4 - 1/60*q**6 + 3*q + 0*q**2 + 0. Factor u(s).
-s**3*(s - 1)/2
Let y(t) be the third derivative of t**6/420 + t**5/70 + t**4/42 - 2*t**2. Factor y(u).
2*u*(u + 1)*(u + 2)/7
Let t(x) be the first derivative of -x**7/126 + x**6/90 - x - 4. Let r(n) be the first derivative of t(n). Find c, given that r(c) = 0.
0, 1
Suppose 0 = -4*i + s + 28, -11 + 31 = 5*s. Let c be (-5)/(-20) + 14/i. Find n such that -n**c - 3*n + 5*n**2 - n**2 = 0.
0, 1
Let t = -1075 + 4349/4. Let h = -12 + t. Factor -h*d + 0 + 1/4*d**3 + 0*d**2.
d*(d - 1)*(d + 1)/4
Factor 3/2*a**2 + a + 0 + 1/2*a**3.
a*(a + 1)*(a + 2)/2
Find n such that 0*n**3 + 0*n + 0 + 0*n**2 + 1/3*n**4 + 1/3*n**5 = 0.
-1, 0
Let x(g) = 12*g**4 - 9*g**3 - 3*g**2. Let h(o) = 3*o**4 - 2*o**3 - o**2. Let b(z) = -15*h(z) + 4*x(z). Factor b(v).
3*v**2*(v - 1)**2
Suppose 4*l + 4*l - 56 = 0. Let i(p) be the second derivative of 1/4*p**2 + 1/20*p**6 + 1/3*p**4 + 3/8*p**3 + 0 + p + 7/40*p**5 + 1/168*p**l. Factor i(t).
(t + 1)**4*(t + 2)/4
Let c be 8 + (-3 - (-1)/(-1)). Factor -a**3 - c - 9*a**2 + 13*a**2 - a**3 + 2*a.
-2*(a - 2)*(a - 1)*(a + 1)
Let z be -2 + 2 - 24/(-8). Determine p, given that -15*p**2 - 6*p + 0*p**3 - 5*p**3 + 4*p**3 + 22*p**z = 0.
-2/7, 0, 1
Suppose -4*m + 0*m - 6 = 2*o, 31 = -4*m + 3*o. Let k(n) = n**3 - n**2 + n - 1. Let i(y) = -6*y**3 + 9*y**2 - 10*y + 7. Let f(l) = m*i(l) - 20*k(l). Factor f(d).
4*(d - 2)*(d - 1)**2
Determine h so that -2/5*h**2 - 13/5*h**3 - 9/5*h**5 - 24/5*h**4 + 0 + 0*h = 0.
-2, -1/3, 0
Let v = -19 + 21. Suppose -v*a - 2*b = -2, -4 = -4*b + 8*b. Let 2/3*u + 0 + 2/3*u**a = 0. What is u?
-1, 0
Let b(t) be the first derivative of -t**4/20 - t**3/15 - 18. Solve b(k) = 0.
-1, 0
Let a be 4 - 156/(-90)*(-6)/4. Suppose 14 = 2*i + 4. Suppose 6/5*u**i + 0*u - 6/5*u**3 + 8/5*u**2 - a*u**4 - 1/5 = 0. What is u?
-1, -1/3, 1/2, 1
Let r(u) = 13*u**3 + 45*u**2 + 64*u + 37. Let a(w) = 84*w**3 + 292*w**2 + 416*w + 240. Let d(h) = -5*a(h) + 32*r(h). Factor d(x).
-4*(x + 1)*(x + 2)**2
Determine p so that -416*p**2 + 679*p**4 - 512*p**5 - 3 - 66*p - 1578*p**4 - 1216*p**3 - 637*p**4 - 1 = 0.
-2, -1/4
Let s(x) = 2*x**2. Let a be s(-1). Factor -4*z - a*z**3 + z - z**3 - z**2 + 7*z**2.
-3*z*(z - 1)**2
Let w(m) be the first derivative of -49*m**6/15 + 77*m**5/10 - 16*m**4/3 + 4*m**3/3 - 2*m + 3. Let p(r) be the first derivative of w(r). Factor p(g).
-2*g*(g - 1)*(7*g - 2)**2
Let u(n) = -n**2 + 31*n + 3. Let o be u(31). Factor 0*b**2 - 1/7*b**5 - 1/7*b + 0 + 0*b**4 + 2/7*b**o.
-b*(b - 1)**2*(b + 1)**2/7
Let r be 9268/(-2318) + -6 + 10. Let q = 2340/12749 - r. Let 4/11*t + q*t**2 + 0 = 0. What is t?
-2, 0
Suppose 4*f**2 + 7 - 20 + 9 = 0. What is f?
-1, 1
Suppose -c = -2*q - 2, 0*c = 3*c - q - 6. Suppose 11/4*h**c - 3*h**5 - 11/4*h**4 + 0 + 1/2*h + 5/2*h**3 = 0. Calculate h.
-1, -2/3, -1/4, 0, 1
Let s(u) be the second derivative of -3*u + 1/108*u**6 + 0*u**2 + 1/2*u**3 - 1/18*u**4 + 0 + 1/60*u**5. Let d(h) be the second derivative of s(h). Factor d(t).
2*(t + 1)*(5*t - 2)/3
Let h(m) be the third derivative of m**6/360 - m**5/60 + m**4/24 - 2*m**3/3 + 2*m**2. Let y(a) be the first derivative of h(a). Factor y(n).
(n - 1)**2
Let c(y) be the first derivative of 0*y**3 + 0*y**2 + 0*y - 2 - 1/4*y**4. What is i in c(i) = 0?
0
Let q = 4 - 2. Factor 2/5*p + 2/5*p**4 + 2/5*p**5 + 2/5 - 4/5*p**q - 4/5*p**3.
2*(p - 1)**2*(p + 1)**3/5
Let z(d) = -14 + 5*d - 6*d**2 - 8 + 17. Let k(j) be the second derivative of j**3/6 + j**2/2 - j. Let l(a) = -3*k(a) - z(a). Solve l(b) = 0 for b.
1/3, 1
Let j(o) be the third derivative of 0*o + 0*o**3 + 1/4*o**4 - 6*o**2 - 1/30*o**5 + 0. Factor j(k).
-2*k*(k - 3)
Let l(g) = -g**2 - 6*g + 9. Let j(q) = -q**2 - q - 1. Let h be j(-3). Let p be l(h). Factor -p*v + 3 - 3 - 4*v**2 - 2*v**3 + 0*v.
-2*v*(v + 1)**2
Suppose f + 34 = 4*a, 5*a + 34 = -2*f - 21. Let k = 32 + f. Solve -12/7*j + 2/7*j**k + 18/7 = 0.
3
Let p(z) be the second derivative of z**6/135 - z**5/45 + z**4/54 + 5*z. Find w such that p(w) = 0.
0, 1
Let h(i) = i**4 + i**3 + 11*i**2 + 11*i - 3. Let f(b) = -10*b**2 - 10*b + 2. Let v(s) = -3*f(s) - 2*h(s). Factor v(y).
-2*y*(y - 2)*(y + 1)*(y + 2)
Determine j, given that -30*j**2 + 10 - 55 + 5*j**3 + 60*j + 5 = 0.
2
Let d(i) be the third derivative of -i**5/15 + 2*i**4/3 - 8*i**3/3 + 40*i**2. Find o, given that d(o) = 0.
2
Let k be 2/6 - (2/3 - 1). Factor 0 - 2/3*i - k*i**2.
-2*i*(i + 1)/3
Let h = -192 - -962/5. Factor -2/5 + 2/5*v**2 - h*v**3 + 2/5*v.
-2*(v - 1)**2*(v + 1)/5
Let j(y) be the second derivative of y**6/24 - 7*y**5/16 + 25*y**4/16 - 65*y**3/24 + 5*y**2/2 - 12*y. Factor j(t).
5*(t - 4)*(t - 1)**3/4
Let x(f) be the third derivative of f**4/24 - f**3 + 4*f**2. Let r be x(8). Factor -1/2*m**3 + 0*m**r + 0*m - 3/2*m**4 + 0.
-m**3*(3*m + 1)/2
Suppose -3*a + 39 = 10*a. Find g such that -2/9 - 14/9*g**2 + 10/9*g + 2/3*g**a = 0.
1/3, 1
Suppose 0 = -r - 6 + 15. Find v, given that -2*v + 3*v**2 - v + 1 + r*v**3 - 2*v = 0.
-1, 1/3
Factor -4*j**2 + 0*j**2 - 6*j**2 - j**3 - 9*j + 4*j**2.
-j*(j + 3)**2
Suppose 3/5*c**3 + 1/5*c + 0 + 1/5*c**4 + 3/5*c**2 = 0. What is c?
-1, 0
Suppose 9*o - 4*o - 10 = 0. Suppose 4*h + h - k = 9, -3*h - 4*k + 10 = 0. Factor -h*j - 3*j**2 - j**2 + o*j**3 + 2*j**2 + 2*j**4.
2*j*(j - 1)*(j + 1)**2
Let p be -2*(3/6 + -1). Let o be 4 - p/1*2. What is q in o*q - 2*q**4 + q**5 + q**5 - 2*q = 0?
0, 1
Let y(p) be the second derivative of p**4/48 - p**3/2 + 9*p**2/2 + 11*p. Factor y(a).
(a - 6)**2/4
Let u(f) be the first derivative of f**4/36 + f**3/9 + f + 3. Let b(q) be the first derivative of u(q). What is v in b(v) = 0?
-2, 0
Suppose 3*z + 5 = 20. Suppose -2*x = -q + 9, -q + z*x = -4*q - 6. Factor 0*c**q - 2/3*c**4 + 4/3*c + 0 + 2*c**2.
-2*c*(c - 2)*(c + 1)**2/3
Let k(c) = -c + 9. Let g be k(6). Suppose -2*j + g*x + 0 = 3, -j + x = 0. What is y in 8/7*y**2 + 0 - 8/7*y - 2/7*y**j = 0?
0, 2
Let c(g) = 11*g**2 - 29*g + 19. Let p(z) = -5*z**2 + 14*z - 10. Let a(l) = -2*c(l) - 5*p(l). Factor a(i).
3*(i - 2)**2
Factor f**3 - 3*f + 2*f**3 - f**2 + 6*f + 7*f**2.
3*f*(f + 1)**2
Let w(k) = 2*k**4 + k**3 + 3*k**2 + 4*k. Let q(i) = -2*i**4 - 2*i**2 - 4*i. Let t(g) = 5*q(g) + 4*w(g). Determine p so that t(p) = 0.
-1, 0, 1, 2
Suppose 4*q = 3*q. Suppose q*a = -a. Find z, given that -6*z**2 - 4*z - z**4 - 4*z**3 + a*z**2 - 3 + 2 = 0.
-1
Let x = -149 - -151. Let c(q) be the second derivative of 1/40*q**5 + 1/24*q**4 - 1/12*q**3 - 1/4*q**x + 0 + q. Let c(n) = 0. Calculate n.
-1, 1
Suppose 4*n - 15 + 7 = 0. Factor 6/7*i + 2/7*i**n + 4/7.
2*(i + 1)*(i + 2)/7
Let d(l) be the third derivative of l**8/3024 + 2*l**7/315 + 47*l**6/1080 + 13*l**5/135 - 2*l**4/9 - 32*l**3/27 + 33*l**2. Determine s so that d(s) = 0.
-4, -1, 1
Suppose -2*n + 8 = -q, 0 = -2*q - 2*n - 2*n + 24. Let p = 3 + 10. Factor -p*d + q*d**3 + 2*d**2 + 13*d.
2*d**2*(d + 1)
Factor 8/3*p**3 + 0 - 2*p + 2/3*p**2.
2*p*(p + 1)*(4*p - 3)/3
Let x(t) be the second derivative of t**4/4 + 3*t**3/2 + 11*t. What is i in x(i) = 0?
-3, 0
Let s(m) = -6*m**2 - 12*m - 4. Let t(n) = -17*n**2 - 37*n - 13. Let o(q) = -7*s(q) + 2*t(q). Factor o(h).
2*(h + 1)*(4*h + 1)
Let l(c) be the third derivative of -1/3*c**3 - 2*c**2 - 1/8*c**4 + 0*c + 0 + 1/30*c**5. Solve l(o) = 0.
-1/2, 2
What is h in 0 + 0*h**4 + 0*h + 0*h**2 + 4/3*h**3 - 4/3*h**5 = 0?
-1, 0, 1
Find v such that -5/3*v**2 + 3 - v - 1/3*v**3 = 0.
-3, 1
Let r(b) = -3*b - 1. Let p be r(3). Let a be 3/45 - 6/p. Suppose -a*v**2 + 4/3 - 2/3*v = 0. What is v?
-2, 1
Let d(i) be the first derivative of i**5 + 5*i**4/4 - 5*i**3/3 - 5*i**2/2 + 1. Factor d(m).
5*m*(m - 1)*(m + 1)**2
Let g be 369/54 - (-1)/6. Solve 8*b**2 - 3*b**3 + 6*b**5 + g*b**3 - 2*b - 4 - 4*b**4 - 8*b**5 = 0 for b.
-2, -1, 1
Suppose -c + 3*n + 14 = 0, -c - 23 = 2*c + 4*n. Let w be (-18)/(-30)*(c + 10). Let -81/5*m - 3/5*m**3 + w*m**2 + 81/5 = 0. Calculate m.
3
Let m(y) = -y**3 + 10*y**2 - 13*y + 8. Let z be m(9). Let t be 2/(-12) + z/(-72). Find x such that 0*x**2 + t*x**3 - 4/9 - 2/3*x = 0.
-1, 2
Let m(k) = 3*k**2 - 15*k - 16. Let d be m(-1). Let 6/5*q**d - 2/5*q + 0 = 0. What is q?
0, 1/3
Let h be ((-18)/27)/(1*(-13)/9). Factor -2/13*r**2 - h*r**3 - 6/13*r**4 - 2/13*r**5 + 0*r + 0.
-2*r**2*(r + 1)**3/13
Factor 0*y - 2/13*y**2 + 0 - 2/13*y**3.
-2*y**2*(y + 1)/13
Suppose 12 = p + 9. Let h(f) be the first derivati