0 + 16*o**3/5 - 9*o**2/10 + 87. Factor g(s).
-s*(s - 1)**2*(5*s - 3)**2/5
Let a(h) be the first derivative of -3*h**4/4 - 28*h**3 - 81*h**2/2 + 462. Find k such that a(k) = 0.
-27, -1, 0
Let 8*l**3 + 1 - 11*l**4 - 4*l**2 - 11*l**4 - 1 - 8*l + 26*l**4 = 0. Calculate l.
-2, -1, 0, 1
Let g(j) be the first derivative of 1/9*j**3 + 1/12*j**4 - 1/4*j**2 - 1/10*j**5 + 1/36*j**6 + 1/6*j + 27. Let g(d) = 0. Calculate d.
-1, 1
Let x(f) be the first derivative of -1/8*f**4 + 0*f + 37 + 0*f**2 + 2/3*f**3. Find c, given that x(c) = 0.
0, 4
Let n = -2374 - -21370/9. Determine x, given that 2/9*x**2 + n*x + 2/9 = 0.
-1
Let b be ((-1470)/(-162) - 9)*(21 + 3). Factor -b - 16/9*w - 4/9*w**2.
-4*(w + 2)**2/9
Let z(t) = 3*t**2 - 24*t - 54. Let y be z(-2). Let g(j) be the second derivative of 4/3*j**3 + 0 + j**4 + y*j + 0*j**2. What is f in g(f) = 0?
-2/3, 0
Solve 58/13*g**2 + 62/13 + 122/13*g - 2/13*g**3 = 0 for g.
-1, 31
Let x(s) = -s**2 - 14*s - 27. Let j(l) = -3*l**2 - 44*l - 82. Let c(z) = -4*j(z) + 14*x(z). Factor c(w).
-2*(w + 5)**2
Let r(w) = 20*w**2 - 116*w - 32. Let v(t) = -4*t**2 + 23*t + 6. Let z(j) = 3*r(j) + 16*v(j). Find n, given that z(n) = 0.
0, 5
Let i be (-6)/(-6)*(0 - 0). Let v be 1/2 - i/4. What is b in 5/6*b**2 + 7/6*b + v + 1/6*b**3 = 0?
-3, -1
Let l = 195 - 6824/35. Let p(x) be the second derivative of 0 + 0*x**4 + 0*x**2 - 1/21*x**6 - 1/21*x**7 + l*x**5 + 0*x**3 - 5*x. Factor p(t).
-2*t**3*(t + 1)*(7*t - 2)/7
Suppose -15*d - 6 = -51. Factor -6*t**4 + d*t**5 - 813 + 813.
3*t**4*(t - 2)
Let x = -32 + 34. Let n(t) = 0 - 64*t + 12*t**3 - x - 9*t**2 + 33*t. Let y(c) = -12*c**3 + 9*c**2 + 30*c + 3. Let h(w) = 3*n(w) + 4*y(w). Factor h(o).
-3*(o - 2)*(o + 1)*(4*o + 1)
Let h(m) be the third derivative of 7*m**8/16 - 23*m**7/10 - 69*m**6/40 + 349*m**5/20 + 2*m**4 - 96*m**3 + 5*m**2 + 14. Solve h(f) = 0.
-1, 8/7, 3
Let p(o) be the first derivative of 2/21*o**3 + 2/7*o - 6 - 2/7*o**2. Determine b, given that p(b) = 0.
1
Let f(o) be the second derivative of 1/5*o**3 + 0*o**2 - 10*o + 0 - 1/20*o**4. Solve f(r) = 0 for r.
0, 2
Let t = 18641/40 + -466. Let l(v) be the third derivative of 0 - t*v**5 + 6*v**2 + 0*v + 1/48*v**4 + 0*v**3 - 1/420*v**7 + 1/80*v**6. Factor l(f).
-f*(f - 1)**3/2
Factor c + 0 - 2/3*c**2 + 1/9*c**3.
c*(c - 3)**2/9
Determine q, given that 0 + 84*q**3 - 38/3*q**4 + 2/3*q**5 - 216*q**2 + 144*q = 0.
0, 1, 6
Let q(s) be the third derivative of -s**8/8960 + s**7/560 - 3*s**6/320 + s**5/40 + s**4/2 - 2*s**2. Let i(w) be the second derivative of q(w). Factor i(y).
-3*(y - 4)*(y - 1)**2/4
Factor -404/7*a + 4/7*a**2 - 408/7.
4*(a - 102)*(a + 1)/7
Let h(d) be the third derivative of d**8/672 - d**7/420 - 11*d**6/120 + d**5/3 + 425*d**2. Find a, given that h(a) = 0.
-5, 0, 2, 4
Factor 8*g**2 - 4 + 7*g**2 + 4*g**2 + 8*g**2 - 25*g**2 + 2*g.
2*(g - 1)*(g + 2)
Let a = 10 - 10. Let i(v) be the third derivative of a*v + 1/6*v**4 + 0 + 1/5*v**5 + 1/24*v**6 - v**2 + 0*v**3. Suppose i(j) = 0. What is j?
-2, -2/5, 0
Let f = -3361 - -141185/42. Let r = -3/14 + f. Solve r - 2/3*v**3 - v**4 + 2/3*v**2 + v - 1/3*v**5 = 0 for v.
-1, 1
Suppose 2*s + 4 = 4*s. Let d(g) = -11*g**2 - 4 + 0 + 8*g + 6*g**s. Let a(k) = k**2 - k. Let v(f) = -4*a(f) - d(f). Determine n so that v(n) = 0.
2
Let n = 1712 - 15394/9. Let u(s) be the first derivative of 14/3*s**4 - 2/9*s + 11 - 122/27*s**3 + n*s**2 - 8/5*s**5. Factor u(j).
-2*(j - 1)**2*(6*j - 1)**2/9
Factor 21*d - 26*d + 51*d - 3*d**3 + 40*d**2 + 59*d + 62*d**2.
-3*d*(d - 35)*(d + 1)
Factor 8/3*d**2 + 0 + 50/3*d**4 + 0*d + 104/3*d**3.
2*d**2*(d + 2)*(25*d + 2)/3
Let r be ((5 - 5)/(-29))/(4 - 2). Suppose -16/13*v**3 + r - 6/13*v + 22/13*v**2 = 0. Calculate v.
0, 3/8, 1
Suppose 0 = -4*y - l - 0*l + 94, 4*y + 4*l - 88 = 0. Let r(g) = -g**3 + 23*g**2 + 23*g + 26. Let o be r(y). Factor -2/5*s**o + 0 - 2/5*s.
-2*s*(s + 1)/5
Let b(u) be the second derivative of -u**5/24 - 25*u**4/72 + 233*u. Factor b(w).
-5*w**2*(w + 5)/6
Factor -76*q + q**2 + 6084 - 244*q + 164*q.
(q - 78)**2
Let n(r) = -2*r**2 - 14*r + 7. Let p be n(-10). Let k = p - -266/5. Solve -k*o + 1/5*o**5 + 2/5*o**4 + 0*o**3 - 2/5*o**2 + 0 = 0.
-1, 0, 1
Let s(g) be the first derivative of g**3 + 0*g + 3/4*g**4 + 9 + 0*g**2. Solve s(m) = 0.
-1, 0
Solve 3*l**2 - 3/5*l**4 + 0 + 9/5*l + 3/5*l**3 = 0.
-1, 0, 3
Let y(i) be the second derivative of -1/70*i**5 + 0*i**3 + 0 - 1/42*i**4 - 15*i + 0*i**2. Factor y(r).
-2*r**2*(r + 1)/7
Let m(b) be the second derivative of 1/11*b**5 + 16*b + 0 + 18/11*b**3 - 1/165*b**6 - 6/11*b**4 - 27/11*b**2. Determine f so that m(f) = 0.
1, 3
Factor 128 + 61*s + 115*s - 4352*s**3 + 52*s**2 + 4356*s**3.
4*(s + 1)*(s + 4)*(s + 8)
Let o(v) be the third derivative of -v**5/15 - 5*v**4/8 + 2*v**3/3 + 505*v**2. Factor o(n).
-(n + 4)*(4*n - 1)
Let g = 7137/8 - 892. Let f(x) be the first derivative of -1 + 1/16*x**4 + 0*x**3 - g*x**2 + 0*x. Factor f(p).
p*(p - 1)*(p + 1)/4
Let h be ((-16)/12)/(2/(-18)). Suppose -3*r**2 - 14*r - 6*r**3 + 14*r - h*r**5 + 21*r**4 = 0. What is r?
-1/4, 0, 1
Let w(v) be the first derivative of 3*v**5/10 - 9*v**4/4 + 9*v**3/2 + 3*v**2 - 18*v - 39. Factor w(l).
3*(l - 3)*(l - 2)**2*(l + 1)/2
Let y = -3565 + 3565. Suppose y + 1/5*x - 4/5*x**3 + 3/5*x**2 = 0. What is x?
-1/4, 0, 1
Factor 0 - 6/17*u**2 + 2/17*u**4 + 4/17*u**3 + 0*u.
2*u**2*(u - 1)*(u + 3)/17
Let q be 17/85 + (83/(-15) - 54/(-9)). Factor -1/6*k**2 - q + 5/6*k.
-(k - 4)*(k - 1)/6
Suppose 0 = c - k + 40, -c - 39 = -2*k + 4. Let z = c - -41. Let 4/5*g**3 + 1/5*g**z + 6/5*g**2 + 4/5*g + 1/5 = 0. Calculate g.
-1
Suppose 43*z = 673 - 157. Let i(g) be the second derivative of 0*g**2 + 0 - z*g + 5/2*g**3 + 5/12*g**4. Factor i(l).
5*l*(l + 3)
Let x(u) be the third derivative of -u**7/420 - u**6/120 + u**5/24 + u**4/8 + 82*u**2. Factor x(c).
-c*(c - 2)*(c + 1)*(c + 3)/2
Let g(a) be the first derivative of 3*a**5/5 + 3*a**4/2 - 12*a**3 - 60*a**2 - 96*a - 134. Find t such that g(t) = 0.
-2, 4
Let z be 6*(-2 + 16/6). Suppose -a + z*a - 1 = 2*l, 0 = 3*l - 12. Factor -4*v**4 - v**3 - a*v**5 + 7*v**3 + v**5 - 8*v**3.
-2*v**3*(v + 1)**2
Let i(k) = 4*k**3 - 2*k**2 + 6*k + 2. Let j(p) = 5*p**3 - 4*p**2 + 7*p + 4. Let n(a) = -6*i(a) + 5*j(a). Let n(u) = 0. Calculate u.
-1, 1, 8
Let c(u) = 5*u + 11. Let i be c(-8). Let q = i + 29. Factor 10/7*g**2 + q - 2/7*g**5 + 6/7*g**3 - 2/7*g**4 + 4/7*g.
-2*g*(g - 2)*(g + 1)**3/7
Let d(f) be the first derivative of -f**4/5 + 44*f**3/15 - 78*f**2/5 + 36*f - 96. Factor d(x).
-4*(x - 5)*(x - 3)**2/5
Let s(b) = b**4 - 36*b**3 + 69*b**2 - 34*b. Let n(q) = 2*q**4 - 71*q**3 + 136*q**2 - 67*q. Let p(u) = 3*n(u) - 5*s(u). Find f such that p(f) = 0.
0, 1, 31
Let v(y) be the first derivative of -y**4/36 + y**3/3 - 5*y**2/6 + 33*y + 24. Let n(d) be the first derivative of v(d). Factor n(f).
-(f - 5)*(f - 1)/3
Let k(q) be the first derivative of -q**7/1120 - q**6/96 - 7*q**5/160 - 3*q**4/32 + 20*q**3/3 + 2. Let g(t) be the third derivative of k(t). Factor g(i).
-3*(i + 1)**2*(i + 3)/4
Let q = -105 - -153. Let j be ((-3)/(-12))/(4/q). Determine z, given that 10/7*z**j + 8/7*z - 26/7*z**2 + 8/7 = 0.
-2/5, 1, 2
Let i = 42997/8 - 5374. Suppose -3/8*h**5 + 1/4*h**2 + i*h**3 + 0*h + 0 - 1/2*h**4 = 0. What is h?
-2, -1/3, 0, 1
Let u(g) be the third derivative of -5*g**8/336 - 5*g**7/42 - g**6/4 + g**5/6 + 35*g**4/24 + 5*g**3/2 + 2*g**2 + 183*g. Solve u(b) = 0 for b.
-3, -1, 1
Let a(p) be the first derivative of 4*p**3/3 - 70*p**2 - 144*p + 61. Factor a(w).
4*(w - 36)*(w + 1)
Suppose -p + 4 = 2. Suppose 5*u - 8 = p. Factor -2/11*z**3 + 2/11 - 2/11*z**u + 2/11*z.
-2*(z - 1)*(z + 1)**2/11
Let p(r) = 5*r**2 - 15*r - 3. Let t(m) = 2*m**2 - 5*m - 1. Let c(n) = 6*p(n) - 17*t(n). Factor c(b).
-(b + 1)*(4*b + 1)
Let m(z) be the second derivative of 0*z**2 - 1/30*z**6 + 3/20*z**5 - 1/42*z**7 - 22*z + 1/3*z**3 + 5/12*z**4 + 0. Let m(f) = 0. What is f?
-1, 0, 2
Let d be (9 + (7 - 12))*4/36. Suppose -d + 2/9*j**4 + 2/9*j**2 + 2/3*j**3 - 2/3*j = 0. Calculate j.
-2, -1, 1
Suppose -3 = 5*p + 22, 0 = -l + 3*p + 54. Let -l*y - y - 20 - 530*y**3 + 15*y**4 + 570*y**3 + 3*y**2 + 2*y**2 = 0. What is y?
-2, -1, -2/3, 1
Let n(i) = 2*i**4 - i**3 - i**2 - i - 1. Let j(s) = 6*s**4 - 64*s**3 - 106*s**2 - 30*s + 2. Let c(h) = -j(h) - 2*n(h). Factor c(w).
-2*w*(w - 8)*(w + 1)*(5*w + 2)
Let 