 = 80/213 + -3/71. Determine a, given that -2/3*a**2 - f*a**5 - 2/3*a**3 - z + a + a**4 = 0.
-1, 1
Suppose 2*z = -5*o + 6, -3*z + 10 - 1 = 2*o. Let y be -3 + -12*z/(-6). Factor -3*r**4 + r**3 - 4*r**2 - 4*r + y*r + 2*r**4 + 5*r**2.
-r*(r - 1)**2*(r + 1)
Let l(i) be the second derivative of -2*i**6/105 - i**5/35 + i**4/21 + 2*i**3/21 - 8*i. Determine q, given that l(q) = 0.
-1, 0, 1
Factor 3/2*o**3 - 3*o**2 + 3/2*o + 0.
3*o*(o - 1)**2/2
Let w(v) = v**2 + v + 2. Let f be w(0). Let n(c) be the first derivative of 0*c**3 - 1/5*c**5 + 0*c + 0*c**f - 1/16*c**4 + 6. Find r, given that n(r) = 0.
-1/4, 0
Let v(i) be the third derivative of 0 + 0*i**3 + 1/12*i**4 - 3/280*i**7 - 7/60*i**5 + 0*i - 17/240*i**6 + 12*i**2. Let v(r) = 0. What is r?
-2, 0, 2/9
Let a(f) be the first derivative of -3*f**4/20 - 41*f**3/5 - 132*f**2 - 240*f - 133. Factor a(s).
-3*(s + 1)*(s + 20)**2/5
Let k(i) = 2*i**3 + 48*i**2 + 290*i. Let s(v) = 4*v**3 + 96*v**2 + 581*v. Let j(h) = -5*k(h) + 2*s(h). What is t in j(t) = 0?
-12, 0
Let f(j) be the second derivative of -j**4/30 - 4*j**3/5 + 28*j**2/5 - j + 38. Factor f(i).
-2*(i - 2)*(i + 14)/5
Solve 0 + 0*d - 18*d**2 + 1/2*d**3 = 0.
0, 36
Let b(g) = -5*g**5 + 5*g**4 - 11*g**3 + 7*g**2 + 4*g. Let p(l) = -l**5 - l**3 + l**2 + l. Let x(j) = -b(j) + 4*p(j). Solve x(v) = 0.
0, 1, 3
Let c(s) be the first derivative of -s**4/20 - 6*s**3/5 - 33*s**2/10 - 16*s/5 + 123. Factor c(f).
-(f + 1)**2*(f + 16)/5
Let c(j) be the first derivative of 3/14*j**2 + 1/21*j**3 - 12 + 2/7*j. Suppose c(k) = 0. Calculate k.
-2, -1
Factor 1/11*v**5 + 5/11*v**4 + 0 + 3/11*v**3 - 9/11*v**2 + 0*v.
v**2*(v - 1)*(v + 3)**2/11
Factor 526/3*b**2 - 128/3 + 96*b + 7/3*b**4 + 39*b**3.
(b + 1)*(b + 8)**2*(7*b - 2)/3
Let p be 18/24 + ((-12)/4)/((-8)/6). Factor 0 + 0*y - 14/15*y**p + 4/15*y**2.
-2*y**2*(7*y - 2)/15
Let y = 428/285 + -26/19. Let k(p) be the second derivative of -p - y*p**6 + 0 + 0*p**3 + 0*p**2 - 2/21*p**7 + 1/5*p**5 + 1/3*p**4. Find t, given that k(t) = 0.
-1, 0, 1
Let a(n) = 20*n**4 - 85*n**2 - 105*n - 35. Let p(q) = q**5 + q**4 + q**3 - q - 1. Let d(m) = a(m) + 5*p(m). Factor d(x).
5*(x - 2)*(x + 1)**3*(x + 4)
Let u(r) be the first derivative of r**6/900 + 2*r**5/75 + 4*r**4/15 - 8*r**3/3 - 6. Let q(x) be the third derivative of u(x). Factor q(t).
2*(t + 4)**2/5
Let r be 12 - 36/54*15. Let -1/4*z**3 + 0*z + z**r + 0 = 0. What is z?
0, 4
Let d(y) be the first derivative of -1/2*y**4 + y**2 + 4/3*y**3 - 7 - 4*y. Determine s so that d(s) = 0.
-1, 1, 2
Let j = -7150 - -28607/4. Factor -2 - 51/4*u**4 + 27/2*u - 121/4*u**2 + j*u**5 + 119/4*u**3.
(u - 4)*(u - 1)**3*(7*u - 2)/4
Let v(a) be the first derivative of -a**8/420 - a**7/42 - 2*a**6/45 - 8*a**3/3 - 13. Let m(q) be the third derivative of v(q). Find h such that m(h) = 0.
-4, -1, 0
Let r(g) be the second derivative of 0 + 1/8*g**5 + 13*g + 5/12*g**3 + 5/12*g**4 + 0*g**2. Factor r(z).
5*z*(z + 1)**2/2
Let d be 4*(-1444)/(-2880) - 2. Let x(a) be the third derivative of 0*a - a**2 + 0 + d*a**5 + 1/72*a**4 - 1/18*a**3 - 1/360*a**6. Suppose x(j) = 0. What is j?
-1, 1
Suppose 4*d - 1 = s, -4*d + 1 = s - 6. Suppose 0 = -s*m + m + 4. Determine a so that 2 + 4*a**2 + 53*a**4 - m - 52*a**4 + 4*a**3 = 0.
-2, 0
Let x = 11829/5 - 2363. Factor -x*h - 4/5*h**2 + 2/5*h**3 - 8/5.
2*(h - 4)*(h + 1)**2/5
Let p(r) be the first derivative of 28*r**3/33 - 111*r**2/11 - 16*r/11 - 129. Let p(d) = 0. Calculate d.
-1/14, 8
Factor -34*s + 4*s**4 - 10*s**2 + 2*s**3 + 21*s + 17*s.
2*s*(s - 1)*(s + 2)*(2*s - 1)
Let c be 51/(-544)*(-20)/225. Let u(f) be the second derivative of c*f**6 - 2*f + 1/16*f**4 + 3/80*f**5 + 0 + 0*f**2 + 1/24*f**3. Factor u(z).
z*(z + 1)**3/4
Let a(w) = 8*w**4 + 115*w**3 - 654*w**2 + 1103*w - 554. Let q(m) = 55*m**4 + 805*m**3 - 4580*m**2 + 7720*m - 3880. Let i(c) = -20*a(c) + 3*q(c). Factor i(n).
5*(n - 2)**2*(n - 1)*(n + 28)
Let q(g) be the second derivative of g**2 - 1/10*g**5 + 0 + 1/2*g**3 - 1/4*g**4 - 11*g. Factor q(s).
-(s - 1)*(s + 2)*(2*s + 1)
Let k be (8 - 8) + 5 + 197/(-40). Let l(c) be the second derivative of -5*c - 3/4*c**3 + k*c**5 + 0*c**4 + 0 - 3/2*c**2. Factor l(a).
3*(a - 2)*(a + 1)**2/2
Let q = -88324/7 + 12618. Find y, given that q*y**3 + 24/7*y**4 - 8/7 + 48/7*y - 66/7*y**2 = 0.
-2, 1/4, 2/3, 1
Let l(i) be the second derivative of -53/95*i**5 + 17/57*i**6 - 25/399*i**7 - 13/57*i**3 + 29/57*i**4 + 0 + 1/19*i**2 + 14*i. Suppose l(x) = 0. Calculate x.
1/5, 1
Let p be (-4)/(-6)*-3*(-168)/16. Let o(j) = -16*j**3 + 3*j**2 + 24*j + 5. Let v(m) = 5*m**3 - m**2 - 8*m - 2. Let a(c) = p*v(c) + 6*o(c). Factor a(y).
3*(y - 2)*(y + 1)*(3*y + 2)
Let f be ((-28)/(-40))/((-12)/(-4)). Let i = f + 4/15. Determine d so that -1/2*d + 1 + i*d**3 - d**2 = 0.
-1, 1, 2
Let q = 873 + -873. Let u(r) be the third derivative of -1/72*r**4 - 1/180*r**5 + 0*r + q + 0*r**3 - 5*r**2. Factor u(x).
-x*(x + 1)/3
Let n be (-6 - -8) + 2 + -1. Let d = -167/7 - -24. What is i in -i + 2/7 + 9/7*i**2 - 5/7*i**n + d*i**4 = 0?
1, 2
Let k(f) = 5*f**3 + 212*f**2 + 2942*f + 13720. Let m(a) = -35*a**3 - 1485*a**2 - 20595*a - 96040. Let x(c) = -15*k(c) - 2*m(c). Factor x(g).
-5*(g + 14)**3
Let 23*k**3 + 7*k - k - 2*k - 21*k**3 - 5*k**2 + 11*k**2 = 0. What is k?
-2, -1, 0
Let m(j) = j**3 + 9*j**2 + 9*j + 16. Let f be m(-8). Factor -44 + 99 - f*b**3 - 47 + 34*b**2 - 40*b.
-2*(b - 2)**2*(4*b - 1)
Let g(h) be the first derivative of -h**3/2 + 63*h**2/4 + 272. Factor g(v).
-3*v*(v - 21)/2
Let x(g) be the third derivative of 1/40*g**5 + 1/80*g**6 + 0*g - 1/4*g**3 + 12*g**2 + 0 - 1/16*g**4. Factor x(z).
3*(z - 1)*(z + 1)**2/2
Factor 13195/2*h**2 + 4205/2*h**3 + 30 + 880*h.
5*(h + 3)*(29*h + 2)**2/2
Let x(k) be the second derivative of -2/27*k**3 - 1/15*k**5 - 12*k + 1/9*k**4 + 0*k**2 + 0 + 2/135*k**6. Suppose x(z) = 0. What is z?
0, 1
Let g = -54/17 + 827/255. Let f(p) be the second derivative of -2/45*p**6 + 1/9*p**4 + 4*p + g*p**5 + 0*p**2 - 2/9*p**3 + 0. Solve f(y) = 0.
-1, 0, 1
Let u(g) = -34*g**2 - 32*g - 12. Let a(d) = 1 - 2 - 3 - 11*d - 12*d**2. Let q(v) = 14*a(v) - 5*u(v). Solve q(j) = 0.
-2, -1
Let f be (5 - 12) + (0 - -9). Determine r so that -15/2*r**3 - 18*r**f - 18*r - 9/8*r**4 - 6 = 0.
-2, -2/3
Let r(a) be the third derivative of 0 - 1/24*a**6 + 0*a + 30*a**2 - 5/8*a**4 - 15/2*a**3 + 5/12*a**5. Factor r(i).
-5*(i - 3)**2*(i + 1)
Suppose a + 27 = 5*f, -4*a - 18 = -2*f - 0*f. Let u = -295 - -297. Determine g, given that u*g**2 + g**3 + 6*g - f*g + 0*g = 0.
-1, 0
Let g(h) = -4*h**4 + 4*h**3 - 4*h**2 + 3*h - 3. Let q(y) = 8*y**3 - 6*y - 11*y - 5 - 8*y**2 - 7*y**4 + 22*y. Let u(w) = 10*g(w) - 6*q(w). Factor u(c).
2*c**2*(c - 2)**2
Let j(v) = -5*v + 25. Let i be j(6). Let x(y) = y**3 + 4*y**2 - 8*y + 4. Let w(h) = -h**3 - 5*h**2 + 9*h - 5. Let u(k) = i*x(k) - 4*w(k). Factor u(a).
-a*(a - 2)*(a + 2)
Let -2/9*i**2 - 14/9*i - 8/3 = 0. What is i?
-4, -3
Suppose -55/3 - 5/3*h**2 + 20*h = 0. Calculate h.
1, 11
Let y(w) be the second derivative of -1/5*w**2 - 1/30*w**4 + 2/15*w**3 + 0 + 3*w. Factor y(i).
-2*(i - 1)**2/5
Find a such that 10/7*a**3 + 2/7*a**2 - 10/7*a + 4/7 - 6/7*a**4 = 0.
-1, 2/3, 1
Let l(q) = 36*q**3 + 73*q**2 + 28*q - 9. Let k(x) = 36*x**3 + 72*x**2 + 28*x - 8. Let v(b) = 5*k(b) - 4*l(b). What is a in v(a) = 0?
-1, 1/9
Let r(d) be the third derivative of -d**5/100 + 11*d**4/24 + 19*d**3/15 + d**2 - 38*d. Factor r(f).
-(f - 19)*(3*f + 2)/5
Let v(b) be the first derivative of -b**4/28 + 11*b**3/21 - 5*b**2/2 + 25*b/7 + 825. Let v(y) = 0. Calculate y.
1, 5
Let x = -717 - -720. Let y(f) be the third derivative of 0 + 4*f**2 - 1/210*f**5 - 1/42*f**4 + 0*f - 1/21*f**x. Factor y(d).
-2*(d + 1)**2/7
Let x(s) be the second derivative of -s**5/40 + s**4/24 + s**3/6 + 7*s - 6. Find l, given that x(l) = 0.
-1, 0, 2
Let w = -1213 + 1218. Let c(f) be the third derivative of 0 - 1/285*f**w + 1/1140*f**6 + 0*f**3 + 0*f**4 + 0*f - 3*f**2. Find j, given that c(j) = 0.
0, 2
Factor 2/5*k**2 + 1458/5 + 108/5*k.
2*(k + 27)**2/5
Let h = 50/51 - 148/255. Factor h*g**2 + 0*g - 8/5.
2*(g - 2)*(g + 2)/5
Suppose -14*i = -9*i. Let m(p) be the second derivative of -1/126*p**7 + 0 + 6*p + 2/45*p**6 - 1/18*p**3 - 1/10*p**5 + i*p**2 + 1/9*p**4. Factor m(a).
-a*(a - 1)**4/3
Solve 1/6*q**2 + 0 - 19/6*q = 0 for q.
0, 19
Suppose -g = -3*m, -3*g - 2*g = -5*