-2
Suppose 8/5*c**4 - 58/5*c**3 + 14/5*c**2 + 0 + 0*c = 0. Calculate c.
0, 1/4, 7
Let m(h) be the first derivative of 3*h**4/8 + h**3 - 93*h**2/4 + 42*h - 281. Factor m(w).
3*(w - 4)*(w - 1)*(w + 7)/2
Let s be 190/70 - 4/(-14). Suppose -2*q = -q - 5*t - 14, -t - 14 = -s*q. Factor 4*l**2 - 9*l**4 - 3*l**q + 0*l**2 + 8*l**4.
-4*l**2*(l - 1)*(l + 1)
Let l be 6*93/(-282) - -2. Let c = 101/329 - l. What is d in 2/7*d**2 + 0 + c*d = 0?
-1, 0
Let q be -2 + 10 + (-24)/3. Let j(l) be the first derivative of -3/28*l**4 + q*l - 3/14*l**2 + 2/7*l**3 - 6. What is n in j(n) = 0?
0, 1
Let f = -403/2211 + -2/67. Let l = f - -13/33. Factor -6/11*r**2 + l*r**3 + 2/11*r**4 - 10/11*r - 4/11.
2*(r - 2)*(r + 1)**3/11
Let u(q) be the first derivative of 4*q**3/3 - 32*q**2 + 256*q - 202. Factor u(k).
4*(k - 8)**2
Let z(g) = -12 - g - 11*g + 13*g. Let y be z(12). Let -k**4 + 0 + k**3 + 0*k + y*k**2 - 3/4*k**5 = 0. What is k?
-2, 0, 2/3
Let n be 36/16 + 6/(-27)*3. Let u(g) be the second derivative of 2*g**2 - n*g**4 + 4/3*g**3 - 2*g + 0 + 7/20*g**5. What is b in u(b) = 0?
-2/7, 1, 2
Let v(x) = -10*x**2 + 97*x - 341. Let f(n) = 3*n**2 - 33*n + 112. Let l(u) = 7*f(u) + 2*v(u). Determine q so that l(q) = 0.
3, 34
Let f = -4271 - -17339/4. Let q = 64 - f. Determine w so that q*w**3 + 0*w**2 + 0 - 1/4*w**5 + 0*w + 0*w**4 = 0.
-1, 0, 1
Suppose -y - 16 = -3*y - 3*q, -12 = -2*y - 2*q. Let a be (-2 - (-3)/(-1))*(-3)/5. Let -19*t + t**2 + 11*t + 4 + a*t**y - 16 = 0. What is t?
-1, 3
Suppose j**4 + 0 + 13/3*j**2 - 14/3*j**3 + 2*j = 0. What is j?
-1/3, 0, 2, 3
Determine l so that 73*l**3 + 11*l**5 - 4*l - 5 + 5 - 80*l**3 + 24*l**4 - 24*l**2 = 0.
-2, -1, -2/11, 0, 1
Let 1481*s + 2185*s**2 - 561*s + 74*s**4 - 3335*s**3 + 171*s**4 - 5*s**5 + 5730*s**2 - 10580 = 0. Calculate s.
-1, 2, 23
Suppose 2/13*u**2 - 48/13*u - 50/13 = 0. Calculate u.
-1, 25
Let g = -231 + 465/2. Let c(d) be the first derivative of 0*d**2 + 3/5*d**5 + g*d**4 + d**3 + 0*d - 4. Solve c(w) = 0 for w.
-1, 0
Let a = 1475 - 2881/2. Factor -6*v**3 + 51*v + a*v**2 + 21/2.
-3*(v - 7)*(v + 1)*(4*v + 1)/2
Determine h so that 15*h**4 - 8*h + 70*h**3 - 80*h + 112*h**3 - 57*h**3 + 8*h + 30*h**2 = 0.
-8, -1, 0, 2/3
Suppose 2*f - 180 = -f. Let p be ((-6)/9)/(f/(-27) + 2). Factor 2/7*a**p + 4/7*a**2 + 0 + 2/7*a.
2*a*(a + 1)**2/7
Let h(y) be the third derivative of 5*y**8/1848 + 4*y**7/165 - y**6/55 - 62*y**2. Suppose h(q) = 0. What is q?
-6, 0, 2/5
Let l(d) = -13*d**2 + 9*d + 6. Let h(i) = -207*i**2 + 144*i + 96. Let m(n) = 2*h(n) - 33*l(n). Solve m(g) = 0.
-2/5, 1
Let u be (2 + 6 - 8)*-1. Let i = 11 + -8. Suppose u*q**2 - 2*q**2 - 9*q - i - 4*q**2 + 0*q = 0. Calculate q.
-1, -1/2
Let i be (0 - (-12)/(-20))*-5. What is m in 4*m**3 + m**i + 0*m**2 - 4*m**3 + m**2 = 0?
-1, 0
Let h be (-84)/(-8) - (-9)/(-6). Solve -h*a + 18*a**3 - 3 - 15*a**3 - 4 + 1 = 0.
-1, 2
Let x = 18 - 12. Suppose 0 = -7*z + x*z + 3. Determine o so that -17*o + 0*o + 24*o**2 - 19*o - 2*o**3 - 2*o**z = 0.
0, 3
Let v(p) be the third derivative of 15*p**2 + 0*p - 4/15*p**5 + 1/30*p**6 + 0 + 0*p**3 + 1/2*p**4. What is h in v(h) = 0?
0, 1, 3
Let c(h) be the third derivative of -h**8/252 - h**7/90 - h**6/180 + h**5/180 + 2*h**2 + 16*h. What is p in c(p) = 0?
-1, 0, 1/4
Suppose 2*s = 3 + 9. Suppose d + 2*d = s. Factor w**3 + 3*w**d + w - 4*w**2 + 0*w**2 + 1 - 2*w.
(w - 1)**2*(w + 1)
Let h(b) be the third derivative of -b**7/630 - b**6/15 - 6*b**5/5 + b**4/24 - b**3/3 - 24*b**2. Let n(t) be the second derivative of h(t). Factor n(y).
-4*(y + 6)**2
Let p = -96 + 121. Factor -13*u - 13*u + 4*u**2 - 9 + p + 10*u.
4*(u - 2)**2
Factor 20*c - 6*c + 8 + 4*c**2 + 25*c**3 - 27*c**3.
-2*(c - 4)*(c + 1)**2
Suppose o + 1 = 2*g, 4*o = 5*g + 4 - 2. Factor -c**g - 10*c - 12 + 5 + 2*c.
-(c + 1)*(c + 7)
Let c(l) be the third derivative of l**8/480 + l**7/105 - l**6/90 - 7*l**4/24 + 6*l**2. Let a(s) be the second derivative of c(s). Solve a(r) = 0 for r.
-2, 0, 2/7
Let b = 4 - 4. Suppose 4*t + b*t = 12. Factor -t - 3*a**2 + a + 14*a - 9*a.
-3*(a - 1)**2
Let z = 208/7 - 1858/63. Factor 200/9 + 40/9*n + z*n**2.
2*(n + 10)**2/9
Let f(l) = -4*l**3 + 28*l**2 - 42*l + 20. Let r(b) = b. Let p(d) = f(d) - 2*r(d). What is m in p(m) = 0?
1, 5
Let y(a) be the second derivative of -a**5/150 - 116*a**4/15 - 53824*a**3/15 - 12487168*a**2/15 + 559*a. Factor y(r).
-2*(r + 232)**3/15
Let u(v) be the first derivative of v**3/5 + 81*v**2/5 + 2187*v/5 + 107. Factor u(f).
3*(f + 27)**2/5
Let c(y) = y**3 + 11*y**2 - 14*y - 9. Suppose 0 = -4*k - 23 - 25. Let r be c(k). What is x in -x**4 + 7*x**4 - 12*x**5 - 6*x**2 - 3*x + r*x**5 = 0?
-1, 0, 1
Let j(x) = 6*x**2 - 12*x - 52. Let m(l) = -14*l**2 + 24*l + 103. Let a(g) = -5*j(g) - 2*m(g). Factor a(v).
-2*(v - 9)*(v + 3)
Let f be (-33)/(-45)*(-51)/((-8415)/30). Factor 2/15*r + 0 + 4/15*r**2 + f*r**3.
2*r*(r + 1)**2/15
Suppose 30/11*i**4 + 160/11*i**3 + 0*i - 512/11 + 320/11*i**2 + 2/11*i**5 = 0. Calculate i.
-4, 1
Let f = -42 + 47. Factor -4*s**2 - 7*s**3 + f*s**3 + s**3 + 3*s**3.
2*s**2*(s - 2)
Let n(h) = -h**4 + 56*h**3 - 1093*h**2 + 1926*h + 4. Let z(p) = -2*p**3 - 2*p**2 + p + 1. Let b(i) = -3*n(i) + 12*z(i). Solve b(c) = 0 for c.
0, 2, 31
Let g(f) be the third derivative of 1/24*f**4 + 0 - 1/48*f**6 + 9*f**2 + 1/40*f**5 + 0*f + 0*f**3. Factor g(u).
-u*(u - 1)*(5*u + 2)/2
Let v(i) be the third derivative of -i**8/336 + 4*i**7/21 - 5*i**6/4 + 11*i**5/3 - 145*i**4/24 + 6*i**3 - 7*i**2 - 27. Find d, given that v(d) = 0.
1, 36
Let h(w) = w**2 + 9*w + 3. Let t(y) = -11*y**2 + 3*y - 1. Let n be t(1). Let b be h(n). Factor 2*d**2 + 0*d - b*d**2 + 0*d**2 - d.
-d*(d + 1)
Let l = -1897/2 - -17089/18. Find c such that -l - 4/3*c - 4/9*c**2 = 0.
-2, -1
Let d be 3 + (-2)/(-1) - -1. Let l be 2/4*(-7 - -7). Factor 2*n**2 + l*n**2 - d*n**2 - 4*n.
-4*n*(n + 1)
Let q(t) = 4*t + 1 - 2 + t**2 + t + 7. Let x be q(-3). Let 0*b - 2/11*b**2 + 2/11*b**3 + x = 0. What is b?
0, 1
Suppose 8*s**2 - 4/7*s**3 + 16/7*s - 2*s**4 + 0 = 0. What is s?
-2, -2/7, 0, 2
Determine g so that 24/5*g + 0 + 26/5*g**2 + 2/5*g**3 = 0.
-12, -1, 0
Let i(d) be the first derivative of -d**6/3060 + d**5/170 - 3*d**4/68 - 7*d**3/3 - 20. Let f(t) be the third derivative of i(t). Factor f(n).
-2*(n - 3)**2/17
Let h be ((-15)/(-12))/(20/640). Solve -h*g**2 - 5 - 55/2*g - 35/2*g**3 = 0 for g.
-1, -2/7
Let l(f) be the second derivative of -13/84*f**4 - 1/70*f**5 + 0 + 0*f**2 - 17*f - 1/7*f**3. Find z, given that l(z) = 0.
-6, -1/2, 0
Suppose 0 = -3*t + 6*t - 15. Find i, given that -33*i**2 + 40*i - 5 - 42*i**2 - t*i**2 = 0.
1/4
Let n(f) = f**2 + 64 - 4*f - 4*f - 60 + 3*f. Let m(v) = 3*v - 10. Let w(b) = 2*b - 7. Let x(s) = -5*m(s) + 7*w(s). Let j(z) = -n(z) + 4*x(z). Factor j(i).
-i*(i - 1)
Suppose -20 = 3*a - a + p, 5*a + 2*p = -50. Let m be ((a/8)/(-5))/((-25)/(-160)). Suppose -2/5*k**2 - m*k + 8/5 + 2/5*k**3 = 0. Calculate k.
-2, 1, 2
Let u(p) be the third derivative of -p**8/47040 - 2*p**5/3 - 9*p**2. Let t(k) be the third derivative of u(k). Factor t(l).
-3*l**2/7
Let k(w) be the first derivative of w**6/24 - w**5/5 - w**4/8 + w**3 + 9*w**2/8 - 18. Factor k(s).
s*(s - 3)**2*(s + 1)**2/4
Find n such that -40*n**2 - 54*n**2 + 175*n - 45 - 53*n**2 + 32*n**2 - 3*n**3 - 12*n**3 = 0.
-9, 1/3, 1
Factor 4/5 + 2/15*t**2 + 2/3*t.
2*(t + 2)*(t + 3)/15
Let h = -83 - -417/5. Suppose -8