g**4/24 - 2*g**3/9 - 16*g**2. Let q(z) = 0. Calculate z.
-1, 4
Let u(a) be the second derivative of a**7/735 - a**6/420 + 4*a**2 - 5*a. Let p(d) be the first derivative of u(d). Determine x, given that p(x) = 0.
0, 1
Let k(v) be the third derivative of v**10/50400 - v**9/10080 + v**7/840 - v**6/240 + v**5/60 - 2*v**2. Let g(r) be the third derivative of k(r). Factor g(d).
3*(d - 1)**3*(d + 1)
Let m = -21 + 6. Let i be (m/20)/(6/(-2)). Factor 0*s + i*s**2 - 3/4*s**3 + 0 + 3/4*s**4 - 1/4*s**5.
-s**2*(s - 1)**3/4
Let o(v) be the first derivative of -v**7/840 + v**6/360 + v**3/3 + 2. Let w(s) be the third derivative of o(s). Factor w(r).
-r**2*(r - 1)
Let j be 4/34 + (75/17)/5. Let y(i) be the first derivative of j - 2/33*i**3 - 2/11*i**2 - 2/11*i. Determine n, given that y(n) = 0.
-1
Let y(v) be the second derivative of 1/5*v**6 + 0*v**4 + 0 + 0*v**2 + v + 0*v**3 - 3/20*v**5 - 1/14*v**7. Factor y(w).
-3*w**3*(w - 1)**2
Let f(q) = -21*q**4 - 93*q**3 - 117*q**2 + 315*q + 639. Let t(z) = -5*z**4 - 23*z**3 - 29*z**2 + 79*z + 160. Let i(a) = 2*f(a) - 9*t(a). Factor i(l).
3*(l - 2)*(l + 3)**3
Let m be 1*(-16)/(-12)*(-3)/(-14). Factor -2/7*l**2 + m*l**3 - 2/7*l**5 + 0 + 2/7*l**4 + 0*l.
-2*l**2*(l - 1)**2*(l + 1)/7
Let m(o) be the first derivative of o**4/12 - 2*o**3/9 - 5. Find a such that m(a) = 0.
0, 2
Let b be 7 - 3 - 8/2. Let n(k) be the third derivative of -k**2 - 1/150*k**5 + 0*k**4 + 0*k + 0*k**3 + b. Let n(h) = 0. What is h?
0
Let j(u) be the second derivative of -3*u + 1/6*u**3 + 0 + 0*u**2 + 1/24*u**4. Factor j(b).
b*(b + 2)/2
Let r = 25/2 - 12. Let q(t) be the third derivative of 43/80*t**5 + 0 + 3/4*t**4 + r*t**3 + 1/40*t**7 + 3/16*t**6 + 0*t - 4*t**2. What is k in q(k) = 0?
-2, -1, -2/7
Let r(x) be the first derivative of -x**6/6 + x**5 - 5*x**4/2 + 10*x**3/3 - 5*x**2/2 + x + 2. Suppose r(l) = 0. What is l?
1
Let s(d) = 16*d**3 - 8*d**2 + 12*d + 12. Let a(i) = i**3 + i + 1. Let h(m) = -12*a(m) + s(m). Factor h(b).
4*b**2*(b - 2)
Let b(x) = -12*x**4 + 3*x**3 - 5*x**2 + 5*x. Let a(g) = -g**5 + 13*g**4 - 4*g**3 + 6*g**2 - 6*g. Let w(f) = -5*a(f) - 6*b(f). Suppose w(l) = 0. What is l?
-1, -2/5, 0
Let i(a) = 3*a**3 + 2*a**2 + 5. Let m(v) = -2*v + 1. Let y be m(3). Let o(r) = 15*r**3 + 9*r**2 + 24. Let l(x) = y*o(x) + 24*i(x). Factor l(b).
-3*b**2*(b - 1)
Let j(y) be the second derivative of y**7/231 + 2*y**6/165 + y**5/110 - 11*y. Factor j(z).
2*z**3*(z + 1)**2/11
Let 0 + 0*h**2 + 2/9*h**5 + 2/3*h**4 + 4/9*h**3 + 0*h = 0. What is h?
-2, -1, 0
Let u(h) be the second derivative of 0 - 1/9*h**3 - h + 2/9*h**2 + 1/54*h**4. Suppose u(i) = 0. Calculate i.
1, 2
Let b(q) be the third derivative of q**5/12 + 5*q**4/6 + 10*q**3/3 - 11*q**2. Factor b(a).
5*(a + 2)**2
Let g(k) be the third derivative of 2/15*k**3 - 1/60*k**4 - 1/150*k**5 + 0*k - 4*k**2 + 0. Let g(q) = 0. What is q?
-2, 1
Let b be 11/4 - 2/(-8). Let u be b/(-12) - (-2)/8. Determine x, given that 1/2*x**5 + 0*x**2 + 0*x**4 - 1/2*x**3 + u*x + 0 = 0.
-1, 0, 1
Let t(f) be the third derivative of 0*f**3 + 0*f - 2*f**2 + 1/12*f**5 + 0 + 1/30*f**6 + 1/24*f**4. Factor t(q).
q*(q + 1)*(4*q + 1)
Let p = 1 - -1. Determine r so that 2*r + p*r - 1 - 2*r - r**2 = 0.
1
Let l(u) be the third derivative of 0 + 1/3*u**4 + 0*u**3 + 1/20*u**6 - 6*u**2 + 0*u + 4/15*u**5. Factor l(d).
2*d*(d + 2)*(3*d + 2)
Let b = 45 + -45. Let 0*q**3 + 0 + 0*q + b*q**2 - 1/4*q**4 = 0. Calculate q.
0
Let h(t) = -t**2 + t + 1. Let i(y) be the first derivative of -y**3 + 3*y**2/2 + 6*y + 1. Let z(k) = -6*h(k) + i(k). Factor z(d).
3*d*(d - 1)
Let d(l) = l**2 - 1. Let q(x) = 4*x**2 + 4*x - 8. Let z(w) = -8*d(w) + q(w). Suppose z(c) = 0. Calculate c.
0, 1
Let n(i) be the third derivative of i**8/1176 + 2*i**7/735 + i**6/420 - 24*i**2. Determine b so that n(b) = 0.
-1, 0
Let u = 10377/4 - 2607. Let a = u + 467/36. Solve -10/9*c - a - 8/9*c**2 = 0 for c.
-1, -1/4
Let a(d) be the first derivative of -2*d**3/15 + d**2 + 33. Suppose a(f) = 0. Calculate f.
0, 5
Let z = 126 - 76. Factor k**2 - 45*k**4 + z*k**4 - 14*k**3 + 2*k + 6*k**3.
k*(k - 1)**2*(5*k + 2)
Let 0*v**3 + 1/3*v - 2/3*v**4 - 1/3*v**5 + 2/3*v**2 + 0 = 0. What is v?
-1, 0, 1
Let h be (46/54 - 1)/((-8)/12). Factor 2*c**2 + h + 4/3*c.
2*(3*c + 1)**2/9
Suppose 5*k + 2*m - 108 = -40, 0 = -k - 3*m + 24. Suppose 0 = 5*u - k + 2. Factor 2*v**4 - v**2 - v**u - v**3 + 2*v - v**3.
2*v*(v - 1)**2*(v + 1)
Factor -3 - 64*w + 12*w**3 - 20*w**2 + 88*w**3 - 13.
4*(w - 1)*(5*w + 2)**2
Let z be (-13)/(-3) - (-1)/(-3). Factor 1/4*w + 0*w**2 - 3/4*w**5 - 3/2*w**3 + 0 + 2*w**z.
-w*(w - 1)**3*(3*w + 1)/4
Let g(x) be the first derivative of -3/2*x**2 + 6/5*x - 3/5*x**3 + 3. Suppose g(c) = 0. Calculate c.
-2, 1/3
Let f(g) be the second derivative of -7*g**5 - 10*g**4/3 + 56*g**3/15 + 16*g**2/5 - 6*g. Find n such that f(n) = 0.
-2/5, -2/7, 2/5
Let f(c) be the third derivative of -c**5/90 - c**4/36 + 6*c**2. Factor f(r).
-2*r*(r + 1)/3
Let j(p) = 4*p - 41. Let w be j(11). Factor 0*q**2 - 1/5*q**4 + 0 + 0*q - 1/5*q**w.
-q**3*(q + 1)/5
Let d(n) be the second derivative of 3*n**5/100 + n**4/10 - 3*n. Determine u so that d(u) = 0.
-2, 0
Let u(p) be the third derivative of 22*p**7/735 - p**6/6 + 13*p**5/35 - 17*p**4/42 + 4*p**3/21 + 14*p**2. Factor u(x).
4*(x - 1)**3*(11*x - 2)/7
Let o(t) = t**3 - t**2 - t + 4. Let w = -1 - -1. Let u be o(w). Solve u*j + 1/2*j**2 + 2 - 1/2*j**5 - 5/2*j**4 - 7/2*j**3 = 0.
-2, -1, 1
Let l(h) be the second derivative of -1/18*h**4 - 3*h + 0*h**2 + 0 + 1/63*h**7 + 0*h**3 - 1/30*h**5 + 1/45*h**6. Factor l(b).
2*b**2*(b - 1)*(b + 1)**2/3
Let a(w) be the first derivative of w**7/1470 + w**6/252 + w**5/210 - 2*w**3/3 + 2. Let v(l) be the third derivative of a(l). Solve v(q) = 0 for q.
-2, -1/2, 0
Let q(u) be the first derivative of -2*u**5/65 - u**4/13 - 2*u**3/39 + 3. Solve q(l) = 0 for l.
-1, 0
Suppose 4/3*h - 32/3*h**2 + 20/3*h**3 + 8/3 = 0. What is h?
-2/5, 1
Factor -18*d + 25*d**2 + 20*d**3 - 20 - 5*d**3 + 3*d - 5*d**4.
-5*(d - 4)*(d - 1)*(d + 1)**2
Let f(j) be the first derivative of -28*j**6/15 - 82*j**5/25 + 22*j**3/15 - 2*j**2/5 + 4. Determine d, given that f(d) = 0.
-1, 0, 1/4, 2/7
Let m = -24 - -27. Suppose m*d = d. Factor -3/7*z + d + 3/7*z**3 + 0*z**2.
3*z*(z - 1)*(z + 1)/7
Let s(x) be the third derivative of -x**5/20 - 5*x**4/8 + 3*x**3 + 2*x**2. Suppose s(i) = 0. What is i?
-6, 1
Factor 32*v**2 - 16 + 11*v**3 - 4*v**2 - 3*v**3 + 4*v**3.
4*(v + 1)*(v + 2)*(3*v - 2)
Let 6 + 14*w - 167*w**4 + 6*w - 192*w**3 - 63*w**5 - 54*w**2 - 25*w**4 - 5*w = 0. What is w?
-1, -1/3, 2/7
Suppose -2*p = -4*q - 10, -3*q - 3*p - 5 = -4*p. Let j(l) be the first derivative of -3/16*l**4 + 0*l**3 + q*l**2 + 0*l + 1 + 3/10*l**5 - 1/8*l**6. Factor j(y).
-3*y**3*(y - 1)**2/4
Let t(c) = -3*c + 0*c - 5*c**3 + 13*c**2 - 2*c**2 + 5*c. Let j(a) = 2*a**3 - 5*a**2 - a. Let y(l) = 7*j(l) + 3*t(l). Find g such that y(g) = 0.
-1, 0
Let f(k) = -16*k**2 + 36*k + 1. Let x(s) = 8*s**2 - 18*s. Let m(o) = -4*f(o) - 9*x(o). Factor m(a).
-2*(a - 2)*(4*a - 1)
Let y(g) = g**3 - 6*g**2 - g - 2. Let p(s) = -s**3 + 5*s**2 + s + 1. Let x(z) = -4*p(z) - 3*y(z). Find q such that x(q) = 0.
-1, 1, 2
Factor -a**3 - 2*a - 7/2*a**2 + 0 + 1/2*a**4.
a*(a - 4)*(a + 1)**2/2
Let h(r) = 44*r - 215. Let a be h(5). Suppose 0*w + 32/5*w**4 - 2/5*w**2 + 0 + 2/5*w**3 - 32/5*w**a = 0. Calculate w.
-1/4, 0, 1/4, 1
Let a = -91 - -95. Let w(v) be the second derivative of 0*v**2 + 1/60*v**5 + 1/36*v**a + 0 - 3*v - 1/18*v**3 - 1/90*v**6. Let w(l) = 0. What is l?
-1, 0, 1
Let y(l) be the first derivative of l**8/10080 - l**7/1260 + l**6/432 - l**5/360 + l**3/3 + 1. Let f(w) be the third derivative of y(w). Factor f(c).
c*(c - 2)*(c - 1)**2/6
Let u(h) be the third derivative of -3/16*h**4 + 0*h**5 + 1/80*h**6 + 0*h - 1/2*h**3 + 0 + 2*h**2. What is c in u(c) = 0?
-1, 2
Let d(t) = 3*t**4 - 5*t**3 - 3*t**2 + t - 4. Let u(x) = 2*x**4 - 4*x**3 - 2*x**2 + x - 3. Let k = -14 + 10. Let s(a) = k*u(a) + 3*d(a). Factor s(j).
j*(j - 1)*(j + 1)**2
Let n(q) be the third derivative of q**6/40 - 3*q**5/10 + q**4 + 2*q**2 - q. Solve n(a) = 0 for a.
0, 2, 4
Let b(p) be the third derivative of -p**5/270 + p**4/18 - p**3/3 + 7*p**2. Factor b(f).
-2*(f - 3)**2/9
Let v(f) = -f - 5. Let j be v(-7). Suppose j*b = 5*b - 3. Suppose 3 + 2*u**2 - 2 - b = 0. What is u?