9*h + 10/9*h**2 = 0. What is h?
-3, -1/2, 1
Let u(m) be the first derivative of 28*m**5/5 + 114*m**4 + 1276*m**3/3 + 528*m**2 + 208*m + 67. Determine j so that u(j) = 0.
-13, -2, -1, -2/7
Let v be (-10)/40 - (-294)/(-8). Let b = v - -37. Determine f so that 3/2*f**2 + f + b + 1/2*f**3 = 0.
-2, -1, 0
Let d = -13517/5 + 2705. Factor -2/5*o**2 - d + 2*o.
-2*(o - 4)*(o - 1)/5
Let u(n) = -n + 1. Let z(s) = -s**3 + 2*s**2 + 2*s - 3. Suppose -1 = 5*w + 4. Let l(p) = 6*p**3 + p + 1. Let o be l(w). Let t(f) = o*u(f) - 2*z(f). Factor t(r).
2*r*(r - 1)**2
Let u be (((-4)/30)/((-7)/105))/49*7. Factor 8/7 - u*q**3 + 12/7*q**2 - 18/7*q.
-2*(q - 4)*(q - 1)**2/7
Let x(v) = 2*v**2 + 17*v + 53. Let c = 25 + -22. Let q(g) = 6*g**2 + 50*g + 160. Let w(u) = c*q(u) - 10*x(u). Factor w(f).
-2*(f + 5)**2
Let x(l) be the second derivative of -1/54*l**4 + 0 + 2/27*l**3 + 0*l**2 + 9*l. Factor x(f).
-2*f*(f - 2)/9
Let u(q) = 17*q**3 + 4*q**2 + 2*q - 2. Let f(b) = 171*b**3 + 39*b**2 + 21*b - 21. Suppose -12 + 8 = -2*h. Let c(k) = h*f(k) - 21*u(k). Factor c(o).
-3*o**2*(5*o + 2)
Let l(w) be the third derivative of 0*w**4 + 0 + 1/224*w**8 + 1/80*w**6 + 0*w + 0*w**3 + 11*w**2 - 1/70*w**7 + 0*w**5. Factor l(r).
3*r**3*(r - 1)**2/2
Let t(c) = -c**3 + c**2 - c + 32. Suppose -2*n - 2*n = 0. Let h be t(n). Find p, given that -p**4 - 32*p + 3*p**3 - 2*p**2 + h*p = 0.
0, 1, 2
Let b(r) = -34*r**2 - 126*r + 168. Let c(t) = t**3 - 68*t**2 - 252*t + 339. Let z(h) = 5*b(h) - 2*c(h). Factor z(y).
-2*(y - 1)*(y + 9)**2
Factor -2*c**2 + 8*c**2 + 72*c + 1296 - 3*c**2 + 0*c**2 - 2*c**2.
(c + 36)**2
Let k = 51 + -41. What is h in 8*h**2 + 12*h**2 + 20*h - 5*h**2 - k*h**3 - 5*h**4 - 20 = 0?
-2, 1
Let z = -192 + 1416. Factor -1224*j**2 + j**4 - 4*j + z*j**2 + 3*j**3.
j*(j - 1)*(j + 2)**2
Let s(x) = -3*x**4 + 1. Let t(u) = 17*u**4 - 15*u**3 - 45*u**2 + 115*u - 64. Let q(f) = 4*s(f) + t(f). Solve q(m) = 0.
-3, 1, 4
Let n(t) = -t**3 + 5*t**2 - 2*t + 7. Let o be n(4). Factor -3*x**2 - 9 + o*x - 9 + 6.
-3*(x - 4)*(x - 1)
Let i = 100 - 89. Let n be 5 + 12/(-48) + i/(-4). What is g in -8/3*g + 1 - g**n = 0?
-3, 1/3
Let n(p) be the third derivative of -p**5/240 - p**4/8 - 4*p**3/3 - 144*p**2. Factor n(b).
-(b + 4)*(b + 8)/4
Let n(x) = -22*x**2 + 33*x - 5. Let m(d) = 211*d - 190*d**2 - 95*d**2 - 65 + 219*d. Let z(y) = -3*m(y) + 40*n(y). Determine w so that z(w) = 0.
1/5, 1
Factor 0 + 6/7*q**4 + 12*q**2 + 0*q + 90/7*q**3.
6*q**2*(q + 1)*(q + 14)/7
Let t be -2 + 12/18 + 4/3. Let s(h) be the third derivative of t*h**3 + 0 + 1/540*h**6 + 1/90*h**5 + 1/54*h**4 + 0*h - 8*h**2. Factor s(a).
2*a*(a + 1)*(a + 2)/9
Let p = 9011 + -9008. What is b in -3*b**2 - 33/7*b - 15/7 - 3/7*b**p = 0?
-5, -1
Solve 0*y + 3/5*y**4 + 21*y**2 + 108/5*y**3 + 0 = 0 for y.
-35, -1, 0
Let u(p) = -3*p**3 - 63*p**2 - 105*p - 48. Let m(b) = 6*b**3 + 128*b**2 + 210*b + 95. Let a(l) = -3*m(l) - 7*u(l). Solve a(w) = 0.
-17, -1
Factor -3*v**2 + 4*v + 4*v**2 - 4 - 13 - 3*v**2 + 23.
-2*(v - 3)*(v + 1)
Suppose -2*m + 38 = 22. Let a be (m/16)/((-14)/(-72)). Suppose -30/7*r**2 + a*r - 6/7*r**4 + 22/7*r**3 - 4/7 = 0. Calculate r.
2/3, 1
Let a(s) be the third derivative of s**5/180 - 5*s**4/24 + 28*s**3/9 + 830*s**2. Factor a(r).
(r - 8)*(r - 7)/3
Let l be (-36)/33*8/96*-6. Determine r so that 4/11*r**3 - 2/11 + l*r**4 - 4/11*r**2 + 2/11*r**5 - 6/11*r = 0.
-1, 1
Suppose 4*l = -16, 3*f + 6 = -3*l - 0. Let j be ((-6)/4)/(-5*(-27)/(-180)). Factor -d**j + d**2 + 5*d**f - 4*d**2.
d**2
Let c be ((-5292)/(-240))/7 + -3. Let p(h) be the second derivative of c*h**5 + 0*h**2 + 0 + 0*h**3 - 1/2*h**4 - 5*h. Factor p(i).
3*i**2*(i - 2)
Factor -1/4*c**2 + 239/2*c - 57121/4.
-(c - 239)**2/4
Suppose -2*j + 135 = 7*j. Suppose -2*f = -3*f. Factor 4*v - 21*v**2 + f*v + 3*v**4 + 42*v**2 + 5*v + j*v**3.
3*v*(v + 1)**2*(v + 3)
Let x be (-3)/(-6) + (-54)/(-4). Suppose -1 - 17*k**2 + x*k**3 + 6*k**4 - 3 + 15*k**2 - 14*k = 0. What is k?
-2, -1, -1/3, 1
Let q be 35/(-20)*(1 + -9). Let u = q + -14. Find i such that 3*i**2 - 3*i - 2 + 3*i**2 - 7*i**2 + u = 0.
-2, -1
Let d(y) be the third derivative of -y**5/150 - y**4/5 - 4*y**3/3 - 57*y**2. Determine u, given that d(u) = 0.
-10, -2
Let s(l) = 3*l**3 - 78*l**2 - 195*l - 104. Let o(n) = n**3 - 38*n**2 - 97*n - 52. Let a(r) = -5*o(r) + 3*s(r). Determine q so that a(q) = 0.
-1, 13
Let m(t) be the third derivative of 0 + t**2 - 1/60*t**4 + 0*t**3 + 0*t + 1/450*t**5. Factor m(x).
2*x*(x - 3)/15
Let s = 28 + -15. Let w = s - 8. Let -10*p**2 + 2*p**3 - p**4 + w*p**2 + 4*p**2 = 0. Calculate p.
0, 1
Let x be 1/6 - 245/30. Let l = x - -12. Factor -g - l*g**2 + 13*g - 5 - 3.
-4*(g - 2)*(g - 1)
Let c(p) be the second derivative of p**5/170 + 20*p**4/51 + 77*p**3/51 + 38*p**2/17 + p + 120. Solve c(z) = 0 for z.
-38, -1
Let r = -257 - -264. Let k(u) be the third derivative of 0*u**3 + 0 + 0*u - 1/120*u**5 - 6*u**2 + 1/480*u**6 + 1/840*u**r + 0*u**4. Factor k(w).
w**2*(w - 1)*(w + 2)/4
Let g be (-2)/4 + 36/(-32)*-4. Let d be 0/g*(-1)/2. Factor 2/5*w**2 + d*w - 1/5*w**4 + 0 + 1/5*w**3.
-w**2*(w - 2)*(w + 1)/5
Let f(s) be the first derivative of -20 + 1/10*s**2 + 2/5*s - 1/15*s**3. Factor f(w).
-(w - 2)*(w + 1)/5
Let d(v) be the second derivative of -v**7/21 - v**6/15 + 3*v**5/5 + 28*v. Let d(j) = 0. What is j?
-3, 0, 2
Let k(z) = 168*z**3 - 84*z**2 + 753*z - 2289. Let t(s) = 11*s**3 - s + 1. Let d(n) = k(n) - 15*t(n). Let d(a) = 0. Calculate a.
8, 12
Suppose -37 = 2*r - 4*s - 13, -3*r = 4*s + 46. Let c = r - -18. Factor 11*z**2 - 14*z**3 + 6*z**3 - 4*z**4 + c*z + 4*z**5 - 3*z**2 - 4.
4*(z - 1)**3*(z + 1)**2
Let l(h) be the second derivative of -h**4/6 - 2*h**3/3 + 15*h**2 + 409*h. Determine y so that l(y) = 0.
-5, 3
Suppose -r - 2*s = 4, 0*s - 5*s = -5*r + 25. What is l in -r*l**5 + 20*l**3 + 20*l**2 - 16*l - 16 - 4*l**4 + 0*l**4 + 0*l**4 - 2*l**5 = 0?
-2, -1, 1, 2
Factor -3/7*q**2 - 108/7 - 36/7*q.
-3*(q + 6)**2/7
Let q(l) be the third derivative of -l**11/582120 - l**10/88200 - l**9/52920 - l**5/20 - 18*l**2. Let n(a) be the third derivative of q(a). Factor n(p).
-4*p**3*(p + 1)*(p + 2)/7
Factor -22*q**2 - 50*q + 107 + 2*q**3 + 119 - 252.
2*(q - 13)*(q + 1)**2
Determine x so that 50*x**3 - 75*x**2 - 3*x**5 - 90*x - 15*x**3 - 2*x**5 + 2 - 2 + 15*x**4 = 0.
-2, -1, 0, 3
Suppose 0 = -4*a - 2*o - 12 + 24, o - 18 = -5*a. Let x(g) be the first derivative of -4 + 0*g**3 + 1/24*g**6 + 0*g**5 + 0*g - 1/8*g**a + 1/8*g**2. Factor x(n).
n*(n - 1)**2*(n + 1)**2/4
Let s(y) = 2*y**2 + 29*y + 14. Let a be s(-14). What is o in 0*o**3 + 0*o + 1/11*o**5 + 0 + a*o**2 + 3/11*o**4 = 0?
-3, 0
Let z(b) be the third derivative of -7*b**8/12 + 82*b**7/5 - 632*b**6/15 + 172*b**5/5 - 32*b**4/3 - 5*b**2 - 43. What is p in z(p) = 0?
0, 2/7, 1, 16
Suppose -m - 4 = 5*c - 1, 2*m + 2*c = 10. Let f = m + -4. Factor -18*j**2 - f*j**3 - 2*j**4 + 0*j**4 + j**3 + 22*j**2.
-2*j**2*(j - 1)*(j + 2)
Let u(c) be the first derivative of -3*c**2 - 9*c - 1/16*c**4 - 9 + 11/12*c**3. Factor u(s).
-(s - 6)**2*(s + 1)/4
Let f(b) be the second derivative of b**7/12600 + b**6/600 + 3*b**5/200 + 11*b**4/12 - 10*b. Let n(m) be the third derivative of f(m). Factor n(l).
(l + 3)**2/5
Let t(x) be the second derivative of x**5/10 + 3*x**4/2 + 2*x**3 - 56*x**2 - 761*x. Find b such that t(b) = 0.
-7, -4, 2
Factor 0 - 1/2*h + 3*h**3 + 45/4*h**4 - 7/4*h**2.
h*(3*h + 1)**2*(5*h - 2)/4
Let y = -1422 + 1424. Let s(c) be the first derivative of 0*c**y + 0*c + 9 + 3/5*c**5 + 1/2*c**6 - 3/4*c**4 - c**3. Suppose s(b) = 0. Calculate b.
-1, 0, 1
Let m(x) = -3*x**2 + x + 1. Let r(z) = -5*z**3 + 20*z**2 - 30*z - 70. Let d(s) = 5*m(s) - r(s). Factor d(a).
5*(a - 5)*(a - 3)*(a + 1)
Let c = 71762/15 - 4784. Factor 2/3*v**4 + 2/5*v**3 - c*v**2 + 4/15*v**5 - 2/15*v + 0.
2*v*(v + 1)**3*(2*v - 1)/15
Suppose 3*w - 13 = -3*m + 11, 0 = -4*w + 20. Let j(g) be the first derivative of 0*g - 2/9*g**m - 5 + 2/15*g**5 + 0*g**2 + 0*g**4. Factor j(k).
2*k**2*(k - 1)*(k + 1)/3
Suppose 2*r - 5*c + 16 = -r, 0 = -3*r + 4*c - 20. Let s be (-3 - (-13)/5)/(r/10). Factor -q**2 - 2/3*q - s*q**3 + 0.
-q*(q + 1)*(q + 2)/3
Let n(u) = -8*u**2 + 33*u + 80. Let g(f) = 2*f**2 - 8*f - 20. Let v(r) = 9*g(r) + 2*n(r). Factor v(j).
2*(j - 5)*(j + 2)
Let k be ((-5)/(-60)*4*0)/(-2). Factor 25/2*m**2 + 5/2*m + k.
5*m*(5*m + 1)/2
Suppose -947*w - 2