0. Let i(o) = -2*o**4 - o**3 + o**2 + o - 1. Let j(a) = 30*i(a) - 3*n(a). Factor j(r).
3*r*(r - 2)*(r - 1)*(r + 1)
Suppose 3*r + 2 - 11 = 0. Let j be -2 - 3*16/(-12). Factor 0*p**5 - j*p**5 - p**2 + p**4 + p**5 + p**3 + 0*p**r.
-p**2*(p - 1)**2*(p + 1)
Let n(r) be the second derivative of -r**5/40 - r**4/12 + 61*r. Find l, given that n(l) = 0.
-2, 0
Let u = -7 + 9. Factor 3*x - x + 7*x**u - 7*x**2 + x**2.
x*(x + 2)
Suppose -4*q + 106 = -0*f + 2*f, -3*q - 5*f + 97 = 0. Suppose g = -3*p - 10 + 27, -4 = -p - 2*g. Suppose q*o + 3*o**2 + 17 - p*o + 10 = 0. Calculate o.
-3
Let k(w) be the second derivative of 2/9*w**3 + 0 + 1/90*w**4 + 17*w + 5/3*w**2. Find m, given that k(m) = 0.
-5
Suppose -4*m = -m - 15. Let s be 0 + (5 - 3/1). Determine k, given that k + s*k**2 - 8*k**2 - m*k - 2*k**3 + 0*k**3 = 0.
-2, -1, 0
Let n(k) be the first derivative of -k**4 - 128*k**3/3 + 280*k**2 - 576*k - 293. Find b, given that n(b) = 0.
-36, 2
Let -8/11*r - 32/11*r**2 + 68/11*r**4 + 0 + 42/11*r**5 + 2/11*r**3 = 0. What is r?
-1, -2/7, 0, 2/3
Suppose -f - 5*a = -208, 2*f = 6*f - 5*a - 732. Let k = 191 - f. Factor -7/6*z**2 - 5/6*z**4 + 3/2*z**k + 0 + 1/3*z + 1/6*z**5.
z*(z - 2)*(z - 1)**3/6
Suppose 177*r**2 - 7*r**3 + 7*r + 20*r**4 - 176*r**2 - 21*r**4 = 0. What is r?
-7, -1, 0, 1
Let p(c) be the third derivative of c**7/168 + c**6/16 + c**5/16 - 25*c**4/48 + 661*c**2. Factor p(d).
5*d*(d - 1)*(d + 2)*(d + 5)/4
Let m = 58958/55 + -11774/11. Factor 0*p - 4/5*p**2 + 0 + 2*p**3 - m*p**4 + 2/5*p**5.
2*p**2*(p - 2)*(p - 1)**2/5
Let g(s) be the second derivative of -21 + 2/5*s**3 + 0*s**2 - 7/20*s**4 + 1/50*s**6 + 3/50*s**5 - 2*s. Let g(d) = 0. Calculate d.
-4, 0, 1
Factor -4/25*f - 2/25*f**2 + 6/25.
-2*(f - 1)*(f + 3)/25
Let c(l) = 28*l**4 + 29*l**3 + 33*l**2 + 30*l + 37. Let d(j) = 13*j**4 + 14*j**3 + 17*j**2 + 16*j + 18. Let r(g) = -6*c(g) + 13*d(g). Solve r(h) = 0.
-3, -2, -1
Let l(a) = -a**2 - 10*a + 21. Let b be l(-11). Factor -5*s**3 + 4*s**2 + b + 7*s**3 + 3*s**3 + 25*s + 16*s**2.
5*(s + 1)**2*(s + 2)
Let y be 0*(3 + -6 + 4). Suppose y*a = -4*a + 12. Factor -2 - 2*h**2 + h**2 - 7*h + 6*h + h**a + 3*h**2.
(h - 1)*(h + 1)*(h + 2)
Let y be 4 + (-164)/42 - 0. Let d(n) be the first derivative of 0*n + 7 - 2/7*n**2 + y*n**3. Determine q, given that d(q) = 0.
0, 2
Let -64/9*o**3 + 0 - 256/9*o**2 - 2/9*o**5 + 0*o + 28/9*o**4 = 0. What is o?
-2, 0, 8
Let a(z) = 12*z**4 - 68*z**3 + 77*z**2 + 32*z + 5. Let i(f) = 12*f**4 - 68*f**3 + 78*f**2 + 32*f + 6. Let t(q) = -6*a(q) + 5*i(q). Factor t(h).
-4*h*(h - 4)*(h - 2)*(3*h + 1)
Let o(s) be the second derivative of s**7/14 + 3*s**6/10 - 3*s**5/20 - 3*s**4/4 - 11*s + 1. Factor o(t).
3*t**2*(t - 1)*(t + 1)*(t + 3)
Let s(t) be the first derivative of t**6/12 + 4*t**5/5 + 9*t**4/4 + 8*t**3/3 + 5*t**2/4 - 392. Factor s(z).
z*(z + 1)**3*(z + 5)/2
Suppose -4*k - 4*h = -12, h - 4 = -3*k + 5. Suppose -o + k*o - 272 = 0. Factor -4*j + 18*j**2 + 136 - o.
2*j*(9*j - 2)
Let r(n) = n**3 + 16*n**2 - 20*n - 3. Let h(p) = -6*p**3 - 97*p**2 + 120*p + 17. Let t(l) = 6*h(l) + 34*r(l). Suppose t(u) = 0. What is u?
-20, 0, 1
Suppose -y + 5*t + 7 = 0, 2*y + 0*t = 5*t + 9. Factor -2*k**y + 29 + 9*k**2 - 4*k - 32.
(k - 1)*(7*k + 3)
Let u = 6 + -3. Factor 14*w**5 + 8*w**3 + 9*w**u + 27*w**3 - 26*w**2 + 4*w - 46*w**4 + 10*w**3.
2*w*(w - 1)**3*(7*w - 2)
Suppose -a - 6 - 1 = -3*h, -3*a + 5*h - 9 = 0. Suppose 0 = 3*t - 5*s - 1, 4*s + 2 - 6 = 0. Find f such that t*f**4 - 2/3*f**3 + 2/3*f + 0 - a*f**2 = 0.
-1, 0, 1/3, 1
Find g such that 4*g**2 - 4*g**4 - 12/5*g**5 - 8/5*g + 0 + 4*g**3 = 0.
-2, -1, 0, 1/3, 1
Let l(d) be the second derivative of d - 1/36*d**4 - 7/18*d**3 - 2 + 0*d**2. Factor l(k).
-k*(k + 7)/3
Let s = -41 + 44. Factor -2*b**3 + b**3 + 60*b + 6*b**s - 30*b**2 - 23 - 17.
5*(b - 2)**3
Suppose -9*w + 6*w + 120 = 0. Suppose -15*q + w = -10*q. Factor -2*z**2 + 3*z**3 - 10*z**2 + 4*z + q*z.
3*z*(z - 2)**2
Suppose 9 = v + 4. Find f, given that 1632*f - 1632*f - v*f**2 = 0.
0
Suppose -122 = -30*g + 28. Let l(x) be the third derivative of 0*x**g + 0*x + 0*x**4 + 1/720*x**6 + 0 + 3*x**2 + 0*x**3. Factor l(m).
m**3/6
Suppose 0 = -10*w - 947 + 287. Let l = w - -265/4. Let 1/2*u**4 - u**2 + u + l*u**5 + 0 - 3/4*u**3 = 0. What is u?
-2, 0, 1
Let u = -20 + 22. Solve -2*o + o**4 + 2*o**u + 124*o**3 - o**4 - 2*o**4 - 122*o**3 = 0 for o.
-1, 0, 1
Let b(g) be the second derivative of -g**6/15 + 13*g**5/20 - g**4/6 - 9*g**3/2 + 9*g**2 + 108*g. Suppose b(c) = 0. Calculate c.
-3/2, 1, 6
Let a be (9/63)/((-9)/441) + 11. Suppose 3*n + 6*n**2 + 15/4*n**5 - 6*n**a - 27/4*n**3 + 0 = 0. Calculate n.
-1, -2/5, 0, 1, 2
Let t(p) be the first derivative of -9/2*p**2 + 9/5*p**5 + 15 + 21/4*p**4 - 6*p + 3*p**3. Determine m so that t(m) = 0.
-1, 2/3
Let s(o) be the first derivative of -14 - 4/15*o**3 + 0*o**2 + 0*o - 1/5*o**4. Let s(b) = 0. Calculate b.
-1, 0
Let t = -279396 + 54482474/195. Let h = -4/39 + t. Factor 27/5*l**2 + 0 - h*l.
3*l*(9*l - 2)/5
Let b(g) = 2*g - 6. Let m(o) = -7*o + 24. Let y(s) = -22*b(s) - 6*m(s). Let w be y(-7). Factor -1/3*l + 0 + 1/2*l**w.
l*(3*l - 2)/6
Let v be (4 - -2)*9/324. Factor v*d**2 + 2/3*d + 1/2.
(d + 1)*(d + 3)/6
Suppose -38*k - 2*w = -43*k - 4, -3*k + 41 = 5*w. Factor 0 - 5/2*p**2 - p - 1/2*p**4 - k*p**3.
-p*(p + 1)**2*(p + 2)/2
Suppose -540*f + 534*f = -18. Let m(p) be the second derivative of -5*p + 0*p**2 - 1/27*p**4 + 1/90*p**5 + 1/135*p**6 + 0 + 0*p**f. Solve m(c) = 0 for c.
-2, 0, 1
Let y(r) be the second derivative of r**5/35 + 26*r**4/21 - 2*r**3/21 - 52*r**2/7 - 745*r. Suppose y(v) = 0. Calculate v.
-26, -1, 1
Let t(n) be the third derivative of 1/5*n**5 + 0 - 1/30*n**6 - 2/105*n**7 + 5*n**2 + 0*n + 4/3*n**3 + 5/6*n**4. What is f in t(f) = 0?
-1, 2
Let w(b) = -10*b + 39*b + 1 + 5 + 34*b**2. Let x(y) = -y**2. Let z(i) = -5*w(i) - 30*x(i). Factor z(u).
-5*(4*u + 3)*(7*u + 2)
Let d(i) be the second derivative of -i**7/28 - 11*i**6/60 + 19*i**5/40 - 5*i**4/24 - 8*i + 17. What is w in d(w) = 0?
-5, 0, 1/3, 1
Let t(a) be the third derivative of -a**5/180 + 5*a**4/72 + 7*a**3/9 + 2*a**2 - 10. Suppose t(m) = 0. What is m?
-2, 7
Let m(q) be the first derivative of -1/2*q**2 + 33 + 0*q - 1/3*q**3. Factor m(z).
-z*(z + 1)
Let r(d) be the third derivative of 7*d**6/960 - 23*d**5/24 - 11*d**4/16 - 171*d**2. Suppose r(q) = 0. Calculate q.
-2/7, 0, 66
Suppose 0 = -h + 4*s - 0*s - 99, -99 = h + 4*s. Let k = 498/5 + h. Suppose -6/5 - k*b**2 - 9/5*b = 0. Calculate b.
-2, -1
Solve 48/5 + 0*a**2 + 52/5*a - 4/5*a**3 = 0.
-3, -1, 4
Suppose -254*o + 224*o + 60 = 0. Determine h, given that 2/3*h**2 + o*h**3 - 2/3*h**4 - 2*h + 0 = 0.
-1, 0, 1, 3
Let j = 21155 + -21153. What is x in 2/13*x**j + 0 - 4/13*x + 2/13*x**3 = 0?
-2, 0, 1
Solve 3/2*u - 9/2*u**2 - 3/2*u**3 + 3*u**4 + 3/2 = 0 for u.
-1, -1/2, 1
Let a(t) be the second derivative of 4*t**3 + 0 + 5*t + 4*t**4 + 3/2*t**2. Let a(z) = 0. Calculate z.
-1/4
Let a be 3/1 + 33 + (1 - 5). Let t = -92/3 + a. Suppose -t*p - 4/3*p**2 + 8/3 = 0. Calculate p.
-2, 1
Suppose -17*g + 19*g = -2*q - 4, 4*g = 5*q - 26. Factor -6/7*d**q + 3/7*d**3 - 9/7*d + 0.
3*d*(d - 3)*(d + 1)/7
Determine i so that 704*i + 369 - 81 + 112*i + 248*i**2 + 20*i**3 = 0.
-6, -2/5
Let v(k) = k**2 + 1. Let i(s) = -s. Let f(b) = -3*b**2 - b. Let d(x) = f(x) - 6*i(x). Let a(y) = -3*d(y) + 3*v(y). Factor a(g).
3*(g - 1)*(4*g - 1)
Suppose 0 = -3*h + 2*b - 0*b + 577, -4*h + 4*b + 772 = 0. Factor 206*x**2 + h*x**2 + 245*x**3 + 160*x - 31*x**2 + 19*x**2 + 20.
5*(x + 1)*(7*x + 2)**2
Let x = 1334 - 3998/3. Let l = 6 - 4. Factor -4*h - x + 4/3*h**5 + 4*h**4 + 8/3*h**3 - 8/3*h**l.
4*(h - 1)*(h + 1)**4/3
Let 2/7*m**5 + 0*m**4 + 8/7*m - 10/7*m**3 + 0 + 0*m**2 = 0. What is m?
-2, -1, 0, 1, 2
Solve 4/3*n**2 + 112/3*n + 0 = 0.
-28, 0
Let j(n) = -5*n**2 - 251*n - 40. Let v(h) = 5*h**2 + 252*h + 30. Let o(w) = 3*j(w) + 4*v(w). Suppose o(s) = 0. What is s?
-51, 0
Let x(t) be the third derivative of t**7/70 - t**6/15 + 7*t**5/60 - t**4/12 - 9*t**2 + 2*t. Suppose x(s) = 0. Calculate s.
0, 2/3, 1
Let c = -3813/2 - -1907. Factor 0*u + c*u**3 - 1/2*u**2 + 0.
u**2*(u - 1)/2
Suppose -36*y**4 - 76*y**3 + 0*y**5 - 12*y**2 + 48 + 4157*y - 4*y**5 - 4077*y = 0. Calculate y.
-6, -2, -1, 1
Let x(c) be the first derivative of 5*c**8/336 + c**7/42 - c**6/12 + c**2/2 + 15*c + 