Let j be (1 + 0)/(1 + 0). Let p = j + 2. What is w in -7*w + 4*w**2 - 4*w**4 + 5*w + 2*w**p + 0*w**3 = 0?
-1, 0, 1/2, 1
Let u(r) be the third derivative of -r**8/84 + 34*r**7/105 + r**6/30 - 17*r**5/15 + 5*r**2 - 11. Suppose u(k) = 0. What is k?
-1, 0, 1, 17
Factor -207*j**3 - 374*j - 360 + 163*j**3 + 4*j**4 - 295*j - 460*j**2 + 200*j - 303*j.
4*(j - 18)*(j + 1)**2*(j + 5)
Let d(l) be the first derivative of -5*l**4/4 - 5*l**3/3 + 25*l**2/2 - 15*l - 3. Let d(g) = 0. What is g?
-3, 1
Let r(a) be the third derivative of -a**7/3780 + a**6/360 - a**5/90 - a**4/3 + a**2. Let s(o) be the second derivative of r(o). Factor s(d).
-2*(d - 2)*(d - 1)/3
Let n be (-39)/(-52)*(-16)/(-6). Let s(l) be the first derivative of -1/5*l**5 + 0*l**4 + 4/3*l**3 + 0*l - 1 + 0*l**n. Factor s(h).
-h**2*(h - 2)*(h + 2)
Let j be 2/(-11) - 52/(-44). Let m(z) = -3*z + 3. Let q be m(j). Factor -1/5*d**4 + 1/5*d**2 - 2/5*d**3 + q + 2/5*d.
-d*(d - 1)*(d + 1)*(d + 2)/5
Let x(v) = -90*v - 80. Let s(j) = j**2 + 90*j + 81. Let z(m) = -5*s(m) - 4*x(m). Factor z(n).
-5*(n + 1)*(n + 17)
Let i be 1/(-8) - (-19745)/(-16632). Let x = -20/27 - i. Factor -x + 6/7*o - 2/7*o**2.
-2*(o - 2)*(o - 1)/7
Let z(g) = 7*g**4 + 52*g**3 + 82*g**2 + 68*g + 23. Let k(p) = -2*p**4 - 17*p**3 - 27*p**2 - 23*p - 8. Let r(v) = 8*k(v) + 3*z(v). Find f such that r(f) = 0.
-1
Let 5/7*g**4 - 191/7*g**2 + 64/7*g + 62/7*g**3 + 60/7 = 0. What is g?
-15, -2/5, 1, 2
Let b = 3807/29602 + -11/82. Let m = b + 365/722. Factor -m*z**3 + 0 + 0*z + 1/4*z**4 + 1/4*z**2.
z**2*(z - 1)**2/4
Suppose 2*q + 5 = 69. Let a be 4/(q/(-12)) - -2. Factor f**2 + 0 - a*f - 1/2*f**3.
-f*(f - 1)**2/2
Suppose -3*v + 1 - 7 = 0. Let n(o) = o**4 + o**3 - 2*o**2. Let c(u) be the second derivative of u**5/10 - u**4/6 - u. Let z(j) = v*n(j) + 3*c(j). Factor z(p).
-2*p**2*(p - 1)**2
Suppose -6 + 0 = -2*u, 3*s - 18 = -u. Let m(h) be the third derivative of 3*h**2 + 0 + 2/3*h**4 + 0*h - 1/30*h**s - 16/3*h**3. Determine y so that m(y) = 0.
4
Suppose 3*h - 2*y + 5 = -1, -15 = 4*h - 5*y. Let r(i) be the third derivative of -1/75*i**5 + 0*i**4 + 0*i - 2*i**2 - 1/300*i**6 + 0 + h*i**3. Factor r(f).
-2*f**2*(f + 2)/5
Factor -130*v**2 - 15842 + 128*v**2 + 99*v - 455*v.
-2*(v + 89)**2
Factor 3 - 1/2*u - 1/2*u**2.
-(u - 2)*(u + 3)/2
Suppose -4*u = -4 - 4. Factor -2*p**u - p - 6*p + 3*p.
-2*p*(p + 2)
Let v(t) be the first derivative of -1/4*t**3 - 9 + 0*t**2 + 0*t. Factor v(i).
-3*i**2/4
Suppose 8*i - 12 = 28. Suppose -12*n**i - 3*n**3 - 12*n**3 - 5*n**3 + 28*n**4 + 4*n**2 = 0. Calculate n.
0, 1/3, 1
Let w(c) be the third derivative of 0 + 0*c + 1/42*c**7 - 1/8*c**6 + 5/8*c**4 - 5/3*c**3 + 1/12*c**5 + 2*c**2. Factor w(b).
5*(b - 2)*(b - 1)**2*(b + 1)
Let f(p) be the third derivative of -55/18*p**4 + 5*p**2 - 10/9*p**3 - 121/36*p**5 + 0*p + 0. Factor f(j).
-5*(11*j + 2)**2/3
Let q(m) be the third derivative of 0 + 1/6*m**4 - 1/3*m**3 + 9*m**2 + 0*m - 1/24*m**5 + 1/240*m**6. Factor q(w).
(w - 2)**2*(w - 1)/2
Let i(a) be the first derivative of 4*a**4 + 20*a**3 + 16*a**2 - 12*a + 79. Let i(k) = 0. What is k?
-3, -1, 1/4
Suppose 4*z - 41 = 47. Determine c, given that 12*c**2 + 2 + 3*c + 4*c**2 + 7*c**2 - z*c**2 = 0.
-2, -1
Suppose 8*s - 3*k = 4*s + 20, 2*s + 4 = -2*k. Let n be 4*(-3)/(-24) - -1. Factor -6*v + n*v**s + 6.
3*(v - 2)**2/2
Suppose -m + 3*z - 38 + 14 = 0, -3*z + 108 = -5*m. Let r = m - -25. Suppose 18*a**2 - 4*a**3 + 3*a**r + a**3 + 12*a + 3 + 15*a**3 = 0. Calculate a.
-1
Let q(o) be the second derivative of 8*o**6/135 + o**5/10 - 7*o**4/54 - o**3/3 - o**2/9 + 895*o. Let q(i) = 0. Calculate i.
-1, -1/8, 1
Let i(a) be the third derivative of a**10/1134000 - a**8/75600 + a**6/5400 + 31*a**5/60 - 29*a**2. Let x(w) be the third derivative of i(w). Factor x(b).
2*(b - 1)**2*(b + 1)**2/15
Factor 10/3 + r - 1/3*r**2.
-(r - 5)*(r + 2)/3
Let m(q) = -12*q - 334. Let n be m(-28). Factor -1/2*c**5 - c**4 + 0 + 0*c + 0*c**n - 1/2*c**3.
-c**3*(c + 1)**2/2
Factor 5/2*c + 9/4 + 1/4*c**2.
(c + 1)*(c + 9)/4
Let b(v) be the first derivative of -v**7/1260 + v**6/180 + 5*v**3 + 21. Let c(j) be the third derivative of b(j). What is l in c(l) = 0?
0, 3
Let d(a) = 7*a**2 - 4*a. Let t(w) be the second derivative of -w**4/6 + w**3/6 + 8*w. Let h(z) = 6*d(z) + 22*t(z). Factor h(f).
-2*f*(f + 1)
Let f = 11800/2569 - 8/367. What is i in 104/7*i**2 + 4*i**3 - f + 80/7*i = 0?
-2, 2/7
Let j(v) be the second derivative of -v**6/150 + v**5/100 + v**4/60 - v**3/30 + 5*v - 13. Factor j(w).
-w*(w - 1)**2*(w + 1)/5
Let z(b) = -b**2 + 10*b - 5. Let l be z(9). Find k such that -453*k**3 - 3*k**5 - 3*k**l + 451*k**3 + 8*k**4 = 0.
0, 2/3, 1
Let b(x) be the third derivative of x**7/1680 + x**6/288 + x**5/240 + x**3/6 + 4*x**2. Let v(c) be the first derivative of b(c). Factor v(d).
d*(d + 2)*(2*d + 1)/4
Let q(k) be the second derivative of k**4/6 - k**2 + 82*k. Factor q(a).
2*(a - 1)*(a + 1)
Let h be (-100)/(-140) - (-99)/77. Factor 5/3*g**h - 1/3*g**3 + 1 - 7/3*g.
-(g - 3)*(g - 1)**2/3
Let p(q) be the third derivative of -2*q**7/525 - 17*q**6/150 - 2*q**5/5 + 9*q**2 - 3. Factor p(w).
-4*w**2*(w + 2)*(w + 15)/5
Let m(h) be the second derivative of h**3/2 - 29*h**2 + 4*h - 1. Let v be m(20). Let 6/5*c**v + 12/5 + 3/5*c**3 - 21/5*c = 0. What is c?
-4, 1
Let v(z) = 4*z - 60. Let r be v(18). Let h be 4/84 - r/(-42). Solve -1/3 + h*j**3 - 1/3*j + 1/3*j**2 = 0 for j.
-1, 1
Let z(t) be the second derivative of 2/15*t**6 + t**4 + 37*t - 3/4*t**5 + 0 + 2/3*t**3 + 0*t**2. Factor z(l).
l*(l - 2)**2*(4*l + 1)
Let n(i) be the second derivative of 4/3*i**4 + 11*i + 0 - 8/3*i**3 + 0*i**2 - 1/5*i**5. Solve n(b) = 0 for b.
0, 2
Factor -58/5*c**2 - 54/5 - 2/5*c**3 - 22*c.
-2*(c + 1)**2*(c + 27)/5
Let w be (20/50)/((4/30)/2). Let k(r) be the third derivative of -1/720*r**w - 1/48*r**4 + 0*r + 1/36*r**3 + 0 - 4*r**2 + 1/120*r**5. Factor k(x).
-(x - 1)**3/6
Suppose -x + 6 = 2*x. Let k(o) be the second derivative of -1/3*o**4 + 0 - 2*o - 8/3*o**3 - 8*o**x. Factor k(v).
-4*(v + 2)**2
Suppose 4*w - 136 = -124. Suppose -5 - 1 = -3*t + w*h, t + 6 = 5*h. Factor 3/2*m**5 + 15/2*m**t + 21/2*m**2 + 3*m + 0 + 27/2*m**3.
3*m*(m + 1)**3*(m + 2)/2
Suppose 5*d = -4*b + 13, -2*b - d = 31 - 36. Let s(p) be the second derivative of -12*p - 4/3*p**4 + 0 - 1/10*p**5 - 16/3*p**3 + 0*p**b. Factor s(u).
-2*u*(u + 4)**2
Let h(i) = -19*i**3 + i - 9. Let x = 16 - 20. Let g(f) = -9*f**3 + f - 4. Let v(d) = x*h(d) + 9*g(d). Suppose v(z) = 0. Calculate z.
-1, 0, 1
Let b(i) be the second derivative of -i**5/120 + i**4/24 - i**3/12 + 13*i**2/2 - 15*i. Let d(n) be the first derivative of b(n). Solve d(r) = 0.
1
Let t(c) be the first derivative of c**5/25 - c**3/5 - c**2/5 + 43. Factor t(n).
n*(n - 2)*(n + 1)**2/5
Let t be 1*((-4)/(-2) - -1). Suppose 21*s = 19*s + 6. Factor -4*c - 2*c**s + 0*c + c**t + 4*c**2.
-c*(c - 2)**2
Let a(s) be the first derivative of -s**3/9 - 34*s**2 - 3468*s - 62. Solve a(w) = 0 for w.
-102
Let d(l) be the third derivative of l**8/336 - l**7/42 + l**6/60 + 2*l**5/15 - 50*l**2. Determine x, given that d(x) = 0.
-1, 0, 2, 4
Let j(s) be the third derivative of -s**6/900 + s**5/50 - s**4/9 + 4*s**3/15 - 130*s**2. Factor j(a).
-2*(a - 6)*(a - 2)*(a - 1)/15
Let k(s) be the third derivative of 0*s**4 + 0*s**3 - 1/35*s**7 + 0*s + 0*s**5 - 1/40*s**6 - 1/112*s**8 + 26*s**2 + 0. Factor k(u).
-3*u**3*(u + 1)**2
Let c be (-131)/((-101)/(-133) + (-4)/14). Let z = 277 + c. Factor -z*l + 2/9 + 2/9*l**2.
2*(l - 1)**2/9
Suppose 56 + 142 = -9*c. Let k be (-4)/(4/3) - 70/c. Let 10/11*t**2 - 14/11*t - k*t**3 + 6/11 = 0. What is t?
1, 3
Suppose 62/11*w**4 + 72/11 + 6/11*w**5 - 134/11*w**2 - 64/11*w + 58/11*w**3 = 0. Calculate w.
-9, -2, -1, 2/3, 1
Let y(k) = 10 + 14*k + k**3 + 12*k - 25*k. Let l be y(0). Factor 2*m + 2 - l*m + 8*m**2 + 2*m**5 - 8*m**4 + 2*m**5 - 2*m**4 + 4*m**3.
2*(m - 1)**3*(m + 1)*(2*m - 1)
Let z(w) be the first derivative of -w**5/15 - 4*w**4/3 - 8*w**3 + 15*w**2 + 5. Let u(q) be the second derivative of z(q). Factor u(d).
-4*(d + 2)*(d + 6)
What is w in -8/7*w**4 + 2/7*w**5 - 6/7*w + 8/7*w**2 + 0 + 4/7*w**3 = 0?
-1, 0, 1, 3
Suppose 5*g = 5 + 5. Suppose -24*o + 37 = -35. Factor 1/3*q**g + 1/3*q**o - 4/3*q - 4/3.
(q - 2)*(q + 1)*(q + 2)/3
Let d(m) be the first derivative of 2*m**3/33 + 14*m**2/11 - 30*m/11 + 141. Fi