4 - 6/7*o**3 + 0*o.
-2*o**2*(o + 1)*(o + 2)/7
Let j be 13214/(-715) - (-4)/26. Let g = j - -228/11. Let 8/5*y**3 - 2/5*y**4 - 2/5 - g*y**2 + 8/5*y = 0. Calculate y.
1
Let k(l) be the third derivative of l**9/181440 - l**7/15120 - l**5/30 + 2*l**2. Let i(q) be the third derivative of k(q). Factor i(m).
m*(m - 1)*(m + 1)/3
Let s = 41/9 + -13/3. Determine b so that -s*b**2 - 2/9*b + 2/9*b**3 + 2/9*b**4 + 0 = 0.
-1, 0, 1
Let p(x) be the first derivative of 0*x**5 + 1/6*x**4 + 3 + 0*x**3 - 1/6*x**2 - 1/18*x**6 + 0*x. Factor p(v).
-v*(v - 1)**2*(v + 1)**2/3
Let l = -1/58 + 589/522. Solve 10/9*n**5 + 0 + 0*n - 4/9*n**4 + 4/9*n**2 - l*n**3 = 0.
-1, 0, 2/5, 1
Let q(b) = -3*b - b**2 + b + 9 + 0*b**2 - 4*b. Let o be q(-7). Factor 2/3*z**o - 8/3*z + 8/3.
2*(z - 2)**2/3
Factor 3/4*v**3 + 0 + 1/2*v - 7/4*v**2.
v*(v - 2)*(3*v - 1)/4
Let i(j) be the first derivative of j**6/3 + 12*j**5/5 + 4*j**4 - 4*j**3/3 - 9*j**2 - 8*j + 58. Find t such that i(t) = 0.
-4, -1, 1
Let z(a) = -66*a**5 + 12*a**4 + 39*a**3 - 66*a**2 + 27*a - 27. Let o(v) = -5*v**5 + v**4 + 3*v**3 - 5*v**2 + 2*v - 2. Let x(p) = -27*o(p) + 2*z(p). Factor x(k).
3*k**2*(k - 1)**2*(k + 1)
Let p = 11 - 7. Suppose -5*r - 16 = -2*q, 4*q - p = 2*q - r. Solve 0*b - 2/3*b**2 + 2/9*b**q + 8/9 = 0.
-1, 2
Let o(c) be the second derivative of 3*c**5/140 + c**4/28 + 16*c. Factor o(u).
3*u**2*(u + 1)/7
Let o be 177/105 + 4/(-14). Find v, given that -v**3 - 1/5*v**4 - 2/5 - 9/5*v**2 - o*v = 0.
-2, -1
Solve 3*o - 7*o**3 + 6*o**3 + 4*o**3 + 6*o**2 = 0 for o.
-1, 0
Let g(s) be the first derivative of 0*s + 3/2*s**2 - 3 + 3*s**3. Factor g(t).
3*t*(3*t + 1)
Let n(y) = 2*y**3 - 58*y**2 - 2*y + 61. Let v be n(29). Solve 1/5*w**2 + 0 + 0*w**v + 0*w - 1/5*w**4 = 0.
-1, 0, 1
Let x(t) be the first derivative of 1/10*t**5 + 0*t**4 + 0*t**2 - 5 + 0*t**3 + 0*t. Suppose x(r) = 0. What is r?
0
Let d(r) be the third derivative of 0*r + 0 + 1/60*r**5 + 2*r**2 + 3/2*r**3 - 1/4*r**4. Factor d(t).
(t - 3)**2
Let u(k) be the second derivative of 3*k + 1/24*k**4 + 0 + 1/6*k**3 + 0*k**2. Suppose u(q) = 0. Calculate q.
-2, 0
Let m(b) = 9*b**4 - 14*b**3 - b**2 + 4*b. Let k(j) = -117*j**4 + 183*j**3 + 12*j**2 - 51*j. Let p(u) = 2*k(u) + 27*m(u). Let p(c) = 0. Calculate c.
-2/3, 0, 1
Let w = -38 + 43. Let l = -1 - 0. Let t(i) = -6*i**2 - 6*i. Let z(p) = -p**2 - p. Let a(d) = l*t(d) + w*z(d). Suppose a(s) = 0. What is s?
-1, 0
Determine q so that -2/17*q**3 + 96/17*q**2 + 8192/17 - 1536/17*q = 0.
16
Factor 3/5*m + 16/5*m**2 - 2/5 + 4/5*m**4 + 3*m**3.
(m + 1)**2*(m + 2)*(4*m - 1)/5
Let u(i) be the third derivative of -i**8/2520 - i**7/315 - 2*i**6/225 - 2*i**5/225 - 16*i**2. Factor u(n).
-2*n**2*(n + 1)*(n + 2)**2/15
Let k be 3 - (1 - (-16)/(-12)) - 3. Solve -2/3*v + k*v**2 + 1/3 = 0 for v.
1
Suppose 5*b - 8 = b. What is a in b - 7*a + a + 3*a + 2*a**2 - 1 = 0?
1/2, 1
Let b(f) = -2*f**2 - 2*f + 3. Let w be b(0). Suppose 14 = 5*g - 2*s, -g + 12 = -0*g - 5*s. Solve 1/6*h**w + 1/6*h + 0 - 1/3*h**g = 0.
0, 1
Let k(w) be the third derivative of 0*w**3 - 1/210*w**5 + 0*w**4 + 0*w + 0 + 3*w**2. Suppose k(t) = 0. Calculate t.
0
Let l = -18 + 11. Let f be 0*(l/(-2))/7. Factor 0*n + f*n**3 + 0 - 2/5*n**2 + 2/5*n**4.
2*n**2*(n - 1)*(n + 1)/5
Let 0 - 3/4*o**2 + 3/2*o**3 + 21/4*o**4 + 0*o + 3*o**5 = 0. Calculate o.
-1, 0, 1/4
Let x be 2/(-11) + (-322)/(-77). Let r = -5 + 8. Factor 0 - 6 - x*h + 3*h**2 + r*h - 2*h.
3*(h - 2)*(h + 1)
Let d(v) be the first derivative of 2 - 2/25*v**5 + 1/15*v**6 - 1/5*v**4 - 2/5*v + 4/15*v**3 + 1/5*v**2. Factor d(t).
2*(t - 1)**3*(t + 1)**2/5
Let h = 6 - 10. Let j be ((-5)/40)/(2/h). Determine v, given that -j*v**4 + 0*v + 0 + 1/2*v**3 - 1/4*v**2 = 0.
0, 1
Suppose -f + 1 + 4 = 0. Let y = f + -2. Determine h, given that -h**y + 0*h**3 + 2*h + 0*h**3 - h**2 = 0.
-2, 0, 1
Factor 19/6*w**2 - 2/3*w - 2/3 + 1/2*w**4 - 7/3*w**3.
(w - 2)**2*(w - 1)*(3*w + 1)/6
Let c = -12 + 62/5. Find u such that 2/5*u**4 + 4/5 - 6/5*u**2 - 2/5*u + c*u**3 = 0.
-2, -1, 1
Let b(x) be the first derivative of -x**4/4 - 2*x**3 - 3*x**2 - 5*x - 3. Let a be b(-5). Factor 2/3*k + 0 + a*k**3 - 4/3*k**2 - 2/3*k**5 + 4/3*k**4.
-2*k*(k - 1)**3*(k + 1)/3
Let d be -1 + (-4)/1*-1. Suppose 2*v + 3 = -2*x + 1, -4*x - d*v = 0. Factor 0 - x*b**2 - b**4 + 0 + 4*b**2.
-b**2*(b - 1)*(b + 1)
Factor 3/4*n**2 + 1/2*n + 1/4*n**3 + 0.
n*(n + 1)*(n + 2)/4
Let q(k) be the second derivative of 3*k**5/40 + 19*k**4/24 - 5*k**3/4 - 7*k**2/4 + 41*k. Factor q(t).
(t - 1)*(t + 7)*(3*t + 1)/2
What is q in -5*q**2 - 20*q - 9*q**2 + 20 + 19*q**2 = 0?
2
Let v be (-105)/(-30)*(-3)/(-7). Factor -v*n**2 - 3*n + 0.
-3*n*(n + 2)/2
Let v(r) be the second derivative of -1/12*r**3 + 0*r**2 + 1/24*r**4 + 0 + 1/40*r**5 - 1/60*r**6 + 5*r. Factor v(i).
-i*(i - 1)**2*(i + 1)/2
Let m be 2/(-24)*4*(-6)/8. Factor -9/4 - 3/2*g - m*g**2.
-(g + 3)**2/4
Factor -50*h**2 + h**3 + 48*h**2 + h**4 + 0*h**4.
h**2*(h - 1)*(h + 2)
Let g(a) be the second derivative of a**6/165 - a**5/55 - a**4/66 + 2*a**3/33 + 18*a. Solve g(z) = 0 for z.
-1, 0, 1, 2
Let 2/7*z**2 - 2/7*z**3 + 4/7*z + 0 = 0. What is z?
-1, 0, 2
Let n = -5 - -7. Suppose 0 = -p - n*p + 6. Find v such that 1/4*v**p + 0*v + 3/4*v**4 + v**3 + 0 = 0.
-1, -1/3, 0
Let c = -3 + 8. Factor 0 + 4 + c*a - 3*a - 2*a**2.
-2*(a - 2)*(a + 1)
Factor -2/7*g**2 + 1/7*g**3 + 0*g + 0.
g**2*(g - 2)/7
Suppose -5*b = -6 - 14. Let x = 6 - b. Factor 0 - 2/7*o + 0*o**x + 2/7*o**3.
2*o*(o - 1)*(o + 1)/7
Let s(r) = -7*r**2 + r + 4. Let q(o) = -48*o**2 + 6*o + 27. Let i(f) = 4*q(f) - 27*s(f). Solve i(y) = 0 for y.
-1, 0
Let d(x) be the second derivative of 5/7*x**4 + 0 - 3*x - 5/2*x**5 + 8/7*x**2 + 44/21*x**3 - 50/21*x**6. Solve d(n) = 0 for n.
-2/5, 1/2
Let v(p) be the first derivative of p**5/50 - p**4/30 - 2*p**3/15 - 5*p + 4. Let k(l) be the first derivative of v(l). Factor k(n).
2*n*(n - 2)*(n + 1)/5
Let v(g) be the second derivative of -3*g**5/20 + g**4/2 + 7*g. Suppose v(s) = 0. What is s?
0, 2
Let o be ((-14)/28)/(4/(-6)). Let 1/4*w**2 + 0*w + 0 - w**3 + o*w**4 = 0. What is w?
0, 1/3, 1
Let p(u) = u**2 - u. Let h be p(1). Factor -9 + 0 + 7 + 6*l + h*l**2 + 2*l**2 - 6*l**3.
-2*(l - 1)*(l + 1)*(3*l - 1)
Let v(i) be the second derivative of -1/3*i**3 + 3*i + 0*i**2 + 0 - 1/10*i**5 + 1/3*i**4. Factor v(s).
-2*s*(s - 1)**2
Find i, given that 3*i - 100*i**2 + 3*i**3 + 3*i + 177*i**2 - 86*i**2 = 0.
0, 1, 2
Let r = -689/4 + 3517/20. Solve 0 - 4/5*g - r*g**2 = 0.
-2/9, 0
Let n = 19087 - 134073/7. Let l = -66 - n. What is z in 2/7 + 0*z - l*z**2 = 0?
-1, 1
Let b(h) be the first derivative of -9*h**5/5 - 7*h**4/4 + 2*h**3/3 + 4. Factor b(w).
-w**2*(w + 1)*(9*w - 2)
Suppose -7 = -5*h + 2*c - 13, -12 = h - 4*c. Factor 3/2*p**2 + 1/2*p + h - 2*p**3.
-p*(p - 1)*(4*p + 1)/2
Let h(u) be the first derivative of -1 + 0*u - 8/21*u**3 + 24/35*u**5 - 3/7*u**6 + 1/7*u**4 - 1/7*u**2. Solve h(f) = 0 for f.
-1/3, 0, 1
Let k be 34 - 0 - (1 - 2). Factor 12*h**4 - k*h + 35*h + 15*h**3 + 3*h**2.
3*h**2*(h + 1)*(4*h + 1)
Let n(f) be the second derivative of f**6/90 + f**5/20 + f**4/12 + f**3/18 - 8*f. Factor n(t).
t*(t + 1)**3/3
Let x = 69 + -66. Let g(c) be the first derivative of 0*c + 1/3*c**x + 2 - 1/2*c**2. Factor g(q).
q*(q - 1)
Let d(l) = l**3 - 34*l**2 + 64*l + 5. Let v be d(32). Determine f so that 1/3*f**v - 1/3*f**4 - 1/3*f**3 + 1/3*f**2 + 0*f + 0 = 0.
-1, 0, 1
Let c = 3/5 - 1/5. Determine o so that 2/5 - c*o - 4/5*o**2 = 0.
-1, 1/2
Let y(p) be the third derivative of -3*p**2 + 0*p**3 + 0 - 1/140*p**7 + 0*p**4 + 0*p**6 + 0*p + 1/40*p**5. Solve y(n) = 0 for n.
-1, 0, 1
Let o(y) be the third derivative of -y**8/32 - 2*y**7/105 + 11*y**6/240 - y**5/60 + 8*y**2. Find k such that o(k) = 0.
-1, 0, 2/7, 1/3
Let x(m) be the second derivative of 1/40*m**5 + 1/36*m**4 + 0*m**2 + 0 - 1/252*m**7 + 0*m**6 + 0*m**3 + 3*m. Factor x(n).
-n**2*(n - 2)*(n + 1)**2/6
Let v(q) = 13*q**2 - 13*q + 5. Let j(x) = 32*x**2 - 32*x + 12. Let k(o) = -5*j(o) + 12*v(o). Factor k(s).
-4*s*(s - 1)
Let b(j) be the second derivative of 2*j**6/105 - j**5/5 - 9*j**4/7 - 58*j**3/21 - 20*j**2/7 + 34*j. Factor b(m).
4*(m - 10)*(m + 1)**3/7
Let 2*l**4 + 0 + 0*l - 5/2*l**3 + l**2 - 1/2*l**5 = 0. Calculate l.
0, 1, 2
Suppose 0 = -3*i + 46*x - 51*x + 31, -3*i = 3*x - 21. Solve -3/5*v - 2/5 + 2/5*v**i = 0 for v.
-1/2, 2
Let n(m) be th