et s = -89/14 - -491/42. Find g such that -2/3*g**2 - 14/3 + s*g = 0.
1, 7
Suppose 8 = -3*b + 11, -5*w = 5*b - 5. Let x(v) be the first derivative of w*v + 3 + 0*v**2 + 3/4*v**4 + 1/2*v**3 + 3/10*v**5. Factor x(f).
3*f**2*(f + 1)**2/2
Let t(p) be the first derivative of -4/3*p**3 - 48*p + 20 + 16*p**2. Factor t(h).
-4*(h - 6)*(h - 2)
Factor 0*n**2 - 1/3*n**3 - 2/3 + n.
-(n - 1)**2*(n + 2)/3
Let i = 5906 + -5904. Factor 1/6*w**i - 2/3*w - 5/6.
(w - 5)*(w + 1)/6
Suppose s - 16*s = -5*s. Let r(m) be the third derivative of 5*m**2 + 0*m**4 + 0 + s*m**3 + 0*m + 1/60*m**5. Find h such that r(h) = 0.
0
Let l(k) = -k**3 - 18*k**2 - 30*k + 32. Let c be l(-16). Let s(x) = x**3 + 15*x**2 - 36*x - 32. Let r be s(-17). Factor -1/4*y**r + 1/4 + c*y.
-(y - 1)*(y + 1)/4
Let i(o) be the first derivative of -1/210*o**6 + 1/42*o**4 + 4 + 1/70*o**5 + 0*o**3 + 0*o + 1/2*o**2. Let j(u) be the second derivative of i(u). Factor j(q).
-2*q*(q - 2)*(2*q + 1)/7
Let k(a) = -3*a**3 + a + 2. Let n be k(-1). Suppose -6 = -2*j - n*v + 6, -5*j = 4*v - 12. Factor -3/2*f**2 + j + 3*f.
-3*f*(f - 2)/2
Let t(v) be the second derivative of -3*v**5/40 - 357*v**4/4 - 42483*v**3 - 10110954*v**2 - 663*v. Factor t(z).
-3*(z + 238)**3/2
Let v(j) = -4*j**3 + 5*j**2 + 4*j. Suppose 4*l = 5 + 15. Let w(k) = 3*k**3 - 4*k**2 - 3*k. Let b(t) = l*w(t) + 4*v(t). Factor b(q).
-q*(q - 1)*(q + 1)
Find c such that 14*c + 6/5*c**3 + 32/5 + 44/5*c**2 = 0.
-16/3, -1
Let p(s) be the third derivative of -s**8/30240 - s**7/2268 - 7*s**6/3240 - s**5/180 + s**4/4 - 10*s**2. Let w(x) be the second derivative of p(x). Factor w(r).
-2*(r + 1)**2*(r + 3)/9
Factor -11/2*k + 1/2*k**2 + 12.
(k - 8)*(k - 3)/2
Let o(m) be the first derivative of -m**3 + 3*m**2/2 - 246. Let o(j) = 0. What is j?
0, 1
Let x(o) be the third derivative of -o**5/60 - 2*o**4/3 + 19*o**3/2 + 857*o**2. Determine z so that x(z) = 0.
-19, 3
Let o(m) = -4*m**2 + 25*m + 5. Let u(b) = -6*b**2 + 38*b + 8. Let j(x) = -8*o(x) + 5*u(x). Determine n, given that j(n) = 0.
0, 5
Let n(d) = d**5 - d**4 + d**3 + d**2 - d - 1. Let b(f) = -f**4 - f**3 + f**2 + 1. Let v(m) = 5*b(m) + 5*n(m). Factor v(p).
5*p*(p - 1)**3*(p + 1)
Let z be (0 + 1)/((-2)/(-28)). Suppose -5*m = 2*s - 6*s + 28, -3*m - z = -s. Factor 2 + s*d - 9*d - 2*d**2 + 5*d**2 + 2*d**2.
(d - 1)*(5*d - 2)
Let g = -2 - 4. Let w(r) = 2*r**4 - 6*r**2 + 4*r - 5. Let o(h) = h**4 - 3*h**2 + 2*h - 2. Let x(m) = g*w(m) + 15*o(m). Factor x(i).
3*i*(i - 1)**2*(i + 2)
Suppose -25 + 15 = -5*q. Let u(l) be the third derivative of -27/35*l**7 - l**4 + 0 - 9/5*l**5 - 3*l**q + 0*l - 9/5*l**6 - 1/3*l**3. Let u(r) = 0. What is r?
-1/3
Let d be (495/83 - 6)*(-2)/3. Let l = d - -245/166. Factor l*a**3 + 0 + 0*a**4 - 3/2*a**5 + 0*a + 0*a**2.
-3*a**3*(a - 1)*(a + 1)/2
Let s(r) = 3*r - 19. Let u be s(6). Let d be u/4*104/(-65). Factor d*n**5 + 6/5 - 2*n**4 - 14/5*n + 4/5*n**2 + 12/5*n**3.
2*(n - 3)*(n - 1)**3*(n + 1)/5
Suppose 13*l - 3*l = 120. Let 41 - 8*x**2 - 41 - 5*x**4 + x**4 + l*x**3 = 0. Calculate x.
0, 1, 2
Let r be 2169/672*2/51. Let x = -1/112 + r. Factor 0*y + 4/17*y**2 + 0 - x*y**4 + 2/17*y**3.
-2*y**2*(y - 2)*(y + 1)/17
Let g = -95083/5 - -19017. Factor 0 + 0*i - 4/5*i**3 - 16/5*i**2 + g*i**4.
2*i**2*(i - 4)*(i + 2)/5
Let u(k) be the third derivative of -1/840*k**7 + 0 + 6*k**2 - 1/6*k**3 - 13/96*k**4 - 1/16*k**5 - 7/480*k**6 + 0*k. Factor u(t).
-(t + 1)**3*(t + 4)/4
Let w = 469/24 - 2951/168. Let i = w + -9/14. Factor 0*t + 0 - 4/3*t**5 - 4*t**4 - 4*t**3 - i*t**2.
-4*t**2*(t + 1)**3/3
Let l(u) be the first derivative of -3*u**5/20 - 3*u**4/2 - 11*u**3/2 - 9*u**2 + 18*u - 21. Let n(b) be the first derivative of l(b). Solve n(t) = 0 for t.
-3, -2, -1
What is u in 79 - 3*u**4 + 38*u**2 - 51*u - 9*u**3 - 61 + 7*u**2 = 0?
-6, 1
Let r be ((-2)/6)/(945/(-9072)). Solve -2/5*w**2 - r + 18/5*w = 0.
1, 8
Factor 1764 + 2169*v**2 - 3696*v - 26*v**3 + v**4 - 150*v**3 + 3*v**4 - 65*v**2.
4*(v - 21)**2*(v - 1)**2
Let p(g) be the first derivative of 27/2*g**2 + 3/4*g**4 + 6*g**3 + 12*g - 33. Determine v so that p(v) = 0.
-4, -1
Let k be 0*(15 + (-2567)/170). Factor k - 1/4*g + 1/8*g**3 - 1/8*g**2.
g*(g - 2)*(g + 1)/8
Let b(q) = 2*q**3 - q**2 - 3. Let n be b(2). Let j be 4/6 + (-6)/n. Determine g, given that -2/5*g**2 + 2/5*g**3 + 2/5*g**4 - 2/5*g**5 + j*g + 0 = 0.
-1, 0, 1
Let c be (-712)/(-6) - 8/(-36)*3. Let y = -118 + c. Factor -7/3*k**4 - 25/3*k**2 - 19/3*k**3 - 1/3*k**5 - 16/3*k - y.
-(k + 1)**3*(k + 2)**2/3
Suppose -2*h + k + 9 = h, 0 = -2*h - 3*k - 5. Factor 4*y**2 - 4*y**3 - 6*y**2 + 4*y**h + 12*y - 10*y**2.
-4*y*(y - 1)*(y + 3)
Let j(f) = 13*f**2 - 2*f - 20. Let i(z) = -28*z**2 + 3*z + 40. Let c(g) = 6*i(g) + 13*j(g). Determine s, given that c(s) = 0.
-2, 10
Suppose -5*z + 4*l = -258, 0*z + 5*z = l + 252. Suppose z*v = 46*v. Determine o so that 1/5*o**4 + 1/5 + 0*o + v*o**3 - 2/5*o**2 = 0.
-1, 1
Suppose z + 11 - 3 = 0. Let p be (-36)/(-15) - z/(-20). Factor 5*h + 7*h**3 - 9*h**3 - 4*h**p + 3*h**3 - 2.
(h - 2)*(h - 1)**2
Let s(i) be the first derivative of 0*i**2 - 30 - 3/16*i**4 + 1/4*i**3 + 0*i. Factor s(q).
-3*q**2*(q - 1)/4
Let s be (-3 - (-1 - -1))*(20 - 2). Let v be (2/18)/((-36)/s). Determine h so that 0*h - v*h**4 + 9/2 - 3*h**2 - 4/3*h**3 = 0.
-3, 1
Let i(q) be the second derivative of -q**7/42 - q**6/10 + 22*q. Let x(f) = f**4 + f**3. Let u(y) = -i(y) - 2*x(y). Factor u(a).
a**3*(a - 1)*(a + 2)
Let m = -434 - -434. Let u(n) be the third derivative of -1/4*n**4 + 1/30*n**5 + 0*n + m*n**3 + 0 + 14*n**2. Factor u(q).
2*q*(q - 3)
Let m(i) = 2*i**2 + 14*i + 22. Let v be m(-2). Let 6 + 4*a + 2/3*a**v = 0. Calculate a.
-3
Let k be (10/(-6))/(6/18). Let h(y) = -y**2 - 4*y + 3. Let x(p) = -8*p + 2*p + 7 - 3*p - 3*p**2. Let j(l) = k*h(l) + 2*x(l). Suppose j(d) = 0. Calculate d.
1
Let y(u) be the first derivative of -3*u**4/10 + 31*u**3/5 + 51*u**2/10 - 48*u/5 - 333. What is r in y(r) = 0?
-1, 1/2, 16
Let u(o) be the second derivative of o**5/5 + 31*o**4/3 - 68*o**3/3 - 128*o**2 - 4*o - 117. Solve u(b) = 0.
-32, -1, 2
Let z(q) be the first derivative of 2/21*q**3 + 6/7*q + 5/7*q**2 - 7 - 1/14*q**4. Let z(t) = 0. Calculate t.
-1, 3
Let l(a) be the second derivative of a**4/3 + 82*a**3/3 - 84*a**2 + a - 68. Factor l(j).
4*(j - 1)*(j + 42)
Let j(b) be the third derivative of -b**7/105 - b**6/30 - b**5/30 + 2*b**2 - 75*b. Factor j(y).
-2*y**2*(y + 1)**2
Let s(f) = 4*f**2 + f - 2. Let c(b) = 11*b**2 + 4*b - 7. Let p(v) = 3*c(v) - 8*s(v). Factor p(z).
(z - 1)*(z + 5)
What is g in -12*g**3 + 223*g + 26*g**2 + 12*g**5 - 20*g**4 - 9*g**3 - 215*g + g**3 - 6*g**2 = 0?
-1, -1/3, 0, 1, 2
Let p(k) be the first derivative of k**4/38 + 32*k**3/57 - 39*k**2/19 - 108*k/19 - 108. Factor p(b).
2*(b - 3)*(b + 1)*(b + 18)/19
Let g be 2 + -1*(0 + -1)*-2. Suppose g = s - 3*o - 6 + 13, -14 = -4*s - 2*o. Factor 3/2*b**s + 0 + 3*b.
3*b*(b + 2)/2
Let r be 285/171*28/5. Factor -16/3 - r*v + 8/3*v**2.
4*(v - 4)*(2*v + 1)/3
Let j be ((-3)/(-9))/1 + (-4840)/30. Let m be 32/42 - (-69)/j. Factor 1/6*g**5 + 0 + 0*g**2 - 1/2*g**3 + 0*g + m*g**4.
g**3*(g - 1)*(g + 3)/6
Let o(b) be the third derivative of -b**7/70 - 81*b**6/40 - 1131*b**5/10 - 5915*b**4/2 - 26364*b**3 + 14*b**2 - 30. Solve o(w) = 0 for w.
-26, -3
Let z = 12 - 10. Factor 2*w**3 + 10 - 10*w**z + 13*w - 7*w - 8*w.
2*(w - 5)*(w - 1)*(w + 1)
Let n(b) be the first derivative of -3*b**5/10 - 3*b**4 - 2*b**3 + 36*b**2 + 475. Find i such that n(i) = 0.
-6, -4, 0, 2
Determine q, given that 6*q**2 + 177*q**2 - 47*q**2 - 32*q + 128*q + 36*q**3 - 4*q**4 = 0.
-2, -1, 0, 12
Let f(y) = -7*y + 15. Let q be f(2). Find v such that -2*v**3 - q - 1/3*v**4 - 4*v**2 - 10/3*v = 0.
-3, -1
Let q(h) = -2*h**4 + 29*h**2 + 28*h - 53. Let b(p) = -p**4 - p**3 + 2*p**2 + p + 1. Let s(y) = -b(y) + q(y). Let s(o) = 0. What is o?
-3, 1, 6
Let i(b) be the first derivative of 2*b**6/3 - 323*b**5/5 + 6315*b**4/4 + 8323*b**3/3 + 1681*b**2/2 + 344. Let i(g) = 0. Calculate g.
-1, -1/4, 0, 41
Let s = -796/89 - -12118/1335. Factor 40/3 + s*x**2 - 8/3*x.
2*(x - 10)**2/15
Factor -48/5*f**3 - 2/5*f**5 - 32/5*f**2 + 0*f + 0 - 18/5*f**4.
-2*f**2*(f + 1)*(f + 4)**2/5
Let z(h) be the first derivative of 0*h + 2/3*h**3 + 1/30*h**5 - h**2 - 7 + 1/4*h**4. Let f(j) be the second derivative of z(j). Suppose f(q) = 0. What is q?
-2, -1
