 (-32)/4*5*2/4. Let g be 6/8*(-1 - 36/r). What is o in -g*o**3 + 0*o - 1/5*o**4 - 2/5*o**2 + 0 = 0?
-2, -1, 0
Determine n so that 0 + 1/2*n**2 - 69/2*n = 0.
0, 69
Let u(q) be the third derivative of -q**5/15 + 4*q**4/3 - 5*q**2 - 7. Let u(n) = 0. What is n?
0, 8
Solve 54/7*k**2 - 18/7 + 15/7*k**3 + 3*k = 0.
-3, -1, 2/5
Let m be ((-2)/(-2) - (-253)/(-161))/(-1). Suppose 0 + m*d**2 + 1/7*d**3 + 4/7*d = 0. What is d?
-2, 0
Let v(g) be the second derivative of -g**4/12 - 21*g. Let k(f) = 12*f**2 + 9*f - 6. Let u(h) = k(h) + 15*v(h). Determine y so that u(y) = 0.
1, 2
Suppose -301*x = -316*x + 30. Factor 36/7*c - 3/7*c**x - 108/7.
-3*(c - 6)**2/7
Let p(o) be the second derivative of 8/15*o**3 - 11/15*o**4 + 0*o**2 + 0 - 3/25*o**5 + 38*o. Factor p(s).
-4*s*(s + 4)*(3*s - 1)/5
Let m(n) = -n**4 + 21*n**3 - 24*n**2 - 50*n. Let w(i) = 6*i**4 - 147*i**3 + 168*i**2 + 351*i. Let v(f) = 15*m(f) + 2*w(f). Factor v(l).
-3*l*(l - 4)**2*(l + 1)
Let p = -1366 - -1369. Solve 1/3*q**p - 1/3*q - 1/3*q**4 + 0 + 1/3*q**2 = 0 for q.
-1, 0, 1
Let t(v) be the third derivative of v**7/210 + 11*v**6/24 + 182*v**5/15 - 98*v**4/3 - 286*v**2. Factor t(p).
p*(p - 1)*(p + 28)**2
Let a be (2*2/(-10))/((-3)/90). Let -3*c**4 - 72*c - 54*c**2 - a*c**2 - 4 - 24*c**3 - 23 = 0. What is c?
-3, -1
Let p(g) be the second derivative of -5*g**7/168 - 2*g**6/3 + 9*g**5/4 - 5*g**4/24 - 175*g**3/24 + 45*g**2/4 + 4*g - 118. Determine q so that p(q) = 0.
-18, -1, 1
Factor -24/5*v**2 - 4/5*v**3 - 32/5 - 48/5*v.
-4*(v + 2)**3/5
Suppose 0 = -5*f - 3*y + 96 - 21, -f - 2*y + 22 = 0. Determine q, given that -7*q**2 - 6 - q**2 - f*q - 12 + 6*q**2 = 0.
-3
Let v(l) be the third derivative of l**7/252 + 17*l**6/720 + 7*l**5/120 + 11*l**4/144 + l**3/18 - l**2 - 35*l. Determine r, given that v(r) = 0.
-1, -2/5
Let r = 10638 + -95740/9. Factor -r - 2/9*k**4 + 8/9*k + 8/9*k**3 - 4/3*k**2.
-2*(k - 1)**4/9
Let w(m) be the first derivative of 4*m**5/5 + 3*m**4 - 8*m**3 - 16*m**2 + 91. Factor w(t).
4*t*(t - 2)*(t + 1)*(t + 4)
Let j(u) be the first derivative of 11*u**7/1470 - u**6/18 - 19*u**5/105 + 4*u**4/21 + 11*u**3 + 40. Let m(p) be the third derivative of j(p). Factor m(k).
4*(k - 4)*(k + 1)*(11*k - 2)/7
Let 13/7*w**2 - 16/7*w + 5/7 - 2/7*w**3 = 0. What is w?
1/2, 1, 5
Let v(s) = -6*s - 60. Let w be v(-11). Let r(n) = -17*n + 105. Let m be r(w). What is c in 0 + 4/7*c + 2/7*c**2 + 38/7*c**4 - 30/7*c**m - 2*c**5 = 0?
-2/7, 0, 1
Let j(l) be the first derivative of -l**7/54 - l**6/30 - l**5/90 - 23*l - 21. Let v(x) be the first derivative of j(x). Solve v(q) = 0 for q.
-1, -2/7, 0
Let j(c) be the second derivative of -1/24*c**3 - 1/96*c**4 + 0*c**2 + 0 + 1/160*c**5 + 17*c. Determine w, given that j(w) = 0.
-1, 0, 2
Let r be (4/(-5))/((-1)/30). Let z be 112/r - (1 - -3). Factor 0*c**4 + 0 + 4/3*c**3 - 2/3*c**5 + 0*c**2 - z*c.
-2*c*(c - 1)**2*(c + 1)**2/3
Let j(z) be the first derivative of -z**4/14 - 8*z**3/21 - 5*z**2/7 - 4*z/7 + 90. Solve j(w) = 0 for w.
-2, -1
Suppose 0 = -3*u + 6. Factor -10*g**5 + 5*g**5 - u*g**3 + 6*g**5 + g**3.
g**3*(g - 1)*(g + 1)
Factor 12 + 2 - 2 - 39*f**2 + 12*f + 15*f**3.
3*(f - 2)*(f - 1)*(5*f + 2)
Let u be (1/(-576)*-4)/((-7)/(-14)). Let m(n) be the second derivative of 5*n + 5/36*n**3 - 1/120*n**5 - 1/4*n**2 + 0 - u*n**4. Find w such that m(w) = 0.
-3, 1
Factor 17*r**3 + r**5 - 51/7*r**4 - 121/7*r**2 + 54/7*r - 8/7.
(r - 4)*(r - 1)**3*(7*r - 2)/7
Suppose 6 = q + z, 11*q + 16 = 14*q + 2*z. Let u(d) be the first derivative of -q - 1/9*d**3 - 1/6*d**2 + 0*d. What is k in u(k) = 0?
-1, 0
Let n be 2*-3 + 2 + 8/2. Let z(b) be the second derivative of n*b**3 + 1/5*b**5 - 1/6*b**4 - 4*b + 0 + 0*b**2 - 1/15*b**6. Factor z(c).
-2*c**2*(c - 1)**2
Suppose -q - 20 = -0*q. Let g(n) = n**2. Let b = 525 + -526. Let w(p) = -15*p**2 + 5*p. Let m(z) = b*w(z) + q*g(z). Let m(l) = 0. What is l?
-1, 0
Factor 12*v**2 + 2*v**3 + 2*v**3 + 112 - 108*v + 12*v.
4*(v - 2)**2*(v + 7)
Let -3*d**2 - 3*d**4 - 12*d**3 - 140*d + 77*d + 81*d = 0. What is d?
-3, -2, 0, 1
Let r = -538/7 + 540/7. Factor 0 + 4/7*n - r*n**3 - 2/7*n**2.
-2*n*(n - 1)*(n + 2)/7
Let s be ((-11)/88)/((-5)/((-10)/(-3))). Let j(b) be the third derivative of -1/30*b**5 + 0*b - 1/60*b**6 + b**2 + s*b**4 + 0 + 1/3*b**3. Factor j(r).
-2*(r - 1)*(r + 1)**2
Let h(m) be the third derivative of m**7/2520 + m**6/540 - 5*m**3/3 + 5*m**2. Let w(v) be the first derivative of h(v). Determine q so that w(q) = 0.
-2, 0
Determine u so that -480/7*u - 444/7*u**2 - 192/7*u**3 - 192/7 - 39/7*u**4 - 3/7*u**5 = 0.
-4, -2, -1
Let p(v) be the first derivative of -98*v + 14*v**2 + 24 - 2/3*v**3. Factor p(a).
-2*(a - 7)**2
Let j = 67/60 - 11/30. Let x(b) be the first derivative of 0*b + j*b**2 - 3 - 1/6*b**3. Find t such that x(t) = 0.
0, 3
Let k(w) be the first derivative of -w**5/30 + 13*w**4/24 - w**3 - 40*w**2/3 - 64*w/3 - 39. Solve k(q) = 0.
-2, -1, 8
Suppose 57 = 26*u + 5. Let f = 223/3 + -70. Solve f*l**u - 3*l**4 + 13/2*l**3 - 2*l - 4/3 - 9/2*l**5 = 0.
-1, -2/3, 2/3, 1
Suppose -2*a = -8, 6*f - 3*a - 4 = 2*f. Find w, given that 5/4*w**3 + 0*w + 1/2*w**2 + 0 + 1/4*w**5 + w**f = 0.
-2, -1, 0
Factor 6*t**4 + 12 - 5*t**4 - 9 + 2*t**3 - 3*t**2 - t**2 - 2*t.
(t - 1)**2*(t + 1)*(t + 3)
Let r(u) = -7*u**3 - 7*u**2 - 8*u**2 + 27*u - 16*u. Let a(i) = -4*i**3 - 8*i**2 + 6*i. Let z(g) = -11*a(g) + 6*r(g). Factor z(x).
2*x**2*(x - 1)
Determine o so that 12/13*o**2 - 10/13*o - 2/13*o**3 + 0 = 0.
0, 1, 5
Suppose 96 = -30*a + 38*a. Factor -3*i**2 + 24*i - a - 25*i + 13*i.
-3*(i - 2)**2
Let k(f) be the first derivative of 3*f**5/20 - 5*f**4/16 - 19*f**3/6 + 5*f**2 - 706. Factor k(m).
m*(m - 4)*(m - 1)*(3*m + 10)/4
Let a(u) = -17*u**3 - 108*u**2 - 107*u + 16. Let r(w) = -6*w**3 - 36*w**2 - 36*w + 6. Let q(k) = 3*a(k) - 8*r(k). Find i such that q(i) = 0.
-11, -1, 0
Let k(n) be the first derivative of -2*n**6/51 + 78*n**5/85 + 71*n**4/34 - 114*n**3/17 + 63*n**2/17 + 408. Let k(a) = 0. What is a?
-3, 0, 1/2, 1, 21
Let -4*f**5 + 1394*f**4 + 8*f**3 - 1388*f**4 + 2*f**5 = 0. What is f?
-1, 0, 4
Let b(i) be the first derivative of -7*i + 6 - 5/4*i**4 + 0*i**2 - i**3 + 21/20*i**5. Let z(l) be the first derivative of b(l). Let z(c) = 0. What is c?
-2/7, 0, 1
Suppose 0 = 2*f - 6*f + 12. Suppose 5*s - 223 = 2*s - 2*h, -2*s + f*h = -127. Factor 2*b**2 + 71*b - s*b.
2*b**2
Factor -21/4*g**3 + 33*g + 15/4*g**2 + 9.
-3*(g - 3)*(g + 2)*(7*g + 2)/4
Let c(n) be the third derivative of n**8/840 + 4*n**7/225 + 49*n**6/900 - 2*n**5/225 - 7*n**4/45 + 383*n**2. Determine a, given that c(a) = 0.
-7, -2, -1, 0, 2/3
Let q(k) = 5*k**3 + 10*k**2 - 15*k - 6. Suppose -8*v - 56 + 8 = 0. Let r(u) = -5*u**3 - 10*u**2 + 15*u + 5. Let j(n) = v*r(n) - 5*q(n). What is c in j(c) = 0?
-3, 0, 1
Let m(a) be the third derivative of a**8/2016 - a**7/315 + a**6/240 + a**5/90 - a**4/36 - 19*a**2 - 5. Solve m(n) = 0 for n.
-1, 0, 1, 2
Suppose 3*p - 5*g + 13 = 0, -p = 9*g - 12*g + 11. Let v(s) be the second derivative of 0*s**2 - 1/20*s**5 + 0*s**4 + 0*s**3 + 0 + 1/30*s**6 - p*s. Factor v(i).
i**3*(i - 1)
Determine z so that 70/3*z**2 + 2/3*z**4 - 28/3*z**3 + 0 + 100/3*z = 0.
-1, 0, 5, 10
Factor 0 + 4*p**3 - 20/3*p**4 - 4/3*p + 8/3*p**5 + 4/3*p**2.
4*p*(p - 1)**3*(2*p + 1)/3
Let g = -352 - -1411/4. Let i = -6 + 8. Factor -g*b**i + 0 + 9/4*b.
-3*b*(b - 3)/4
Let t(x) = -2*x + 3. Let b be t(-2). Suppose 4 = -b*n + 18. Factor -2/5 - 12/5*h**n + 8/5*h**3 + 8/5*h - 2/5*h**4.
-2*(h - 1)**4/5
Let q be (20/50)/((-2)/(-490)). Factor q*x**4 + 120*x**2 + 53*x - 125*x + 56*x - 252*x**3.
2*x*(x - 2)*(7*x - 2)**2
Let x(h) be the first derivative of -7*h**5/5 + 17*h**4/2 - 17*h**3 + 10*h**2 + 4*h + 496. Let x(l) = 0. What is l?
-1/7, 1, 2
Let f(u) be the second derivative of u**7/77 - 26*u**6/165 + 61*u**5/110 - 3*u**4/11 - 68*u**3/33 + 40*u**2/11 - 258*u. Suppose f(r) = 0. What is r?
-1, 2/3, 2, 5
Let w(o) be the first derivative of o**4/4 + o**3 - 39. Factor w(u).
u**2*(u + 3)
Let i(t) be the second derivative of t**5/90 + 2*t**4/27 + t**3/9 + 16*t - 1. Determine a so that i(a) = 0.
-3, -1, 0
Let g(j) be the first derivative of 56*j**3/3 + 20*j**2 + 50*j/7 + 44. Factor g(p).
2*(14*p + 5)**2/7
Let j(r) be the third derivative of -r**8/112 + r**7/21 - r**6/10 + r**5/10 - r**4/24 + 388*r**2 - r. Solve j(i) = 0 for i.
0, 1/3, 1
Let j = 