 c(d) be the second derivative of d**5/15 + 64*d**4/9 - 262*d**3/9 + 44*d**2 - 189*d. Determine f so that c(f) = 0.
-66, 1
Let k(t) be the second derivative of -t**4/21 + 20*t**3/21 + 22*t**2/7 - 2*t + 2. Find x such that k(x) = 0.
-1, 11
Suppose 4 + 4 = -4*v. Let m be ((-2 - v)/(-3))/2. Factor 0 + 2/11*h**3 + m*h + 0*h**2 - 2/11*h**4.
-2*h**3*(h - 1)/11
Let k(w) be the second derivative of -w**7/126 + w**6/10 + 11*w**5/30 + w**4/18 - 7*w**3/6 - 11*w**2/6 - 64*w. Factor k(y).
-(y - 11)*(y - 1)*(y + 1)**3/3
Let h(c) be the first derivative of c**8/420 + 2*c**7/525 - c**6/150 - c**5/75 + 15*c**2/2 + 5. Let p(q) be the second derivative of h(q). Factor p(r).
4*r**2*(r - 1)*(r + 1)**2/5
Let q = -3389/10 - -339. Let x(l) be the second derivative of q*l**3 - 3/5*l**2 + 4*l + 1/20*l**4 + 0. Suppose x(h) = 0. What is h?
-2, 1
Let m = 1907/5 - 381. Let 0 + 8/5*i + 0*i**2 + 0*i**4 - 2*i**3 + m*i**5 = 0. Calculate i.
-2, -1, 0, 1, 2
Let r be ((-72)/144)/((-6)/(-8) - 1). Let n(c) be the first derivative of c**r + 0*c - 2/3*c**3 + 4. Let n(p) = 0. What is p?
0, 1
Let u be (-4 - (-22)/4)*(-8)/6. Let g be ((-60)/(-44) - 3)*u/6. Find s, given that -2/11 + g*s**2 + 4/11*s = 0.
-1, 1/3
Find i, given that -30*i**2 - i**3 + 0*i**4 + 2*i**4 + 11*i**3 + 77 - 87 + 38 - 10*i = 0.
-7, -1, 1, 2
Let 1171*i - 20*i**3 - 8*i**2 + 5*i**4 + 7*i**4 - 1171*i = 0. Calculate i.
-1/3, 0, 2
Let h be 1214/(-22) + -1 + 4/22. Let s be h/102 + ((-180)/27)/(-10). Determine y so that -8/17*y + 2/17*y**3 + s*y**2 - 8/17 = 0.
-2, -1, 2
Let c be ((-24)/18)/(2/3*(-13 - -12)). Suppose 2/3 - 50/3*f**3 - 22/3*f + 70/3*f**c = 0. Calculate f.
1/5, 1
Factor -3/2*v - 27*v**2 + 27 + 3/2*v**3.
3*(v - 18)*(v - 1)*(v + 1)/2
Let x(m) be the third derivative of m**6/120 + m**5/30 - m**4/24 - m**3/3 + 65*m**2 + 1. Let x(o) = 0. Calculate o.
-2, -1, 1
Let c(h) = 2*h + 58. Let a be c(-18). Let v be 33/a*(-20)/(-6). Factor 0 + 2/7*l**2 - 2/7*l**4 + 2/7*l**3 - 2/7*l**v + 0*l.
-2*l**2*(l - 1)*(l + 1)**2/7
Let a(v) = 19*v**2 - 66*v + 55. Let w(f) = -f**2 - f. Let u(d) = a(d) + 4*w(d). Let o(s) = -s**2 + 5*s - 4. Let n(j) = 55*o(j) + 4*u(j). Factor n(l).
5*l*(l - 1)
Let s(u) be the third derivative of 9*u**8/2240 - u**7/42 + 13*u**6/240 - u**5/20 - u**4/12 - 3*u**2. Let r(y) be the second derivative of s(y). Factor r(f).
3*(f - 1)**2*(9*f - 2)
Let v(l) be the third derivative of -l**7/1050 + 7*l**6/600 + l**5/30 - 2*l**4/15 + 2*l**2 + 23*l. Let v(d) = 0. What is d?
-2, 0, 1, 8
Let f(h) = -3*h**3 - 20*h**2 - 17*h - 5. Let r(l) = l - 3*l**2 + 2 + 0*l + 4*l**2 - 1. Let c(s) = -f(s) - 5*r(s). Factor c(a).
3*a*(a + 1)*(a + 4)
Suppose -6 = 2*s + 18. Let f be 6/2 + 12/s. Find z, given that -4 - 5*z**4 + 9*z**f - z**2 - 2*z**2 + 2*z - 2*z**3 + 3*z**4 = 0.
-2, -1, 1
Let a be (34 - -1) + -6 + -3. Suppose w - a = -22. Factor w - 17/2*d**3 - 6*d - 3/2*d**4 - 15*d**2.
-(d + 2)**3*(3*d - 1)/2
Let x = -28389/2 + 14195. Factor 1/2*i**3 - i - x*i**2 + 0.
i*(i - 2)*(i + 1)/2
Let n be 33/(-88)*28 + 12. Factor n*t + 3/2 - 3/2*t**3 - 3/2*t**2.
-3*(t - 1)*(t + 1)**2/2
Let w(a) be the third derivative of -a**6/600 + 3*a**5/100 - 9*a**4/40 + 9*a**3/10 - 20*a**2 - 12. Factor w(z).
-(z - 3)**3/5
Let f(o) be the third derivative of o**8/392 + o**7/735 - o**6/210 + 84*o**2. Factor f(s).
2*s**3*(s + 1)*(3*s - 2)/7
Let f be 9/(-36) - 21/(-4). Factor -196*v**3 - 5*v - 7*v**f + 2*v**5 + 206*v**3.
-5*v*(v - 1)**2*(v + 1)**2
Let l(g) be the first derivative of g**5/45 + g**4/6 - g**3/9 - 28*g**2/9 - 16*g/3 - 97. Factor l(q).
(q - 3)*(q + 1)*(q + 4)**2/9
Let p be -2*(-4)/24*1*2. Find z such that 0*z**2 + 2*z + p - 8/3*z**3 = 0.
-1/2, 1
Let o(a) = 37*a + 0*a**2 + a**2 - 29*a + 0*a**2 - 12. Let x be o(-10). Factor x*w - 5*w - 2*w**2 + 5*w**2 + 6 - 12*w.
3*(w - 2)*(w - 1)
Determine p so that 1/2*p - 1/2*p**3 + 1/2 - 1/2*p**2 = 0.
-1, 1
Let r(l) = 16*l - 78. Let b be r(5). Let k(s) be the third derivative of -1/2*s**4 + 0 + 0*s - 3/20*s**5 - 1/2*s**3 + 6*s**b. Suppose k(c) = 0. What is c?
-1, -1/3
Let z be -5 + ((-9328)/160)/(-11). Suppose -1/10*r - 3/10*r**2 - 1/10*r**4 + 0 - z*r**3 = 0. What is r?
-1, 0
Let f(u) = 3*u**3 + 10*u**2 - 37*u - 32. Let s(m) = -6*m**3 - 19*m**2 + 73*m + 65. Let x(v) = -7*f(v) - 4*s(v). Factor x(g).
3*(g - 3)*(g + 1)*(g + 4)
Let l(v) = -19*v**3 + 37*v**2 - 18*v + 5. Let z(u) = -48*u**3 + 93*u**2 - 45*u + 12. Let j = -15 - -20. Let c(i) = j*z(i) - 12*l(i). Factor c(p).
-3*p*(p - 1)*(4*p - 3)
Let m(s) be the third derivative of -s**6/480 + 37*s**5/240 - 323*s**4/96 - 361*s**3/24 - 2*s**2 + 276. Factor m(r).
-(r - 19)**2*(r + 1)/4
Let d = 155 + -155. Let q be (20/(-105) - d)*(-6)/4. Let 0 + 0*k - 2/7*k**3 + q*k**2 = 0. What is k?
0, 1
Let p(h) be the first derivative of h**6/900 - h**5/300 + 22*h**3/3 - 48. Let b(d) be the third derivative of p(d). Factor b(m).
2*m*(m - 1)/5
Let u be (4/8)/((-3)/6). Let g be 3/((6/(-4))/u). Solve 3/2*s + 3/2*s**5 - 3*s**3 - 3/2 - 3/2*s**4 + 3*s**g = 0 for s.
-1, 1
Let q(s) be the second derivative of s**4/84 - s**3/42 - 6*s**2/7 + 21*s. Factor q(t).
(t - 4)*(t + 3)/7
Let y = -171 + 176. Let l(f) = -f + 15. Let b be l(11). Let 0*g**2 - 2/3*g**b + 0 + 1/3*g**3 + 0*g + 1/3*g**y = 0. What is g?
0, 1
Let k(j) be the first derivative of j**7/420 - j**6/240 - j**5/60 - 11*j**2 - 7. Let p(t) be the second derivative of k(t). Factor p(h).
h**2*(h - 2)*(h + 1)/2
Let s(c) = 5*c**5 - 12*c**4 + 20*c**3 - 4*c**2 - 2. Let q(j) = 31*j**5 - 71*j**4 + 120*j**3 - 22*j**2 - 13. Let z(n) = -6*q(n) + 39*s(n). Factor z(a).
3*a**2*(a - 2)**2*(3*a - 2)
Let c be ((-1)/3)/(2/((-16)/24)). Let k(u) be the first derivative of 0*u + c*u**2 - 2/45*u**5 - 1/18*u**4 + 2/27*u**3 - 4. What is d in k(d) = 0?
-1, 0, 1
Let z(h) be the third derivative of -1/2*h**3 - 1/14*h**7 + 5/8*h**4 + 1/4*h**6 + 1/112*h**8 + 0*h + 0 + 5*h**2 - 1/2*h**5. Factor z(r).
3*(r - 1)**5
Suppose 2*d + 23*d - 87 = -4*d. Factor 8/7*o**d - 20/7 + 54/7*o**2 + 66/7*o.
2*(o + 2)*(o + 5)*(4*o - 1)/7
Let h(y) be the first derivative of 28*y**5/85 - 25*y**4/34 - 16*y**3/51 + 4*y**2/17 - 69. What is f in h(f) = 0?
-1/2, 0, 2/7, 2
Let x(p) be the second derivative of 3*p**7/14 - 14*p**6/5 + 61*p**5/5 - 56*p**4/3 + 32*p**3/3 - p - 98. Solve x(f) = 0.
0, 2/3, 4
Let t(q) be the first derivative of -3*q**5/5 - 3*q**4 - 4*q**3 + 87. Determine l, given that t(l) = 0.
-2, 0
Let j(h) = -26 + 0*h**2 + 37 - 33 + 24*h**3 + 24*h**2. Let p(s) = -s**3 - s**2 + 1. Let m(b) = -2*j(b) - 44*p(b). Suppose m(g) = 0. Calculate g.
-1, 0
Suppose -r + 5*n - 8 = 0, 0 = 6*r + 3*n - 13 - 5. Let 4*g**3 + 6*g**r + 2/3*g**4 - 8 - 8/3*g = 0. What is g?
-3, -2, 1
Let v(n) be the second derivative of -n**7/1260 + n**6/270 - n**5/180 - 5*n**3/6 - 14*n. Let u(k) be the second derivative of v(k). What is z in u(z) = 0?
0, 1
Let w = -3200 - -3204. Factor 0*l**2 + 0*l + 1/5*l**3 + 0 + 1/5*l**5 + 2/5*l**w.
l**3*(l + 1)**2/5
Let h(w) be the first derivative of -2*w**3/45 - 16*w**2/15 - 138. Let h(o) = 0. What is o?
-16, 0
Suppose -5*w + 4*a = -26, -5*w + 5*a + 0*a + 30 = 0. Factor 3*u**w - 45 + 45 + 10*u + 2*u**2.
5*u*(u + 2)
Let g(p) be the third derivative of p**7/1050 + p**6/150 + p**2 + 88. Factor g(u).
u**3*(u + 4)/5
Let p(d) = 18 - 7*d**3 + 6*d**3 - 2*d**3 + 6*d**2 - 30*d + 13*d**3. Let k(b) = -b**4 - 21*b**3 - 12*b**2 + 61*b - 37. Let t(x) = 2*k(x) + 5*p(x). Factor t(l).
-2*(l - 4)*(l - 1)**2*(l + 2)
Let w(y) be the second derivative of y**6/30 + y**5/5 + y**4/3 - 68*y. Factor w(n).
n**2*(n + 2)**2
Let i(k) be the first derivative of -25*k**6/2 - 169*k**5 - 775*k**4/2 - 140*k**3/3 + 180*k**2 + 93. Find c such that i(c) = 0.
-9, -2, -2/3, 0, 2/5
Let r(v) be the second derivative of 1/33*v**3 - 24*v + 0 + 1/110*v**5 + 0*v**2 - 1/33*v**4. Factor r(z).
2*z*(z - 1)**2/11
Let p(k) be the first derivative of -35/4*k**4 + 23 - 4455/2*k**2 - 260*k**3 - 1210*k. Factor p(n).
-5*(n + 11)**2*(7*n + 2)
Let x(g) be the first derivative of -g**5/12 + 35*g**4/24 - 5*g**3 - 6*g**2 + 24. Let v(d) be the second derivative of x(d). Factor v(j).
-5*(j - 6)*(j - 1)
Let s(w) be the first derivative of 2*w**3/3 + 9*w**2 + 28*w - 42. Solve s(p) = 0.
-7, -2
Factor 27/2*m - 39*m**2 + 36*m**3 - 9*m**4 + 0 - 3/2*m**5.
-3*m*(m - 1)**3*(m + 9)/2
Suppose -2*l - l = -3*i + 42, -3*i = -2*l - 33. Let p be 1/l*-2*3. Let 2/3*