**8/1260 - k**6/270 + k**5/180 - k**3/3 + 2*k**2. Let o(c) be the first derivative of f(c). Factor o(h).
-2*h*(h - 1)**3*(h + 1)/3
Let y(f) be the second derivative of f**7/3360 + f**6/1440 + 7*f**3/6 + 5*f. Let i(m) be the second derivative of y(m). Factor i(x).
x**2*(x + 1)/4
Let q(b) be the third derivative of b**9/12096 - b**8/2240 + b**6/360 - b**3/2 - 9*b**2. Let v(o) be the first derivative of q(o). Let v(t) = 0. What is t?
-1, 0, 2
Let z(m) be the first derivative of -m**6/1620 - m**5/180 - m**4/54 - 7*m**3/3 - 7. Let h(i) be the third derivative of z(i). Suppose h(u) = 0. Calculate u.
-2, -1
Let a(v) be the second derivative of 0*v**3 - 3*v + 1/24*v**4 - 1/60*v**5 + 3/2*v**2 + 0. Let g(u) be the first derivative of a(u). Find h, given that g(h) = 0.
0, 1
Let w(u) = -u**3 + 12*u**2 + 11*u + 30. Let z be w(13). Determine d, given that 0*d**3 - 3*d**z + 0 - 3/2*d**5 + 3/2*d + 3*d**2 = 0.
-1, 0, 1
Let n be (-68)/7 + 2/(-7). Let t be (-30)/n - (-6)/(-2). Factor t + 2/9*o**2 + 2/9*o.
2*o*(o + 1)/9
Let c = 1/395 - -1181/1580. Let -3/2*o + 0 - c*o**2 = 0. Calculate o.
-2, 0
Let m(x) be the third derivative of x**6/300 - x**5/75 - x**4/15 + 8*x**3/15 + 4*x**2. Solve m(d) = 0 for d.
-2, 2
Let f(t) = t**3 + t**2 - t - 1. Let j(n) = 20*n**3 + 24*n**2 - 44*n. Let i(p) = -16*f(p) + j(p). Factor i(l).
4*(l - 1)**2*(l + 4)
Find m such that -2/3*m**3 + 1/3*m - 1/3*m**2 + 0 = 0.
-1, 0, 1/2
Let a(w) be the third derivative of -w**6/200 + 9*w**5/100 - 27*w**4/40 + 27*w**3/10 + 6*w**2. Factor a(z).
-3*(z - 3)**3/5
Let f(z) be the second derivative of z**7/210 + z**6/50 - z**5/100 - z**4/20 + 20*z. Factor f(k).
k**2*(k - 1)*(k + 1)*(k + 3)/5
Let x(a) be the third derivative of -a**5/105 + a**4/84 + 5*a**2. Let x(u) = 0. What is u?
0, 1/2
Let k(g) = -g**2 - 3*g - 8. Let f(v) = 3*v**2 + 9*v + 24. Let n(z) = 2*f(z) + 7*k(z). Let x(l) = -l - 1. Let o(h) = n(h) - 6*x(h). Factor o(s).
-(s - 2)*(s - 1)
Let o(x) be the third derivative of 0*x**3 + 0*x + 0 + 1/1260*x**7 + 0*x**4 - 1/720*x**6 - 1/360*x**5 + 4*x**2 + 1/2016*x**8. Let o(z) = 0. Calculate z.
-1, 0, 1
Let f(t) = t**2 + 11*t + 15. Let n be f(-10). Suppose n*j - j - 12 = 0. Factor -3*i**2 - 2*i**2 + 2 - j*i + 6*i**2.
(i - 2)*(i - 1)
Let t(d) be the third derivative of -1/120*d**6 + 0 + 3*d**2 - 1/24*d**4 + 0*d + 1/30*d**5 + 0*d**3. Determine w, given that t(w) = 0.
0, 1
Let n(c) be the first derivative of 11/12*c**3 - 11/20*c**5 + 0*c + 1/2*c**6 - 1/4*c**2 - 4 - 5/8*c**4. Solve n(o) = 0 for o.
-1, 0, 1/4, 2/3, 1
Let z(s) be the third derivative of s**7/70 - 3*s**6/20 + 13*s**5/20 - 3*s**4/2 + 2*s**3 - 5*s**2. Find a such that z(a) = 0.
1, 2
Factor 18*s + 87/4*s**2 + 3 + 27/4*s**3.
3*(s + 1)*(s + 2)*(9*s + 2)/4
Let c = 147 - 1025/7. Let -2/7*r**3 + c*r**2 - 2/7*r + 0 = 0. What is r?
0, 1
Let u(j) = 2*j**3 + 6*j**2 - 1. Let n be u(-4). Let g = n - -137/4. Determine c, given that 1/2*c + g*c**2 + 0 = 0.
-2/5, 0
Let u be 0 + 3 + 5/25*0. Let -6/7*g**4 - 6/7*g + 2/7*g**5 + 2/7 + 4/7*g**2 + 4/7*g**u = 0. Calculate g.
-1, 1
Let m(x) = x**3 - x + 1. Let g = 3 + 0. Let t(k) = -8*k**g - 30*k + 3*k**2 + 22 + 4*k**3 - 39*k**2. Let h(b) = 6*m(b) - t(b). Factor h(f).
2*(f + 2)**2*(5*f - 2)
Let m(o) be the second derivative of 1/6*o**3 + 0*o**5 - o - 1/15*o**6 + 0 - 1/42*o**7 + 0*o**2 + 1/6*o**4. Factor m(g).
-g*(g - 1)*(g + 1)**3
Let q(u) be the third derivative of u**6/840 - u**5/140 + u**4/56 - u**3/42 + 7*u**2. Factor q(a).
(a - 1)**3/7
Let t(w) be the first derivative of 3*w**4/4 + 6*w**3 + 18*w**2 + 24*w - 16. Factor t(v).
3*(v + 2)**3
Let c be 282/9 + (-3)/9. Factor 9*o**2 - c*o - 5*o + 16 + 12*o - 4.
3*(o - 2)*(3*o - 2)
Let o = 20 - 16. Factor 2*w + w - 2*w**2 + 0*w**4 + 2*w**o - w - 2*w**3.
2*w*(w - 1)**2*(w + 1)
Let u(d) be the second derivative of 7*d**6/30 - d**5/10 - 7*d**4/12 + d**3/3 - 3*d. Factor u(m).
m*(m - 1)*(m + 1)*(7*m - 2)
Let w = 7 + -10. Let i = w - -5. Solve 2*o - 2*o**2 + 2*o**5 + 5*o**4 + 3*o**3 - o + o**i - 2*o = 0.
-1, 0, 1/2
Let j = -1364/5 - -274. Factor 0*l + 2/5*l**5 + 2/5*l**2 + j*l**3 + 6/5*l**4 + 0.
2*l**2*(l + 1)**3/5
Let k(g) be the first derivative of -g**4 + 8*g**3/3 - 8. Solve k(q) = 0 for q.
0, 2
Let p(y) be the third derivative of 1/273*y**7 + 0*y + 7/780*y**6 - 3*y**2 - 7/156*y**4 + 0 - 1/130*y**5 - 2/39*y**3. Find t such that p(t) = 0.
-1, -2/5, 1
Let y(g) be the first derivative of 1/22*g**4 + 4/55*g**5 + 0*g - 2/33*g**3 + 1 + 0*g**2. Factor y(b).
2*b**2*(b + 1)*(2*b - 1)/11
Let j be 6/((-1)/(4/(-8))). Suppose 3*y = -3*p + 9, -y - 2*y - 3 = -j*p. Solve 1/2*i**3 + 1/2*i**p + 0*i + 0 = 0.
-1, 0
Suppose -24*w = -28*w. Factor w*a - 1/2*a**2 + 1/2*a**3 + 1/2*a**4 + 0 - 1/2*a**5.
-a**2*(a - 1)**2*(a + 1)/2
Let x(a) be the third derivative of 1/30*a**5 + 0*a + 1/6*a**3 + 3*a**2 - 1/60*a**6 + 0 - 1/70*a**7 + 1/8*a**4 - 1/336*a**8. What is m in x(m) = 0?
-1, 1
Let u(m) = 10*m**2 + 7*m. Let a(i) = 2*i**2 + 2*i. Let q(r) = 9*a(r) - 2*u(r). Determine z, given that q(z) = 0.
0, 2
Let a(s) = 9*s - 97. Let h be a(11). Let -1/2*f + 1/6*f**h + 1/3 = 0. What is f?
1, 2
Suppose 4*t + 0*r - 2 = -2*r, 5*r = t - 17. Let f(o) be the first derivative of t + o**2 + 0*o - 2/3*o**3. Determine y so that f(y) = 0.
0, 1
Let o be (-2)/35*(-24)/9. Let s(r) be the third derivative of 0 + 1/30*r**5 + 2*r**2 + 0*r + 0*r**4 + o*r**7 + 0*r**3 + 2/15*r**6. Suppose s(y) = 0. What is y?
-1/4, 0
Factor -30 + 96*h + 27/2*h**3 - 171/2*h**2.
3*(h - 5)*(3*h - 2)**2/2
Suppose l - 2*k - 9 = 0, 3*l - 5*k = 13 + 11. Suppose -5*o + l*i - 4 = 2*i, 2*o + 3*i - 12 = 0. Find y, given that 1/2*y**2 + o - y + 1/2*y**3 = 0.
-2, 0, 1
Let y(j) be the second derivative of 2/15*j**5 - 2*j + 2/3*j**3 + 0 - 1/2*j**4 - 1/3*j**2. Factor y(g).
2*(g - 1)**2*(4*g - 1)/3
Suppose 0 = -o - 2*o + 15. Suppose -5*p - 9 + 22 = -2*j, 4*j + 11 = o*p. Factor -5*l**p + 2*l**2 - 2 + 0*l**2 + 2*l + 3*l**3.
-2*(l - 1)**2*(l + 1)
Let t = 394 - 394. Factor -4/5*g**2 + 4/5*g**4 + t*g + 4/5*g**3 - 4/5*g**5 + 0.
-4*g**2*(g - 1)**2*(g + 1)/5
Let v(j) be the second derivative of -3*j**8/224 - j**7/28 + j**6/48 + j**5/8 - j**3/3 - 2*j**2 - 4*j. Let c(n) be the first derivative of v(n). Factor c(x).
-(x + 1)**3*(3*x - 2)**2/2
Let -32*h**3 + h + 0*h**2 - 8*h**2 + 9*h + 34*h**3 - 4 = 0. What is h?
1, 2
Let c(k) be the first derivative of -k**5/180 + k**4/36 - k**3/18 + 3*k**2 + 4. Let w(m) be the second derivative of c(m). Factor w(n).
-(n - 1)**2/3
Let f be 12/3*3/6. Factor -q**2 + 16*q + 4*q**f - 15*q + q**3 - 5*q**2.
q*(q - 1)**2
Solve -6/5*n**2 + 1/5 + 0*n - 8/5*n**3 - 3/5*n**4 = 0 for n.
-1, 1/3
Let a(l) be the first derivative of 25*l**7/28 - 5*l**6 + 9*l**5 - 8*l**4 + 4*l**3 + l**2/2 + 3. Let i(q) be the second derivative of a(q). Factor i(h).
3*(h - 2)*(5*h - 2)**3/2
Let m(l) = -l**3 + 7*l**2 + l. Let o be m(7). Let y = -4 + o. Suppose -4*u - u**2 + 2*u + y*u**2 = 0. Calculate u.
0, 1
Suppose -5*q = u + 5, -q - 22 = -5*u + u. Let j = u - 9/2. Determine o, given that 1/4*o - 1/4*o**5 + 0*o**3 + 0 + 1/2*o**4 - j*o**2 = 0.
-1, 0, 1
Let w(r) be the first derivative of 2/15*r**3 + 0*r + 1/15*r**4 - 2 + 1/15*r**2. Find z, given that w(z) = 0.
-1, -1/2, 0
Let b(j) = 5*j - 6. Let u be b(2). Find f such that 2/3*f**3 + 2/9*f**5 - 2/3*f**u + 0 - 2/9*f**2 + 0*f = 0.
0, 1
Let m(i) = -7*i**3 - 5*i**2 - 5*i - 7. Let r(u) = 48*u**3 + 36*u**2 + 36*u + 48. Let f be (-3)/1 - (0 + 1). Let a(x) = f*r(x) - 27*m(x). Factor a(o).
-3*(o + 1)**3
Let m(n) = n**4 + n. Let u(d) = -2 + 18*d + 8*d**4 + 1 - 1 + 8*d**3 - 12*d**2. Let h(c) = 10*m(c) - u(c). Factor h(k).
2*(k - 1)**4
Let x(v) be the second derivative of -v**4/30 - v**3/5 - 2*v**2/5 + 2*v. Suppose x(t) = 0. What is t?
-2, -1
Suppose x - 4*x = -9. Suppose 5*f - x = 7. Find v such that 2/7*v**f - 2/7 + 0*v = 0.
-1, 1
Suppose g - x = -2*g + 3, -3*g = x - 9. Let b be (-3 + 4)*(-2)/(-8). Factor 1/4 + 0*f - b*f**g.
-(f - 1)*(f + 1)/4
Let s(g) be the second derivative of g**7/210 + g**6/30 - 2*g**4/3 + 2*g**3/3 - 7*g. Let h(r) be the second derivative of s(r). Factor h(u).
4*(u - 1)*(u + 2)**2
Let t(i) = -i**3 + 11*i**2 - 9*i - 7. Suppose -s - s = -20. Let h be t(s). Factor 24/7*v - 16/7 + 2/7*v**h - 12/7*v**2.
2*(v - 2)**3/7
Let r be 3/(5/(120/(-9))). Let m = r - -13. Suppose -2 - 1 - 24*p**3 - m + 36*p - 30*p**2 - p**3 = 0. W