uch that j(m) = 0.
1
Let k(d) be the first derivative of -d**6/3 + d**5/5 + d**4 - 2*d**3/3 - d**2 + d + 2. Suppose k(j) = 0. What is j?
-1, 1/2, 1
Let r(l) be the third derivative of -l**7/21 + 3*l**6/8 - 7*l**5/6 + 15*l**4/8 - 5*l**3/3 + 11*l**2 - 2*l. Let r(u) = 0. What is u?
1/2, 1, 2
Let v(g) = -g - 1. Let t be v(-3). Let w - w**2 - 3*w**t + 3*w**2 = 0. What is w?
0, 1
Let o be 6/21 + 10/(-35). Let g(d) be the first derivative of 1/6*d**4 + 0*d**3 + o*d - 1 + 0*d**2. What is i in g(i) = 0?
0
Let w be (-2)/(-6)*10/180. Let n(r) be the third derivative of 0*r**5 + 0*r + 1/27*r**3 - r**2 + 0 + 1/270*r**6 - 1/945*r**7 - w*r**4. Factor n(z).
-2*(z - 1)**3*(z + 1)/9
Factor -1/6 - 2/3*g**3 - 1/6*g**4 - g**2 - 2/3*g.
-(g + 1)**4/6
Let g be -6 - -4 - (-1 + -1). Let w be (g + 5)*(-3)/(-5). Solve -2*x**3 + 0*x**3 + 3*x**3 - w*x + 2*x**3 = 0 for x.
-1, 0, 1
Let a = -163 + 163. Factor a - 1/4*w + 1/2*w**2.
w*(2*w - 1)/4
Let k = 175/543 - -2/181. Factor -1/2*h + k + 1/6*h**2.
(h - 2)*(h - 1)/6
Let z(r) be the third derivative of -1/96*r**6 + 0 + 0*r**4 + 1/120*r**5 + 0*r + 0*r**3 - r**2. Factor z(o).
-o**2*(5*o - 2)/4
Let g be (-426)/18 + 2/(-6). Let j = g - -49/2. Factor j*w**2 + 2*w + 2.
(w + 2)**2/2
Let l = 57 + -1139/20. Let f(v) be the first derivative of 0*v**2 + 0*v**4 - 1 + 0*v - 1/12*v**3 + l*v**5. Determine i, given that f(i) = 0.
-1, 0, 1
Let l(p) = -5*p + 14. Let o be l(2). Let 2/3*i**o - 2*i**2 + 4/3 - 2/3*i + 2/3*i**3 = 0. What is i?
-2, -1, 1
Suppose -s + 6*s = 15. Find y such that -y**3 - 3 + 0 + s*y - 2*y**3 + 2*y**2 + y**2 = 0.
-1, 1
Let v = -24 + 15. Let w be v/(-36) - (-2)/(-8). Let 30*g**3 + 56*g**4 - 2*g + 4*g**2 + 2*g + w*g**4 = 0. What is g?
-2/7, -1/4, 0
Suppose 0 = b - 8 + 6. Factor -8/9*o + 32/9*o**2 - 14/3*o**3 + 0 + b*o**4.
2*o*(o - 1)*(3*o - 2)**2/9
Let l(k) = -k + 9. Let g be l(7). Suppose g*j = -0*j + 6. Factor 5*x**3 + x**4 - x + 3*x**2 - 2*x**j + 2*x.
x*(x + 1)**3
Let o(j) = -j + 9. Let u be o(9). Factor u*g**2 - 11*g**3 + 3*g - 6 + 8*g**3 + 6*g**2.
-3*(g - 2)*(g - 1)*(g + 1)
Let q = -2 + 12. Suppose -l + 2*m - q = 0, -4*l + 5*m - 25 = l. Solve l + 1/3*o**5 + 0*o**3 + 0*o + 0*o**2 - 1/3*o**4 = 0.
0, 1
Let x = 1/3 + 1/3. Let w(o) be the first derivative of -1/3*o - 1/15*o**5 - x*o**2 - 1/3*o**4 - 2/3*o**3 + 2. Solve w(m) = 0 for m.
-1
Let b(k) be the third derivative of k**7/210 - k**6/120 - k**5/60 + k**4/24 - 8*k**2. Factor b(a).
a*(a - 1)**2*(a + 1)
Factor 4/3*q**2 + 16/3*q - 20/3.
4*(q - 1)*(q + 5)/3
Let n = 20 - 18. Let p(i) be the second derivative of -2/9*i**4 + 0 + 2*i - 1/9*i**6 - 8/15*i**5 + 25/63*i**7 + 0*i**3 + 0*i**n. Factor p(q).
2*q**2*(q - 1)*(5*q + 2)**2/3
Factor -8/13*i + 0 + 8/13*i**2 - 2/13*i**3.
-2*i*(i - 2)**2/13
Let o = 7 - 4. Let d = -49 - -49. Find i such that -2/7*i**o + 4/7 + 6/7*i + d*i**2 = 0.
-1, 2
Let w(k) be the third derivative of k**7/210 - k**6/120 - k**5/30 + k**2 + 20. What is r in w(r) = 0?
-1, 0, 2
Let s(a) be the first derivative of -8*a**5/5 - 3*a**4/2 + 2*a**3/3 - 30. Solve s(k) = 0.
-1, 0, 1/4
Let i(o) be the second derivative of -o**4/6 - 4*o**3/3 - 14*o + 1. Solve i(k) = 0 for k.
-4, 0
Let r(s) = -s**3 + 8*s**2 - s + 11. Let x be r(8). Find y, given that 4*y**4 - x - 4*y**4 - y**4 + 6*y**2 - 2*y**4 = 0.
-1, 1
Let -8/5*m**2 + 0 + 2/5*m**5 + 0*m + 6/5*m**4 + 0*m**3 = 0. Calculate m.
-2, 0, 1
Let i(r) be the first derivative of 2 + 1/27*r**6 + 0*r**4 + 0*r**2 + 0*r + 0*r**5 + 0*r**3. Factor i(c).
2*c**5/9
Find o such that 8/9*o - 4/3 + 4/9*o**2 = 0.
-3, 1
Let g = 14/145 + 3/29. What is p in -g*p**3 + 1/5*p**5 + 0 + 0*p + 0*p**4 + 0*p**2 = 0?
-1, 0, 1
Let a be (-4)/(-10) - 424/(-165). Let y = 40/11 - a. Find w such that -2*w + 2*w**2 + 2/3 - y*w**3 = 0.
1
Let t = -176 + 355/2. Find q, given that -3/2 - 15/4*q + 15/4*q**3 + t*q**2 = 0.
-1, -2/5, 1
Factor 0 + 108*u**2 + 25*u + 64*u**4 + 176*u**3 - 6 + 8.
(u + 2)*(4*u + 1)**3
Let b = 954/1205 - -2/241. Factor -2/5*g - 2/5*g**5 - 2/5 - 2/5*g**4 + 4/5*g**2 + b*g**3.
-2*(g - 1)**2*(g + 1)**3/5
Let o(k) be the first derivative of k**4 + 4*k**3/3 + 10. Factor o(x).
4*x**2*(x + 1)
Factor 0 + 0*q - 2/3*q**2 + 8/3*q**3.
2*q**2*(4*q - 1)/3
Let l(p) be the second derivative of -121*p**6/15 - 407*p**5/10 - 63*p**4 - 100*p**3/3 - 8*p**2 + 18*p. What is u in l(u) = 0?
-2, -1, -2/11
Let i = -1124 - -10120/9. Factor -2/9*s + 2/9*s**3 - i*s**2 + 4/9.
2*(s - 2)*(s - 1)*(s + 1)/9
Let x(t) be the second derivative of t**4/84 + 4*t**3/21 + 8*t**2/7 - 4*t. Factor x(c).
(c + 4)**2/7
Let d = 18 - 13. Factor z - 2*z**d - 4*z + 6*z**3 - z**5.
-3*z*(z - 1)**2*(z + 1)**2
Let -6/7*t**3 + 8/7*t**5 + 10/7*t**4 + 0 - 10/7*t**2 - 2/7*t = 0. Calculate t.
-1, -1/4, 0, 1
Let a(f) = f. Let s(u) = -u. Let j(o) = 7*a(o) + 6*s(o). Let z(d) = d**2 - 4*d + 1. Let r(b) = 6*j(b) + z(b). Find w, given that r(w) = 0.
-1
Let -4/9 + 4/9*b**4 - 14/9*b + 20/9*b**2 - 16/9*b**5 + 50/9*b**3 = 0. What is b?
-1, -1/4, 1/2, 2
Let s(g) = 2*g**3 - 4*g**2 + 4*g - 3. Let r be s(2). Suppose r*l - 15 = 2*p + p, -3*p + 12 = 4*l. Factor -v**2 + 0*v**l - v**3 + 2*v**2.
-v**2*(v - 1)
Factor 6*v**4 + 0*v**4 - v**4 - 7*v**3 - 8*v**3.
5*v**3*(v - 3)
Let k be ((-1)/(-1))/(1/2). Let b = -113/4 - -581/20. Let 0 + 1/5*j**4 + j**k - 2/5*j - b*j**3 = 0. What is j?
0, 1, 2
Suppose -4*b = 11*b - 60. Solve -4/3*y**2 - 1/3*y**b + 0*y - 4/3*y**3 + 0 = 0.
-2, 0
Find x, given that 2/9 + 2/9*x**3 - 2/9*x - 2/9*x**2 = 0.
-1, 1
Let x(j) be the third derivative of -j**8/6720 - 11*j**7/7560 - j**6/360 - j**4/12 - 4*j**2. Let r(y) be the second derivative of x(y). Factor r(t).
-t*(t + 3)*(3*t + 2)/3
Let x(j) be the second derivative of 2*j**4/15 - j**3/15 - 3*j**2/5 - 5*j. Factor x(q).
2*(q - 1)*(4*q + 3)/5
Let x(b) be the second derivative of b**7/105 + b**6/75 - b**5/10 - b**4/30 + 8*b**3/15 - 4*b**2/5 - 7*b. Factor x(l).
2*(l - 1)**3*(l + 2)**2/5
Suppose 6 - 8 = -k. Let i(p) be the second derivative of 0*p**3 + 0*p**k - 1/60*p**4 + 1/100*p**5 + 0 + 1/150*p**6 - 1/210*p**7 + 3*p. Factor i(z).
-z**2*(z - 1)**2*(z + 1)/5
Let r(d) be the third derivative of -d**8/12 + d**7/7 + 13*d**6/420 - 4*d**5/35 + d**4/21 - 6*d**2. What is l in r(l) = 0?
-1/2, 0, 2/7, 1
Let b = -3/1276 + 45951/6380. Let j(x) be the first derivative of -3*x**4 - 9/2*x**2 + b*x**5 - 14*x**3 + 6*x + 7/2*x**6 - 2. Solve j(o) = 0 for o.
-1, 2/7, 1
Let a(g) be the first derivative of 1/3*g**3 + 0*g - 1/4*g**4 - 3 - 1/5*g**5 + 1/2*g**2. Solve a(s) = 0 for s.
-1, 0, 1
Let k be 0*(-2 - (-5)/2). Let l(p) be the third derivative of -3*p**2 + k*p**5 + 0*p**3 - 1/540*p**6 + 0 + 0*p + 0*p**4. Factor l(v).
-2*v**3/9
Let t(p) be the first derivative of p**7/630 + p**6/180 - p**5/180 - p**4/36 - p**2 - 4. Let v(q) be the second derivative of t(q). Factor v(o).
o*(o - 1)*(o + 1)*(o + 2)/3
Let y be (4/(-6))/((-2)/3). Let g(a) be the first derivative of -y + 0*a**2 + 1/12*a**3 - 1/4*a. Solve g(x) = 0 for x.
-1, 1
Suppose -h + 0 = -6. Let 6*q - 16*q**4 + 0*q**4 - 5*q**4 - h*q**3 + 21*q**2 = 0. What is q?
-1, -2/7, 0, 1
Let x(y) = 5*y - 22. Let o be x(5). Find p such that 2*p**o - 8/5*p**2 + 2/5*p - 4/5*p**4 + 0 = 0.
0, 1/2, 1
Factor 1/7*n + 0 + 2/7*n**2.
n*(2*n + 1)/7
Let i = -78 + 78. Let b(q) be the third derivative of 1/150*q**5 + i*q - 1/120*q**4 + q**2 + 1/600*q**6 + 0 - 1/15*q**3. Find y such that b(y) = 0.
-2, -1, 1
Let l(u) be the third derivative of 0 - 1/660*u**6 - 1/330*u**5 + 1/33*u**3 + 0*u + 1/132*u**4 + 3*u**2. Suppose l(t) = 0. Calculate t.
-1, 1
Determine r so that -1/3 + 2/3*r**2 + 2/3*r**3 - 1/3*r - 1/3*r**5 - 1/3*r**4 = 0.
-1, 1
Suppose 5 = 4*c + o, 4*o = 2*c + 3 - 1. Determine w, given that 10*w**2 - 1 - c - 4*w**2 + 4*w**3 = 0.
-1, 1/2
Let n be (-23)/(-6) - 11/(-66). Let a(m) be the second derivative of 0*m**3 + 0*m**2 + 0 + 1/54*m**n + m. Factor a(y).
2*y**2/9
Suppose 0 = -l - r + 8 - 4, 0 = 5*l - r - 26. Let b(w) be the third derivative of 1/60*w**6 - w**2 + 0 + 1/30*w**l - 1/12*w**4 - 1/3*w**3 + 0*w. Factor b(n).
2*(n - 1)*(n + 1)**2
Let 4/3*l**2 - 2 - 1/3*l**3 - 1/3*l = 0. What is l?
-1, 2, 3
Suppose -22*t = -17*t - 20. Let 2/3*r**t + 0 - 2/3*r**2 + 0*r + 0*r**3 = 0. Calculate r.
-1, 0, 1
Let a(x) = -6*x**3 - 14*x**2 - 17*x - 8. Let c(b) = b**3 - b. Let t(o) = a(o) + 3*c(o). Factor t(n).
-(n + 2)**2*(3*n + 2)
Let r(z) = -z**2 - z - 1. Le