**4/18 - 3*q**3/2 + 13*q. Let m(j) be the second derivative of i(j). Factor m(b).
2*(b - 1)**2*(5*b + 2)/3
Let j be (-81)/567*(3 - 2)/(-1). Let j*b**2 - 4/7 + 0*b = 0. What is b?
-2, 2
Let b(u) be the third derivative of 0*u**4 - 1/540*u**6 + 0*u + 1/270*u**5 - 15*u**2 + 0*u**3 + 0. Let b(p) = 0. Calculate p.
0, 1
Let s = -50 + 48. Let w(d) = -2*d**2 + 13*d. Let v(b) = -3*b**2 + 12*b. Let m(z) = s*w(z) + 3*v(z). Factor m(c).
-5*c*(c - 2)
Let f(s) be the first derivative of -10/21*s**3 + 10/7*s - 9 + 1/7*s**2 - 1/14*s**4. Factor f(k).
-2*(k - 1)*(k + 1)*(k + 5)/7
Let z(m) = -45*m + 12. Let s be z(-6). Factor -1296*w + 947*w**4 + s*w**2 - 1948*w**3 + 243 - 179*w**4 - 356*w**3 + 2310*w**2.
3*(4*w - 3)**4
Let x(l) = 10*l**4 + 64*l**3 - 98*l**2 + 72*l + 16. Let v(r) = 3*r**4 + 21*r**3 - 33*r**2 + 24*r + 5. Let n(m) = -16*v(m) + 5*x(m). Let n(j) = 0. Calculate j.
0, 1, 3, 4
Let x(q) = 45*q**2 - 172*q + 144. Let s(w) = 8*w**2 - 29*w + 24. Let z(b) = -34*s(b) + 6*x(b). What is p in z(p) = 0?
-24, 1
Let i(o) be the first derivative of 1/21*o**3 + 2/7*o**2 - 2 + 3/7*o. Solve i(q) = 0.
-3, -1
Let u(q) be the third derivative of q**5/40 - 3*q**4/4 + 27*q**3/4 - 277*q**2. Factor u(p).
3*(p - 9)*(p - 3)/2
Find h such that -16*h**2 - 15*h**2 + 46*h**2 - 5*h - 20*h**2 = 0.
-1, 0
Let m(g) = -19*g**2 - 13*g. Let n(c) = 28*c**2 + 15491 - 15491 + 20*c. Let t be 2 + 2*14/(-4). Let w(q) = t*n(q) - 8*m(q). Factor w(x).
4*x*(3*x + 1)
Suppose 0 = -2*z + 2*u + 3*u + 9, -3*u = 3. Factor 10/3*r**z + 2/3*r**3 + 8/3 + 16/3*r.
2*(r + 1)*(r + 2)**2/3
Let r(j) be the third derivative of -j**6/600 - j**5/100 - j**4/60 - 492*j**2. Find d, given that r(d) = 0.
-2, -1, 0
Let x(f) be the first derivative of -f**5/20 - 7*f**4/16 - 17*f**3/12 - 17*f**2/8 - 3*f/2 + 39. Let x(g) = 0. What is g?
-3, -2, -1
Let a(n) be the second derivative of -n**8/1344 + n**7/504 + n**6/72 + 7*n**4/4 - 18*n. Let v(x) be the third derivative of a(x). Solve v(s) = 0.
-1, 0, 2
Let p(m) be the third derivative of -m**6/180 + m**5/90 + m**4/36 - m**3/9 + 26*m**2 - m. Factor p(c).
-2*(c - 1)**2*(c + 1)/3
Let g(a) = 6*a + 134. Let h be g(-22). Factor 0*d - 1/4*d**4 + 1/8*d**5 - 3/8*d**3 + 0*d**h + 0.
d**3*(d - 3)*(d + 1)/8
Let r(j) be the first derivative of j**5 + 25*j**4/2 + 160*j**3/3 + 80*j**2 - 353. Factor r(h).
5*h*(h + 2)*(h + 4)**2
Find p such that -1785*p**5 + 18*p**2 + 85*p + 17*p**2 - 100*p**3 - 30 + 15*p**2 - 20*p**4 + 1800*p**5 = 0.
-2, -1, 1/3, 1, 3
Factor 6 - 28/5*w - 2/5*w**2.
-2*(w - 1)*(w + 15)/5
Let i = 16 - 7. Let r = i - 5. Suppose 4*f**2 - 2*f**2 + 4*f - r*f**2 + 4*f**2 = 0. What is f?
-2, 0
Let j be 2*(-8)/16*-3. Find r, given that 3/2*r**2 - 1/2*r**4 - 1 - 1/2*r + 1/2*r**j = 0.
-1, 1, 2
Let t(u) be the third derivative of 1/30*u**3 - 44*u**2 + 1/300*u**5 + 0 + 0*u - 1/60*u**4. What is q in t(q) = 0?
1
Let f be 496/36 + (-10)/(-45). Let z = f + -11. Factor 9*w**4 - 9*w**5 + 2*w**3 + 6*w**4 - 8*w**z.
-3*w**3*(w - 1)*(3*w - 2)
Let t(n) be the third derivative of -3/8*n**4 + 17*n**2 + 0*n - 2*n**3 + 0 + 1/20*n**5. Solve t(p) = 0.
-1, 4
Let o(f) be the second derivative of -f**8/10080 - f**7/945 + f**6/216 - 3*f**4/4 - 10*f. Let n(g) be the third derivative of o(g). Find s such that n(s) = 0.
-5, 0, 1
Let g(y) be the second derivative of y**7/147 + 2*y**6/21 + 17*y**5/70 + 4*y**4/21 + 183*y. Factor g(s).
2*s**2*(s + 1)**2*(s + 8)/7
Let v(m) be the second derivative of -m**5/10 + 4*m**4 - 39*m**3 - 338*m**2 + 7*m - 1. Factor v(a).
-2*(a - 13)**2*(a + 2)
Let z(d) be the second derivative of -2*d**6/15 - 14*d**5/5 - 19*d**4 - 24*d**3 + 216*d**2 + 73*d + 2. Suppose z(j) = 0. Calculate j.
-6, -3, 1
Let q(g) be the third derivative of g**9/7560 + g**8/1680 + g**7/1260 + g**4/8 - 3*g**2. Let z(w) be the second derivative of q(w). Factor z(p).
2*p**2*(p + 1)**2
Let r(f) = -f - 1. Let l(z) = -z - 1. Let p(k) = 2*l(k) - r(k). Let a be p(-1). What is x in x - x + a - 3*x - 2 - x**2 = 0?
-2, -1
Suppose 3*n + 4*k - 71 = 0, 3*k = -6*n + 2*n + 90. Find f, given that 12 + 12*f**3 + 44*f + 72*f**2 - n*f**2 + 16*f = 0.
-2, -1/4
Let w(l) = -12*l**2 - 83*l + 26. Let b(k) = 2*k**2 + k + 2. Let a(v) = -6*b(v) + 2*w(v). Let a(y) = 0. What is y?
-5, 2/9
Let q(j) = j**3 - 2*j**2 + 192*j - 476. Let i(k) = 2*k**3 - 7*k**2 + 576*k - 1429. Let f(h) = -4*i(h) + 11*q(h). What is r in f(r) = 0?
-10, 4
Suppose 3*c - 10 = c. Find y, given that 2*y**c + 2*y**2 + 3*y**4 + 0*y**4 + 0*y**4 - 5*y**4 - 2*y**3 = 0.
-1, 0, 1
Suppose 25 = 5*i + 5*n, -4*n + n - 3 = -3*i. Suppose 15 = -2*g - 3*j, 5*g + 4*j + 5 = i*j. Factor -1/3*q**4 - 1/3*q**5 + 0*q**2 + 0*q**3 + g*q + 0.
-q**4*(q + 1)/3
Let m(b) be the third derivative of -b**5/210 + 83*b**4/42 - 6889*b**3/21 + 14*b**2 + 11*b. Factor m(y).
-2*(y - 83)**2/7
Let g = 7937/8 + -992. Let t(r) be the third derivative of 0 + 1/20*r**6 - 5*r**2 + 1/8*r**5 + 0*r**3 + g*r**4 + 1/140*r**7 + 0*r. Factor t(z).
3*z*(z + 1)**2*(z + 2)/2
Let d(n) = -n**2 + 5*n - 2. Let k(y) = -y**3 - y**2 + y + 2. Let w be k(-2). Let f be d(w). Solve -6*r + r - r**3 + 4*r - 2*r**f = 0 for r.
-1, 0
Factor -2 - 12*c - 49/8*c**4 + 21*c**3 - 11*c**2.
-(c - 2)**2*(7*c + 2)**2/8
Let h(n) be the first derivative of -n**6/1080 - n**5/36 - 25*n**4/72 - 17*n**3/3 + 15. Let w(o) be the third derivative of h(o). Determine y so that w(y) = 0.
-5
Let z be (0 - 0) + (3 - 3). Suppose -3*n + n + 6 = z. Factor 2*o**3 + 0*o**3 + 21*o**2 - 5*o**n - 45*o + 27 + 0*o**3.
-3*(o - 3)**2*(o - 1)
Let u be (3 - 1)*(-178)/36. Let a = -86/9 - u. Determine y, given that 0 + y**2 - 1/3*y**3 - y**4 - a*y**5 + 2/3*y = 0.
-2, -1, 0, 1
Determine c, given that 55*c**3 + 30*c**4 + 42*c + 30*c**2 + 5*c**5 + 36*c - 78*c = 0.
-3, -2, -1, 0
Let i(o) be the second derivative of 1/4*o**4 - 9/2*o**2 + 11*o + 0 - o**3. What is c in i(c) = 0?
-1, 3
Let v(c) be the third derivative of -4/135*c**5 + 0*c + 0*c**3 + 0 + 5*c**2 - 5/216*c**4 - 1/60*c**6 - 1/3024*c**8 - 4/945*c**7. What is r in v(r) = 0?
-5, -1, 0
Let g(u) be the second derivative of u**5/70 - 37*u**4/14 + 1369*u**3/7 - 50653*u**2/7 - 88*u. Suppose g(h) = 0. Calculate h.
37
Let o = 1422 - 1422. Factor -4/7*w**3 + o*w + 0 - 4/7*w**2.
-4*w**2*(w + 1)/7
Let z(s) be the first derivative of s**4/28 - 5*s**3/21 + s**2/7 + 8*s/7 - 41. Solve z(b) = 0 for b.
-1, 2, 4
Factor 25*s**3 - 3*s**2 - 160*s - 23*s**3 - 168 - 31*s**2.
2*(s - 21)*(s + 2)**2
Let k(o) = -2*o + 2. Let r be k(-2). Let x(a) = 75*a**2 - 21*a + 11. Let u(q) = -15*q**2 + 4*q - 2. Let c(w) = r*x(w) + 33*u(w). Factor c(g).
-3*g*(15*g - 2)
Let t(w) be the second derivative of -w**5/20 - 3*w**4/8 - 9*w**2 + w. Let u(v) be the first derivative of t(v). Factor u(k).
-3*k*(k + 3)
Suppose -2*r - 8 = -2*v, 1 = r - 0. Factor -g**2 + 2*g**2 - v + 8*g - 15*g + 11*g.
(g - 1)*(g + 5)
Let k = 3532 + -45944/13. Let l = k - -192/65. Let 8/5*d**2 + 12/5*d**3 + 0 - l*d = 0. Calculate d.
-1, 0, 1/3
Let p(y) = -y**2 - 1210*y + 73187. Let d(s) = s**2 + 2420*s - 146377. Let x(w) = -6*d(w) - 11*p(w). Factor x(z).
5*(z - 121)**2
Factor -34*n**2 + 15*n**3 + 5*n**4 - 45*n + 14*n**2 + 45*n.
5*n**2*(n - 1)*(n + 4)
Let m(f) be the second derivative of -f**6/60 - 11*f**5/20 - 121*f**4/24 - 4*f + 7. Factor m(d).
-d**2*(d + 11)**2/2
Let d(h) = 2*h**2 + h - 2*h**3 + 0*h**3 - h**3. Let x(i) = -4*i - 9*i**2 + 13*i**3 - 294 + 294. Let y(n) = 9*d(n) + 2*x(n). Factor y(c).
-c*(c - 1)*(c + 1)
Let d be 1*5 - (5 + -2). Suppose -r - d = -2*r. Factor -2*w**r + w**2 + 2 - 4 - 3*w.
-(w + 1)*(w + 2)
Suppose 3*y = 3*t - 6 - 0, -4*t + 5*y + 7 = 0. Suppose 0 = -2*h - 8, -7 - 7 = -k + t*h. Find v, given that 2/3*v**5 + 0 + 0*v**k - v**4 + 1/3*v**3 + 0*v = 0.
0, 1/2, 1
Let y = -280 + 280. Let r(d) be the third derivative of 6*d**2 + 0 + y*d**3 + 0*d**5 + 0*d + 0*d**4 + 1/40*d**6. Factor r(i).
3*i**3
Suppose 5*o - 3*o = 5*a - 8, o + 4 = -5*a. Let c = a - -5. Determine p so that 0*p**2 + 4*p + 0*p - 9*p**2 + c*p**3 + p**2 - p**4 = 0.
0, 1, 2
Let v(o) be the second derivative of o**4/6 - 122*o**3/3 + 3721*o**2 - o - 188. Factor v(q).
2*(q - 61)**2
Let w be (40/884)/(74/1258). Find n, given that w*n + 2/13*n**2 + 12/13 = 0.
-3, -2
Let i be (115/2300)/((-2)/(-80)). Find f, given that 0 + 8/7*f**i + 0*f + 0*f**3 - 2/7*f**4 = 0.
-2, 0, 2
Let a be (-5278)/377*(0 - 6/7). Let o(j) be the first deriva