
Suppose -5*f + 11 + 4 = 5*y, -10 = -3*f - 4*y. Let u be (((-12)/(-81))/1)/(f/3). Factor -1/9*g - 1/9*g**2 + u.
-(g - 1)*(g + 2)/9
Suppose s + 76 = 76. Let g(p) be the second derivative of 2/3*p**3 - 1/6*p**4 - p + s + 0*p**2. What is v in g(v) = 0?
0, 2
Let y(m) be the first derivative of m**7/84 - m**5/20 + m**3/12 + 7*m - 9. Let x(w) be the first derivative of y(w). Factor x(s).
s*(s - 1)**2*(s + 1)**2/2
Let l(a) = 6*a**2 - 152*a - 154. Let d(i) = 7*i**2 - 154*i - 155. Let h(o) = 2*d(o) - 3*l(o). Factor h(s).
-4*(s - 38)*(s + 1)
Let o(v) be the second derivative of -1/12*v**4 + 5/18*v**3 - 1/60*v**5 + 6*v + 0 - 1/3*v**2 + 1/90*v**6. Let o(q) = 0. What is q?
-2, 1
Let m = -129 + 133. Let t(z) = -z**3 - z**2 + z - 1. Let v(q) = 3 - 10*q**4 + 0*q**3 + 1 - 4*q + 8*q**2 - 2*q**3. Let f(x) = m*t(x) + v(x). Solve f(g) = 0.
-1, 0, 2/5
Let q(i) = -i**3 - i**2 - 120*i - 128. Let r(d) = 3*d**3 - 3*d**2 + 240*d + 255. Let u(p) = 9*q(p) + 4*r(p). Factor u(y).
3*(y - 11)*(y + 2)**2
Let f(r) = 70*r**4 - 1400*r**3 - 210*r**2 + 4255*r - 2970. Let c(x) = 5*x**4 - 100*x**3 - 15*x**2 + 304*x - 212. Let t(n) = -85*c(n) + 6*f(n). Factor t(z).
-5*(z - 20)*(z - 1)**2*(z + 2)
Let w(k) be the first derivative of -k**6/135 - k**5/30 - k**4/27 + 21*k - 3. Let y(q) be the first derivative of w(q). Factor y(b).
-2*b**2*(b + 1)*(b + 2)/9
Let v(t) be the first derivative of -5*t**3/3 - 225*t**2/2 + 177. Factor v(m).
-5*m*(m + 45)
Let l(g) be the second derivative of -g**6/80 + 51*g**5/160 - 39*g**4/16 + 2*g**3 + 24*g**2 + g - 1. Solve l(c) = 0 for c.
-1, 2, 8
Let b(n) be the second derivative of 7/4*n**4 + 6*n**2 + 19*n - 8*n**3 + 0. Let b(s) = 0. Calculate s.
2/7, 2
Let p(k) = k**4 + k**2 + k. Let l(z) = z**4 - 8*z**3 - 6*z**2 + 4*z - 2. Let g(u) = l(u) + 3*p(u). Factor g(r).
(r - 2)*(r + 1)*(2*r - 1)**2
Let g = -98 + 118. Suppose -4*x - 5*d + g = -d, 5*x + 4*d = 24. Factor 1/5*m - 1/5*m**2 + 0 + 1/5*m**x - 1/5*m**3.
m*(m - 1)**2*(m + 1)/5
Let s(t) = -t**2 - 14*t + 17. Let a = -20 + 5. Let o be s(a). Factor 3*r**2 - 3*r - 4*r - o*r.
3*r*(r - 3)
Let k(p) be the first derivative of -p**6/12 + 67*p**5/10 - 1579*p**4/8 + 4935*p**3/2 - 10584*p**2 + 18522*p + 58. Solve k(l) = 0 for l.
2, 21
Let t(o) = -o**3 + 4*o**2 + 4. Let m be t(4). Let y be (-10)/20 + 18/m. Solve y*n**2 - 2*n**2 - 5*n + 3*n - 4 = 0 for n.
-1, 2
Factor -1/8*n**2 + 15/8*n - 7/4.
-(n - 14)*(n - 1)/8
Factor -9*n**3 + 0*n**3 + 15*n**2 - 7*n**3 + 2*n**3 - 11*n**3 - 10*n**4.
-5*n**2*(n + 3)*(2*n - 1)
Let x(y) be the first derivative of y**5/15 - y**4/6 - y**3/3 + 4*y**2/3 - 4*y/3 + 19. Find g, given that x(g) = 0.
-2, 1, 2
Let z(y) = -7*y**3 - 23*y**2 + 29*y + 65. Let c(i) = -4*i**3 - 11*i**2 + 14*i + 33. Let l(b) = -5*c(b) + 3*z(b). Factor l(n).
-(n - 2)*(n + 1)*(n + 15)
Let f(z) be the first derivative of -80/33*z**3 + 12/11*z**2 + 0*z - 7/22*z**4 - 2. Factor f(y).
-2*y*(y + 6)*(7*y - 2)/11
Let g(y) be the first derivative of y**4/2 + 38*y**3 + 216*y**2 + 424*y - 358. Find r, given that g(r) = 0.
-53, -2
Find f, given that 5/6*f**2 + 0 + 1/6*f**3 - 1/6*f**4 + 1/2*f = 0.
-1, 0, 3
Let v(q) be the second derivative of -5/16*q**3 + 17*q + 9/16*q**2 + 0 + 3/160*q**5 + 1/32*q**4. Factor v(m).
3*(m - 1)**2*(m + 3)/8
Let h = 37/78 + 1/39. Let l be 11/12 + (-2)/3. Determine v so that 3/4*v**4 - l*v**5 - 1/2*v**2 - 1/4 + 3/4*v - h*v**3 = 0.
-1, 1
Let a(b) = -b**3 + 13*b**2 + 8. Let p be a(13). Suppose p = 5*c - c. What is f in -1 - 1 + 5*f**2 - 1 - c*f**2 = 0?
-1, 1
Let r(f) be the third derivative of -f**8/2240 - f**7/280 - f**6/160 + 5*f**3/6 - 6*f**2. Let j(a) be the first derivative of r(a). Factor j(m).
-3*m**2*(m + 1)*(m + 3)/4
Let g(m) be the first derivative of -m + 1/4*m**4 + 1/3*m**3 + 9 - 1/2*m**2. Suppose g(t) = 0. Calculate t.
-1, 1
Let c(o) be the first derivative of 12 - 9/2*o**2 - 1/2*o**3 - 15/2*o. Let c(k) = 0. What is k?
-5, -1
Suppose 20*c - 2*c**3 - 19*c**2 + 5*c**2 + 585 - 553 = 0. What is c?
-8, -1, 2
Let g(u) = -u**2 - u - 1. Let a(n) = -2*n**3 + 110*n**2 + 6*n - 102. Let l(v) = -a(v) - 4*g(v). Factor l(o).
2*(o - 53)*(o - 1)*(o + 1)
Let -16*r**2 + 20 + 169*r**3 - 171*r**3 - 10*r + 8 = 0. Calculate r.
-7, -2, 1
Let l(h) be the second derivative of -3*h**5/100 + h**4/10 - h + 99. Factor l(i).
-3*i**2*(i - 2)/5
Let v(q) be the second derivative of -q**4/24 - 7*q**3/6 + 15*q**2/4 - q + 7. Factor v(m).
-(m - 1)*(m + 15)/2
Let y(z) be the third derivative of -z**6/60 - z**5/15 + z**4/4 - 3*z**2 - 4*z. Factor y(w).
-2*w*(w - 1)*(w + 3)
Let i be (-21)/((-1)/(-2 - (-12)/9)). Let w be -3*(4 + i/3). Factor 0 - 1/4*d + 1/4*d**3 + 1/4*d**w - 1/4*d**4.
-d*(d - 1)**2*(d + 1)/4
Let h = 25 + -22. Let y(i) be the first derivative of -1/4*i**2 + 1/10*i**5 + 0*i - 6 - 1/6*i**h + 1/8*i**4. Find d, given that y(d) = 0.
-1, 0, 1
Let k = -94 + 96. Find t such that 4*t**3 - 2*t + k*t**3 - 4*t**3 - t**3 - t**2 = 0.
-1, 0, 2
Let o(p) be the third derivative of 0 + 1/420*p**5 + 0*p + 5/168*p**4 + 1/14*p**3 + 24*p**2 - 1/840*p**6. Solve o(f) = 0 for f.
-1, 3
Let m = -184 + 188. Let j(s) be the second derivative of -1/3*s**6 + 6*s - 1/5*s**5 + 2/3*s**3 + 5/6*s**m + 0 + 0*s**2. What is n in j(n) = 0?
-1, -2/5, 0, 1
Suppose 111*g**3 + 237/2*g - 24*g**4 - 30 - 3/2*g**5 - 174*g**2 = 0. Calculate g.
-20, 1
Let b(n) be the first derivative of -n**7/6300 - n**6/900 + n**3/3 + 7. Let a(u) be the third derivative of b(u). Solve a(p) = 0.
-3, 0
Let 26/7*k - 60/7 - 2/7*k**2 = 0. Calculate k.
3, 10
Let s(y) be the first derivative of -y**3/3 + 173*y**2 - 29929*y + 837. Factor s(c).
-(c - 173)**2
Let a = 28 + -24. Find j such that j**3 + 4*j**3 + a*j**4 - j**3 = 0.
-1, 0
What is t in 64*t**3 - 117*t**3 - 4*t**2 + 57*t**3 - 4*t + 4*t**4 = 0?
-1, 0, 1
Determine i so that 24 + 66*i**4 + 3338*i**3 + 132*i + 97*i**2 + 9*i**5 - 3155*i**3 + 137*i**2 = 0.
-2, -1, -1/3
Let j(r) = -r**2 + 4*r + 1. Let q(b) = 3*b**2 - 8*b - 1. Suppose 87 = -2*w - 3*w + 4*u, -5*w - 4*u - 63 = 0. Let n(f) = w*j(f) - 6*q(f). Factor n(s).
-3*(s + 1)*(s + 3)
Let d = -109 - -154. Suppose -8 = 4*x - 5*a, -5 = 5*x - 0*a - 5*a. Factor 0 - 5 + 89*y**x + 15*y + d*y**2 - 224*y**3.
-5*(3*y - 1)**2*(3*y + 1)
Let f(j) be the first derivative of -1/20*j**5 - 12*j + 1/6*j**3 + 1/12*j**4 - 1/2*j**2 - 1. Let p(s) be the first derivative of f(s). Let p(l) = 0. What is l?
-1, 1
Factor -2/5*i - 3/5 + 1/5*i**2.
(i - 3)*(i + 1)/5
Let w(n) be the first derivative of -n**5 + 55*n**4/2 + 115*n**3/3 - 29. Solve w(k) = 0 for k.
-1, 0, 23
Suppose 4*g + l - 29 = 0, -30 + 9 = -g - 3*l. Let x(a) be the first derivative of 0*a**2 - 1/3*a**6 - g*a**4 - 16/3*a**3 - 6 + 0*a - 12/5*a**5. Factor x(f).
-2*f**2*(f + 2)**3
Let o(g) be the third derivative of g**7/735 + g**6/210 - 23*g**5/210 - 2*g**4/7 + 48*g**3/7 + 23*g**2. Factor o(k).
2*(k - 3)**2*(k + 4)**2/7
Let c(l) be the second derivative of -4*l**4 - 10*l + 0*l**2 - 8/3*l**3 + 0 + 3/5*l**5 + 4/3*l**6 + 2/7*l**7. Determine x, given that c(x) = 0.
-2, -1/3, 0, 1
Let o(s) be the second derivative of -s**4/42 - 22*s**3/21 - 3*s**2 - 2*s + 7. Factor o(q).
-2*(q + 1)*(q + 21)/7
Let q(y) be the first derivative of -29645*y**3/9 - 385*y**2/3 - 5*y/3 + 299. Factor q(s).
-5*(77*s + 1)**2/3
Suppose -2*o = 8, f - o - 13 = 31. Determine v, given that v**3 - 8*v**3 + 31 + f*v - 11 + 15*v**2 - 3*v**3 - 5*v**4 = 0.
-2, -1, 2
Let q(l) = -40*l**2 + 4535*l - 130010. Let g(v) = -5*v**2 + 567*v - 16251. Let n(x) = 25*g(x) - 3*q(x). Determine w, given that n(w) = 0.
57
Let r(p) = 2*p**3 - 8*p**2 + 5*p + 5. Let c be r(3). Determine k, given that 0 - 3/2*k - 3*k**c - 3/2*k**3 = 0.
-1, 0
Suppose 0 = 3*p - p - 7*i + 1, -3*p - 4*i + 13 = 0. Let 0*x**2 + 4/9*x**p + 0*x + 0 + 2/9*x**4 = 0. What is x?
-2, 0
Factor -147*s**2 + 29747 - 46850 - s**3 - 2748*s - 59758 - 40788 - 4455*s.
-(s + 49)**3
Let w be -2*(4 - (0 - 11/(-2))). Factor -1097*h + w*h**2 - 4*h**2 + 1103*h.
-h*(h - 6)
Let r(s) = 20*s**3 - 10572*s**2 + 1879752*s - 110904648. Let d(q) = 8*q**3 - 4228*q**2 + 751901*q - 44361859. Let z(v) = 12*d(v) - 5*r(v). Solve z(a) = 0 for a.
177
Let b(i) be the first derivative of 2/21*i**3 + 0*i**2 - 1/28*i**4 + 0*i + 4. Find j such that b(j) = 0.
0, 2
Suppose -2*o - 27 = -7. Let b be (-2)/(-4)*4/o + 1. Factor 8/5*l**2 + 2/5*l**3 + b + 2*l.
2*(l + 1)**2*(l + 2)/5
Let g(p) be t