**5/20 + 4*k**2. Determine w so that g(w) = 0.
-1, 0
Let y be (-6 - -7)*3/6. Find j, given that -y*j**3 + 0 + 1/8*j - 3/8*j**2 = 0.
-1, 0, 1/4
Let -2/3*i**3 - 4/3*i**2 + 2/3*i + 1 + 1/3*i**4 = 0. Calculate i.
-1, 1, 3
Let y(n) be the second derivative of -n**6/225 + n**4/30 + 2*n**3/45 + 9*n. Find h such that y(h) = 0.
-1, 0, 2
Let y(x) be the third derivative of x**7/315 - 2*x**6/45 + 13*x**5/90 - x**4/6 + 41*x**2. Solve y(a) = 0 for a.
0, 1, 6
Let o(q) be the second derivative of -q**4/24 + q**3/4 - 5*q. Suppose o(p) = 0. Calculate p.
0, 3
Let p(g) be the second derivative of 3*g**5/20 + g**4/4 - g**3/2 - 3*g**2/2 + 8*g. Factor p(u).
3*(u - 1)*(u + 1)**2
Let x = 34 - 32. Suppose 3*a - 8 = -x. Determine f so that -1/3*f**a + f + 0 = 0.
0, 3
Let x = -49580 + 199309/4. Let u = x - 246. Let -u*q**2 + 7/4*q - 1/2 = 0. Calculate q.
2/5, 1
Let p(r) be the third derivative of -r**8/40320 + r**7/3360 - r**6/720 + r**5/20 + 2*r**2. Let c(n) be the third derivative of p(n). Factor c(q).
-(q - 2)*(q - 1)/2
Let g be 5 - ((-8)/(-12) + 3). Determine k, given that -2/3 - 2/3*k**2 - g*k = 0.
-1
Let n(v) be the third derivative of -28*v**5/15 - 5*v**4/2 - 4*v**3/3 + 25*v**2. Suppose n(w) = 0. Calculate w.
-2/7, -1/4
Let d be (-2)/(-6)*(-9)/(-6). Suppose -1 + 3/2*l**3 + 1/2*l**2 - 3/2*l + d*l**4 = 0. Calculate l.
-2, -1, 1
Let d(v) be the first derivative of -v**3/2 + 3*v**2/4 - 11. Find h such that d(h) = 0.
0, 1
Let g(n) be the third derivative of -5*n**2 + 0 - 1/30*n**5 + 1/3*n**3 + 0*n**4 + 0*n. Factor g(d).
-2*(d - 1)*(d + 1)
Suppose 6*t + 13*t - 14*t = 0. Let i = 9 - 5. Determine z so that -3/4*z**5 - 1/2*z**i + 0*z + 3/4*z**3 + t + 1/2*z**2 = 0.
-1, -2/3, 0, 1
Let g(h) be the first derivative of -1/7*h**4 + 0*h**3 + 0*h + 7 + 1/7*h**2 + 0*h**5 + 1/21*h**6. Factor g(r).
2*r*(r - 1)**2*(r + 1)**2/7
Let s(t) be the first derivative of -4*t**3/21 - 4*t**2/7 + 32*t/7 - 25. Solve s(d) = 0 for d.
-4, 2
Let g = 517/1190 - 1/170. Determine h so that 3/7*h - 3/7*h**2 + g - 3/7*h**3 = 0.
-1, 1
Let q(n) be the second derivative of n**7/147 + 2*n**6/105 - 3*n**5/70 - 2*n**4/21 + 4*n**3/21 - 34*n. Factor q(a).
2*a*(a - 1)**2*(a + 2)**2/7
Factor 10/7*y**3 + 6/7*y**2 + 0*y + 0 - 4/7*y**4.
-2*y**2*(y - 3)*(2*y + 1)/7
Let v(d) be the third derivative of d**6/30 + d**5/30 - d**4/12 - 2*d**2. Factor v(x).
2*x*(x + 1)*(2*x - 1)
Factor -76/11*h**2 + 50/11*h**3 - 16/11*h**4 - 16/11 + 2/11*h**5 + 56/11*h.
2*(h - 2)**3*(h - 1)**2/11
Factor 0*y**3 + 3*y**3 + 3*y**2 - 7 + 16 - 15*y.
3*(y - 1)**2*(y + 3)
Suppose -6*c = -5*c. Let t = 46 - 91/2. Factor t*a - 3/2*a**2 + c.
-a*(3*a - 1)/2
Let q(l) be the first derivative of -1/3*l**3 + 1/12*l**4 - 1/3*l + 1/2*l**2 + 4. Factor q(p).
(p - 1)**3/3
Let p(y) be the first derivative of 3 - 2/5*y**5 + 2*y + 0*y**3 - y**4 + 2*y**2. Factor p(h).
-2*(h - 1)*(h + 1)**3
Let a(o) be the third derivative of -21*o**6/20 - 167*o**5/30 - 22*o**4/3 - 4*o**3 + 9*o**2 + 2. Find c such that a(c) = 0.
-2, -3/7, -2/9
Let k = -77 + 77. Determine h, given that 0 + k*h**2 - 1/3*h**4 + 0*h**3 + 0*h = 0.
0
Let j = 0 + 3. Factor 0*k**3 + 6*k**2 + 1 - 2*k**j + 6*k + 4*k**3 + 1.
2*(k + 1)**3
Let l = 22 - 22. Let y(z) be the second derivative of -1/12*z**4 + 1/4*z**5 - 2/15*z**6 + l*z**2 + 0*z**3 - z + 0. Solve y(b) = 0 for b.
0, 1/4, 1
Let x(k) be the first derivative of -1/9*k**2 - 3 + 0*k + 2/27*k**3. Factor x(d).
2*d*(d - 1)/9
Let v(s) be the second derivative of -s**4/54 + 8*s. Factor v(o).
-2*o**2/9
What is k in -3/4*k**2 - 3 - 3*k = 0?
-2
Let l = 6 + -11. Let n be ((-12)/l)/(2/10). Factor n*x**2 + x**4 - 3 - 6*x**3 - 8*x + 3.
x*(x - 2)**3
Let q(n) = n**3 - 8*n**2 - 18*n - 20. Let m be q(10). Factor -3/2*w**3 + 0*w - 1/2*w**2 - w**4 + m.
-w**2*(w + 1)*(2*w + 1)/2
Factor 2 + 5*l**2 - 13 + 4 + 2.
5*(l - 1)*(l + 1)
Let h(d) = d**3 - 8*d**2 + 8*d - 3. Let l be h(7). What is t in t**2 - 2 + l*t + 2*t**2 - 4*t**2 - 2 = 0?
2
Let o be ((-128)/(-30) - 4)*5. Suppose -o*r**3 + 0*r**2 - 2/3 + 4/3*r + 2/3*r**4 = 0. Calculate r.
-1, 1
Let p = 22/39 - 3/13. Let x(u) be the third derivative of 0*u - 1/60*u**6 + u**2 + 0 + 1/12*u**4 + 1/30*u**5 - p*u**3. Let x(m) = 0. What is m?
-1, 1
Suppose 0 = -4*g + 5*h - 3, 3*g + 3*h - 5*h - 3 = 0. Factor -2*s**3 + 3*s**2 - s - 7*s**4 - s**g + 8*s**4.
s*(s - 1)**3
Let o(q) be the first derivative of 0*q - 3/4*q**4 + 0*q**2 + q**3 - 6. Factor o(v).
-3*v**2*(v - 1)
Let h(n) be the third derivative of -1/140*n**5 + 0*n - 2*n**2 + 0 - 1/14*n**3 + 1/28*n**4. Suppose h(v) = 0. Calculate v.
1
Let r(w) be the second derivative of -w**5/90 + 5*w**4/108 + 2*w**3/27 + 2*w**2 - 4*w. Let p(s) be the first derivative of r(s). Determine g so that p(g) = 0.
-1/3, 2
Let x be 26/5 - 105/21. Factor x + 0*u - 1/5*u**2.
-(u - 1)*(u + 1)/5
Let x = 6 + -2. Let z = -2 + x. Factor 4*y + 0*y**2 + 0*y**z - 2*y**2.
-2*y*(y - 2)
Let a(m) be the second derivative of m**7/252 + m**6/60 - m**5/120 - m**4/24 + 2*m. Factor a(s).
s**2*(s - 1)*(s + 1)*(s + 3)/6
Let n(r) be the first derivative of 0*r + 0*r**3 + 0*r**5 + r**4 - r**2 + 1 - 1/3*r**6. Factor n(y).
-2*y*(y - 1)**2*(y + 1)**2
Let t(k) be the third derivative of -k**5/240 + k**4/48 - k**3/24 - 8*k**2. Let t(f) = 0. Calculate f.
1
Let s(m) be the second derivative of m**6/6 - 5*m**5/4 + 15*m**4/4 - 35*m**3/6 + 5*m**2 - 18*m. Factor s(t).
5*(t - 2)*(t - 1)**3
Let f(a) be the second derivative of 5*a**4/72 - 5*a**3/12 + 4*a. Determine k so that f(k) = 0.
0, 3
Let b(d) be the first derivative of 3*d**5/10 - 5*d**4/8 - 5*d**3/6 + 5*d**2/4 + d + 52. Solve b(k) = 0 for k.
-1, -1/3, 1, 2
Let l be 9/(-6)*-2*3. Let j(b) be the first derivative of 0 + l*b**2 + 2 + 1 + 27*b + b**3. Find x, given that j(x) = 0.
-3
Let h(l) be the third derivative of -l**6/40 + l**5/10 + l**4/8 - l**3 + 9*l**2. Factor h(x).
-3*(x - 2)*(x - 1)*(x + 1)
Suppose 0 = -2*n - 1 + 5. Let j(x) be the first derivative of -1/9*x**2 + 1/9*x**4 + 4/27*x**3 - 1/27*x**6 - 2/45*x**5 + n - 2/9*x. Factor j(v).
-2*(v - 1)**2*(v + 1)**3/9
Let 3/5*r**4 + 9/5*r**3 - 9/5*r + 0 - 3/5*r**2 = 0. What is r?
-3, -1, 0, 1
Solve 11*a**2 + 63*a**4 + 59*a**3 + a**2 - 131*a**3 + 147*a**5 = 0.
-1, 0, 2/7
Let q be 8 - 3 - (-1 - 0). Let b(z) be the second derivative of 0*z**2 + 0*z**4 + 0 - 1/70*z**5 - 1/105*z**q + z + 0*z**3. Factor b(s).
-2*s**3*(s + 1)/7
Factor -2*x**4 - 39*x**5 + 71*x**5 - 34*x**5.
-2*x**4*(x + 1)
Let t(l) = -1. Let o(q) = -q + 2. Let g(n) = o(n) + 5*t(n). Let j be g(-3). What is s in 2/5*s**3 + 2/5*s**2 - 2/5*s**4 + j - 2/5*s = 0?
-1, 0, 1
Suppose 0 = -2*z - 2*y + 4, -3*z = -6*z - 4*y + 6. Let q be (-2)/((-1 - 5)/12). Solve 1/3*l**5 + 0*l**3 + 0*l**z + 0 + 0*l**q + 0*l = 0.
0
Suppose -k - 9 = -15. Let t(b) be the third derivative of 0*b**5 + 1/300*b**k - b**2 - 1/120*b**4 + 0 + 0*b + 0*b**3 - 1/1680*b**8 + 0*b**7. Factor t(w).
-w*(w - 1)**2*(w + 1)**2/5
Let q be (3*-1)/(-3) + 4. Let m = q - 1. Factor -1 + z**3 + z**2 - z + 4*z - m*z.
(z - 1)*(z + 1)**2
Let s(u) be the first derivative of u**3/4 - u**2 - 3*u/4 + 1. Factor s(m).
(m - 3)*(3*m + 1)/4
Let y be (-8)/(-28) - 50/(-21). Let -16/3 + 2/3*g**3 - 8/3*g - y*g**4 + 20/3*g**2 + 2/3*g**5 = 0. Calculate g.
-1, 2
Let o(r) be the second derivative of r**5/10 + r**4/3 - r**3/3 - 2*r**2 + 2*r. Factor o(y).
2*(y - 1)*(y + 1)*(y + 2)
Let w = -22 + 47/2. Determine p so that w*p**3 + 0 - p - 1/2*p**2 = 0.
-2/3, 0, 1
Let y = -391199/300 + 1304. Let x(n) be the third derivative of 0*n + 0 + 0*n**4 + 1/300*n**6 - n**2 + 0*n**3 - 1/350*n**7 + y*n**5. Factor x(b).
-b**2*(b - 1)*(3*b + 1)/5
Let c be (-1 - -3) + 1*2. Factor -2 - y**5 + 2*y**c + 2 - 2*y**3 + y**3.
-y**3*(y - 1)**2
Factor 1/4 + 0*s**3 + 0*s - 1/2*s**2 + 1/4*s**4.
(s - 1)**2*(s + 1)**2/4
Let c = -770 + 1573/2. Let n = -16 + c. Determine p so that 0 - n*p**2 + 0*p**3 + 1/2*p**4 + 0*p = 0.
-1, 0, 1
Let v(y) be the first derivative of y**3/2 - 3*y**2/2 - 3. Factor v(h).
3*h*(h - 2)/2
Let t(y) be the first derivative of -3*y**5/35 + 15*y**4/14 - 13*y**3/7 - 90*y**2/7 - 108*y/7 - 10. Let t(u) = 0. Calculate u.
-1, 6
Let 2/3*y**4 + 0 + 2/3*y**3 - 2/3*y - 2/3*y**2 = 0. Calculate y.
-1, 0, 1
Let b(f) be the first derivative of 5*f**6/18 + 4*f**5/3 + 5*f**4/3 - 10*f**3/9 - 25*f**2/6 - 10*f/3 + 11. Factor b(n).
5*(n - 1)*(n + 1)**3*(n + 2)/3
Let x(u) = 3*u**4 - 7*u