et c(w) be the second derivative of -w**5/60 - w**4/24 + w**3/3 - w**2 - 2*w. Let h(x) be the first derivative of c(x). Factor h(a).
-(a - 1)*(a + 2)
Let a(i) be the second derivative of -1/12*i**4 + 0 - 4*i + 1/18*i**3 + 0*i**2. Factor a(q).
-q*(3*q - 1)/3
Factor 2/3*u**4 + 2/15*u**5 + 14/15*u**2 + 0 + 6/5*u**3 + 4/15*u.
2*u*(u + 1)**3*(u + 2)/15
Let v(k) be the second derivative of -k**8/1344 - k**7/840 + k**6/360 + 5*k**4/12 + 5*k. Let y(c) be the third derivative of v(c). Factor y(i).
-i*(i + 1)*(5*i - 2)
Let o(z) = z + 15. Let b be o(-13). Let h be 8/5 - (-6)/15. Determine y so that 0*y - y**b + 3*y**2 + h*y = 0.
-1, 0
Let f(a) be the first derivative of -a**4/12 - 2*a**3/9 + 7*a**2/6 - 4*a/3 - 3. Factor f(m).
-(m - 1)**2*(m + 4)/3
Let d(a) be the third derivative of 5*a**2 - 1/12*a**6 + 0*a**3 + 0 + 7/30*a**5 - 1/6*a**4 + 0*a. What is j in d(j) = 0?
0, 2/5, 1
Suppose 12 = 7*n - 2. Factor 0*p + 0 - 1/2*p**n.
-p**2/2
Let b(p) be the third derivative of p**6/120 + p**5/5 - 7*p**4/12 - 13*p**3/6 + 5*p**2. Let g be b(-13). Factor 0*o + 1/2*o**4 + 0*o**2 + 0*o**3 + g.
o**4/2
Factor 2/5*c**4 + 0 + 6/5*c**3 + 6/5*c**2 + 2/5*c.
2*c*(c + 1)**3/5
Factor 0*v**2 - 2*v**2 + 3*v**2 + v.
v*(v + 1)
Let u(p) be the third derivative of 0*p**4 + 2*p**2 + 0*p + 1/3*p**3 + 0 - 1/420*p**5 - 1/1260*p**6. Let r(x) be the first derivative of u(x). Solve r(c) = 0.
-1, 0
Let w(j) be the second derivative of j**6/90 + j**5/5 + 3*j**4/2 - 5*j**3/6 - 8*j. Let k(p) be the second derivative of w(p). Determine t so that k(t) = 0.
-3
Determine g so that -1/7*g**4 - 1/7*g**3 + 1/7*g**2 + 0 + 1/7*g = 0.
-1, 0, 1
Let u(y) be the first derivative of 1/42*y**4 + 0*y**3 + 3 + 1/2*y**2 + 0*y - 1/42*y**5 - 1/60*y**6. Let k(o) be the second derivative of u(o). Factor k(q).
-2*q*(q + 1)*(7*q - 2)/7
Suppose 5*t - 5*k - 30 = 0, k + 11 = 3*t - 3. Let l = -1 + t. Solve -4/9*z**2 + 0 - 14/9*z**4 + 0*z + 2*z**l = 0.
0, 2/7, 1
Let x be (-4)/(-8)*-6 - 3. Let n be (x/(-20))/(4/60). Determine z so that 3*z + 1/2*z**2 + n = 0.
-3
Find r such that 0*r + 0*r**3 + 2/5 - 4/5*r**2 + 2/5*r**4 = 0.
-1, 1
Let i(q) be the third derivative of -q**6/24 + q**5/12 + 25*q**4/24 + 5*q**3/2 + 35*q**2. Solve i(p) = 0.
-1, 3
Let z(u) be the first derivative of u**4/22 + 2*u**3/33 - 2*u**2/11 - 16. Suppose z(f) = 0. Calculate f.
-2, 0, 1
Let f = 21434/4465 - 2/4465. Factor 18*i**2 + 21/5*i**3 + f + 108/5*i.
3*(i + 2)**2*(7*i + 2)/5
Determine u, given that -8/7*u**3 + 0*u**2 + 4/7*u**4 - 4/7 + 8/7*u = 0.
-1, 1
Let d(t) be the first derivative of 4*t**3 - 26*t**2 - 40*t - 41. Factor d(o).
4*(o - 5)*(3*o + 2)
Determine m so that 1063 - 6*m**5 + 2*m**4 - 1063 = 0.
0, 1/3
Suppose 0 = 3*x - 13 + 4. Suppose 0 = -x*z + 4 + 5, -5*k = z - 3. Suppose 2*m**2 + k + 2/3*m**4 - 2*m**3 - 2/3*m = 0. Calculate m.
0, 1
Let p(r) be the second derivative of r**5/35 + 2*r**4/21 + 7*r. Determine o so that p(o) = 0.
-2, 0
Suppose -2*s**3 + 21*s**4 + 2*s**2 + 2*s**3 - 23*s**4 = 0. Calculate s.
-1, 0, 1
Let m(y) = -5*y**4 - y**3 + y**2 + y - 4. Let q(c) = 6*c**4 + 2*c**3 - 2*c**2 - c + 5. Let d(r) = -5*m(r) - 4*q(r). Suppose d(f) = 0. Calculate f.
0, 1
Let k be 5*(-3 - 77/(-25)). Let p = 73/3 + -359/15. Suppose -p*l**5 + 0*l**4 + 0 + 4/5*l**3 + 0*l**2 - k*l = 0. What is l?
-1, 0, 1
Let k(d) be the first derivative of d**6/420 + d**5/210 + 2*d**2 + 2. Let s(i) be the second derivative of k(i). Suppose s(l) = 0. What is l?
-1, 0
Let r = -34 + 15. Let a = 37 + r. Suppose 8*y + a*y**2 + 8/9 = 0. Calculate y.
-2/9
Let l = -88 - -91. Let p(g) be the first derivative of 0*g**2 + 2/3*g**l + 0*g - 2. Suppose p(y) = 0. Calculate y.
0
Let i = 10 - 6. Let p(k) be the second derivative of 1/2*k**i + 0 + 4/3*k**3 + k**2 - k. Determine j, given that p(j) = 0.
-1, -1/3
Let i = 63 - 58. Let f(l) be the second derivative of 0*l**4 + 0*l**2 + 0 + 1/6*l**3 - 3*l - 1/20*l**i. Let f(c) = 0. What is c?
-1, 0, 1
Let r be 1 - (6/(-3) - 19/(-7)). Determine f so that 0 - 2/7*f + r*f**2 = 0.
0, 1
Let n(v) be the first derivative of -1/36*v**4 - 1/60*v**5 + 1 + 0*v**2 + v + 0*v**3. Let k(h) be the first derivative of n(h). Suppose k(y) = 0. Calculate y.
-1, 0
Let i(k) be the second derivative of k**4/42 - k**3/3 - 8*k**2/7 - 9*k. Factor i(f).
2*(f - 8)*(f + 1)/7
Let q(p) be the third derivative of p**8/70560 - p**6/2520 + p**5/15 - p**2. Let u(b) be the third derivative of q(b). Let u(j) = 0. What is j?
-1, 1
Suppose -5*w - 4 = b, 3*w - b - 4 = w. Solve -1/2*y**3 + 0*y**2 + 0*y - 1/4*y**4 + w = 0 for y.
-2, 0
Let k(n) be the third derivative of -n**6/60 - n**5/10 - n**4/6 - n**2. Factor k(p).
-2*p*(p + 1)*(p + 2)
Determine g so that 0*g + 2*g - 8 - 6*g**2 + 12 = 0.
-2/3, 1
Let t(g) be the first derivative of 3*g**4/4 - 3*g**2/2 - 28. Let t(m) = 0. What is m?
-1, 0, 1
Suppose -4*r + 6 = j + 2*j, -4*r + 5*j = -22. Suppose 5*c - 13 = -r. Find k, given that -2 + 3*k**c + 3 - 4*k**2 = 0.
-1, 1
Let v be -2*(-9)/(-6)*(-2)/10. Factor -v*c**3 - 3/5*c**4 + 0 + 3/5*c + 3/5*c**2.
-3*c*(c - 1)*(c + 1)**2/5
Let u(b) be the second derivative of -b + 0*b**2 - 1/24*b**4 + 0 + 1/12*b**3. Let u(w) = 0. Calculate w.
0, 1
Let u = -75/4 + 20. Factor 3*i - 1 - u*i**2.
-(i - 2)*(5*i - 2)/4
Let g(y) be the second derivative of -y**6/60 + y**5/40 + y**4/12 + 26*y. Solve g(c) = 0 for c.
-1, 0, 2
Let z(m) be the third derivative of -m**5/30 + m**3/3 - 12*m**2 + 3. Find d such that z(d) = 0.
-1, 1
Let h = -8 - -8. Let k(m) be the second derivative of 1/6*m**3 + 0 + h*m**4 + 0*m**2 - 1/20*m**5 + m. Let k(g) = 0. What is g?
-1, 0, 1
Let p be (-4)/(-6)*(1 + 2). Factor -6*r**3 - r**p - 6*r**3 + 11*r**3.
-r**2*(r + 1)
Factor 2/17*v**2 + 72/17 + 24/17*v.
2*(v + 6)**2/17
Let r(d) = -6*d**2 - 12*d - 28. Let g(t) = -5*t**2 - 13*t - 29. Let u(k) = 4*g(k) - 3*r(k). Let u(x) = 0. What is x?
-4
Suppose -4*n + 2 + 10 = -3*m, 5*n - 15 = -4*m. Factor 0*a**n + 6*a**2 - 24*a - 2*a**3 + 6*a**2 + 16.
-2*(a - 2)**3
Let o be 6/(-20)*30/(-36). What is a in -o*a + 1/4*a**2 + 0 = 0?
0, 1
Let p be (-15 + 11 + -3)*4/(-14). Find z such that 2 + 1/2*z**3 - 3/2*z**p + 0*z = 0.
-1, 2
Let g(n) be the second derivative of -n**9/15120 + n**7/1260 - n**5/120 + n**4/12 - 2*n. Let w(u) be the third derivative of g(u). Factor w(p).
-(p - 1)**2*(p + 1)**2
Let y = -2 + 4. Let f = -179/4 - -45. What is u in -f*u**y - 1 - u = 0?
-2
Let c be 7 - 8*4/8. Let b be -1 - -1 - 12/(-9). Factor 1/3*j**2 - 4/3*j**c + b*j - 1/3.
-(j - 1)*(j + 1)*(4*j - 1)/3
Let u be (((-8)/(-10))/1)/((-14)/(-35)). Factor 2/5*p**u + 3/5*p - 2/5*p**3 - 3/5*p**4 - 1/5*p**5 + 1/5.
-(p - 1)*(p + 1)**4/5
Let t(z) be the third derivative of -2*z**7/315 - z**6/18 - 7*z**5/45 - z**4/6 + 8*z**2. Factor t(j).
-4*j*(j + 1)**2*(j + 3)/3
What is q in -136*q + 64*q + 3*q**2 + 172 + 152 + q**2 = 0?
9
Let l(h) = -h**3 - h**2 - h. Let i(p) = 9*p**4 - 10*p**3 - 3*p**2 - 4*p. Let g(n) = -i(n) + 4*l(n). Factor g(w).
-w**2*(3*w - 1)**2
Let h(w) be the first derivative of 0*w + 1/3*w**6 + 0*w**2 + 1 + 2/3*w**3 - 2/5*w**5 - 1/2*w**4. Factor h(d).
2*d**2*(d - 1)**2*(d + 1)
Suppose -3*p + 8 = p + 4*r, -2*r - 8 = -2*p. Solve 0*y**4 + 2*y**3 - 8*y**p - 15*y**4 = 0 for y.
-2/5, 0
Let g = -62 - -62. Factor 0 - 2/5*d**2 + g*d.
-2*d**2/5
Factor -3/2*y**3 - 3*y**2 - 3/2*y + 0.
-3*y*(y + 1)**2/2
Let d(g) be the third derivative of g**8/1176 - g**6/420 + g**2. Factor d(v).
2*v**3*(v - 1)*(v + 1)/7
Let z(t) be the second derivative of t**4/48 - t**3/4 + 9*t**2/8 - 6*t. What is g in z(g) = 0?
3
Let s(o) = 16*o - 12. Let q(c) = c**2 - 48*c + 37. Let p(l) = -4*q(l) - 11*s(l). Solve p(a) = 0.
2
Let g = 63/236 + -1/59. Suppose 0 + 0*l + g*l**2 + 1/4*l**3 = 0. What is l?
-1, 0
Let j be 15/(1 - -2) + (19 - 22). Let 8/5*l + 1/5*l**j + 16/5 = 0. What is l?
-4
Suppose 10*r + 21/2*r**2 - r**3 + 2 - 7/2*r**4 = 0. Calculate r.
-1, -2/7, 2
Suppose -3*r + 3 + 6 = 3*q, 5*r = -q + 7. Factor c**3 - 22*c**2 + 16*c**q - 4*c**3.
-3*c**2*(c + 2)
Let x = -60845 + 546734/9. Let a = 97 + x. Factor 4/9*j + a + 2/9*j**2.
2*(j + 1)**2/9
Let v = -12 + 15. Let -1/2*z**4 + 0 + 0*z**v + 1/2*z**2 + 0*z = 0. Calculate z.
-1, 0, 1
Let v = -67 + 69. Let f(n) be the second derivative of 0*n**3 + 0 + n - 1/42*n**4 + 0*n**v. Factor f(x).
-2*x**2/7
Let w(f) be the third derivative of -1/45*f**5 - 2/315*f**7 + 1/72*f**4 + 0*f**3 - 3