 11)*(m - 2)*(m - 1)
Let a(n) be the first derivative of 0*n + 2/15*n**3 - 13 - 2/25*n**5 + 1/5*n**2 - 1/10*n**4. Factor a(t).
-2*t*(t - 1)*(t + 1)**2/5
Suppose 0 = 7*m + 12 - 26. Solve 3*d**5 - 4*d**4 + d**2 - 5*d**m - d - 2*d**5 + 2*d + 6*d**3 = 0.
0, 1
Suppose 2*y - 5*n + 25 = 0, n = 5*n - 20. Suppose 14 = u - 4*o, -u - 4*o - 5 - 5 = 0. Find g such that -2/3*g**u + y + 1/3*g + 1/3*g**3 = 0.
0, 1
Let a(v) = v**2 + 2*v - 9. Let q be a(-4). Let s be q/(-2) + 60/8. Determine w so that 40*w - 40*w + s*w**3 - 2*w**2 = 0.
0, 1/4
Let r(w) = 2*w**3 - 5*w**2 + 3*w - 6. Let o be r(4). Solve 129*a**3 + 2 + 486*a**2 - 980*a**3 - o*a - 607*a**3 = 0.
1/9
Let z be (45 - 41)*(2/(-8) - -1). Let r(y) be the third derivative of 0 - 1/32*y**4 + 10*y**2 - 1/48*y**5 + 1/12*y**z + 0*y. Find f such that r(f) = 0.
-1, 2/5
Let k(b) be the first derivative of -2*b**5/5 - 29*b**4/2 + 2*b**3 + 89*b**2 + 116*b + 890. Find w, given that k(w) = 0.
-29, -1, 2
Factor -1345 + n**3 - 7*n**3 - 2006 + 2*n**3 - 1833 - 5472*n - 292*n**2.
-4*(n + 1)*(n + 36)**2
Let d = -838 - -841. Let g(j) be the third derivative of 0*j + 0 + 1/660*j**6 + 1/1155*j**7 - 5*j**2 - 1/110*j**5 - 5/132*j**4 - 2/33*j**d. Factor g(s).
2*(s - 2)*(s + 1)**3/11
Suppose 3*l + 5*h + 10 = h, h = 3*l - 10. Suppose -3*x + 11 = l. Let -4*c**3 - 3*c**2 + 7*c**4 + 3*c**5 - 4*c**4 + c**x = 0. What is c?
-1, 0, 1
Let l(p) be the second derivative of p**5/110 - 37*p**4/66 + 391*p**3/33 - 867*p**2/11 - 121*p. Suppose l(z) = 0. Calculate z.
3, 17
Let f(u) be the first derivative of u**2 - 10 + 3*u + 1/9*u**3. Factor f(o).
(o + 3)**2/3
Let u(b) be the first derivative of -b**3/8 + 501*b**2/8 - 83667*b/8 - 443. Factor u(f).
-3*(f - 167)**2/8
Suppose -f = -2*f + 4*y - 150, 0 = -y. Let j be ((-20)/f)/((-6)/(-10)). Factor 2/9*k + j*k**2 + 0.
2*k*(k + 1)/9
Let y(m) be the first derivative of 2*m**3/3 + 4*m**2 - 63. Let y(o) = 0. What is o?
-4, 0
Determine f, given that 3/2*f**2 - 57/2*f + 27 = 0.
1, 18
Let i(k) be the second derivative of -5*k**7/84 - k**6/6 + 3*k**5/8 + 5*k**4/6 - 5*k**3/3 + 85*k. Factor i(t).
-5*t*(t - 1)**2*(t + 2)**2/2
Let p(b) = -b + 19. Suppose -8 = -i + 4*k, -2*i - 4*k + 8 + 32 = 0. Let v be p(i). Let -10*g**3 - 4*g**5 - 6*g**3 + 6*g**4 + 2*g**5 + 12*g**v = 0. What is g?
0, 1, 2
Let -5/4 + 1/8*k**5 + 1/2*k**4 + 23/8*k - k**3 - 5/4*k**2 = 0. What is k?
-5, -2, 1
Let a(c) be the second derivative of c**6/15 + 11*c**5/10 + 3*c**4/2 - 11*c**3/3 - 10*c**2 + 2*c + 104. Factor a(s).
2*(s - 1)*(s + 1)**2*(s + 10)
Let b be ((-7)/(-42) - 0)*(-15)/(-20). Let m(q) be the second derivative of -1/60*q**6 + 1/12*q**3 + 9*q + 0 - 1/40*q**5 + b*q**4 - 1/2*q**2. Factor m(a).
-(a - 1)**2*(a + 1)*(a + 2)/2
Suppose 1 = r, 0 = 5*b - 0*b - 3*r - 7. What is j in -8*j**b + 3*j**3 - 3*j + 7*j**2 + 3 - 2*j**2 = 0?
-1, 1
Let v(m) be the third derivative of 0*m + 8*m**2 + 2/9*m**3 + 0 - 1/180*m**6 + 1/12*m**4 + 0*m**5. Determine u, given that v(u) = 0.
-1, 2
Let n(o) be the first derivative of o**5/60 - 5*o**4/36 + 2*o**3/9 + 8*o + 11. Let l(v) be the first derivative of n(v). Factor l(b).
b*(b - 4)*(b - 1)/3
Let o(r) = r**3 - 17*r**2 + 8*r + 17. Let f(w) = w**3 + 18*w**2 - 7*w - 18. Let m(q) = -3*f(q) - 2*o(q). Factor m(i).
-5*(i - 1)*(i + 1)*(i + 4)
Let z(v) be the second derivative of v**6/70 - 9*v**5/70 + 11*v**4/28 - 3*v**3/7 + v - 29. Factor z(b).
3*b*(b - 3)*(b - 2)*(b - 1)/7
Let z(v) be the third derivative of -v**6/60 + v**4/3 - 2*v**2 - 30*v. Suppose z(j) = 0. Calculate j.
-2, 0, 2
Let j = -3443/13 + 265. Factor -j*m**2 - 4/13 - 6/13*m.
-2*(m + 1)*(m + 2)/13
Let x be (-4 + 228/24)*2. Let p(a) be the first derivative of -17/3*a**2 + 4/3*a + 31/3*a**3 - 175/24*a**4 + 49/30*a**5 - x. Determine c so that p(c) = 0.
2/7, 1, 2
Let u = 2429 + -2426. Factor 2/3*w + 0 + 2/3*w**u + 4/3*w**2.
2*w*(w + 1)**2/3
Let y(g) be the first derivative of g**4/15 + 2*g**3/15 + 2*g + 8. Let l(i) be the first derivative of y(i). Factor l(d).
4*d*(d + 1)/5
Let r be -1 + 2 + -198*(-14)/1008. Suppose -3/8*w**2 + r + 9/8*w = 0. What is w?
-2, 5
Solve 9*o - 1/2*o**4 + 3*o**3 + 25/2*o**2 + 0 = 0.
-2, -1, 0, 9
Let y(w) be the first derivative of 8*w**5/15 - 2*w**4/3 - 14*w**3/9 - 2*w**2/3 + 206. Factor y(k).
2*k*(k - 2)*(2*k + 1)**2/3
Let m(n) = -n**2 - 7*n + 2. Suppose 0*f = -2*f - 12. Let t be m(f). Find b such that -21*b**3 - 5*b - t*b**4 + 23*b**4 + 6*b**2 + 5*b = 0.
0, 2/5, 1
Let w(f) be the first derivative of 1/2*f**3 - 4 - 3/20*f**5 + 7*f + 0*f**2 + 0*f**4. Let v(o) be the first derivative of w(o). Suppose v(l) = 0. What is l?
-1, 0, 1
Factor -4/3 + 4/3*d**2 + 2/3*d**3 - 2/3*d.
2*(d - 1)*(d + 1)*(d + 2)/3
Let i = -10395/2 - -5199. Solve 3/2*z - 3*z**3 + 0 + 0*z**2 + i*z**5 + 0*z**4 = 0.
-1, 0, 1
Let j(v) be the first derivative of 1/17*v**2 - 2/51*v**3 - 8 + 2/85*v**5 - 1/34*v**4 + 0*v. Let j(i) = 0. Calculate i.
-1, 0, 1
What is i in 9/2*i - 1/2*i**2 - 4 = 0?
1, 8
Let f(j) be the second derivative of 3*j**5/5 - 4*j**4/3 + 2*j**3/3 - 401*j. Factor f(y).
4*y*(y - 1)*(3*y - 1)
Let f(t) be the third derivative of -1/36*t**4 + 1/360*t**6 + 0*t**3 - 1/180*t**5 - 19*t**2 + 0 + 0*t. Solve f(b) = 0 for b.
-1, 0, 2
Let u(s) = 3*s**2 - 174*s + 192. Let q(z) = -2*z**2 + 176*z - 192. Let j(o) = -7*q(o) - 6*u(o). Factor j(f).
-4*(f - 1)*(f + 48)
Let d be (56/(-7))/(-1 + 2). Let o(v) = -4*v**3 + 36*v + 16. Let m(g) = -g**3 + 12*g + 5. Let c(a) = d*m(a) + 3*o(a). Factor c(x).
-4*(x - 2)*(x + 1)**2
Let d(q) be the third derivative of q**7/168 + q**6/24 + q**5/12 + 10*q**3/3 + q**2. Let g(z) be the first derivative of d(z). Factor g(w).
5*w*(w + 1)*(w + 2)
Let g(h) be the second derivative of 9*h + 1/2*h**4 + 0 - 2*h**3 - 12*h**2 + 3/20*h**5. What is v in g(v) = 0?
-2, 2
Let n(r) = r**3 + 7*r**2 + r + 5. Let b be n(-7). Let g be ((-1)/b)/(2/28). Solve -9*f**2 - 12*f - f**3 + 3*f - g - 2*f**3 + 4 = 0 for f.
-1
Factor -4*q**3 + 0*q + 5*q - 271 - q + 187 + 37*q**2 + 47*q**2.
-4*(q - 21)*(q - 1)*(q + 1)
Suppose -5*y + 5 = 5*q, 4*q - 2*q - 2*y - 2 = 0. Suppose 3*v - 5 = q. Factor -25*s**2 + 11*s**v + 5*s**2 + 6*s - 3 + 6*s**2.
-3*(s - 1)**2
Suppose 732 = -18*d + 2244. Let a = 87 - d. Factor 1/3*m**5 + 0 + 2/3*m**4 + 0*m**2 + 1/3*m**a + 0*m.
m**3*(m + 1)**2/3
Let u(h) be the second derivative of h**5/120 - h**4/24 + h**3/12 - 8*h**2 - 8*h. Let l(t) be the first derivative of u(t). Factor l(f).
(f - 1)**2/2
Factor 6*v**2 + 6*v**2 - 18*v - 3*v**2 - 10*v**2.
-v*(v + 18)
Let a(k) be the third derivative of -2*k**2 - 1/1155*k**7 + 0*k**3 + 1/66*k**4 - 1/330*k**6 + 0 + 0*k + 1/330*k**5. Determine p, given that a(p) = 0.
-2, -1, 0, 1
Suppose 88 = 4*u + 4*u. Let f be 2/12*(u/2 + -1). Factor f*q**4 + 0 + 3/4*q**5 + 0*q**2 + 0*q**3 + 0*q.
3*q**4*(q + 1)/4
Let y(n) be the second derivative of n**5/20 + n**4/2 + 4*n**3/3 + 35*n + 3. Determine o, given that y(o) = 0.
-4, -2, 0
Suppose 47 = -3*g + 53. Let h(n) be the third derivative of -1/16*n**4 + n**g - 1/6*n**3 + 0*n + 0 + 1/24*n**5. Factor h(j).
(j - 1)*(5*j + 2)/2
Let k = 34642 - 34642. Factor -36/13*h**2 + k*h - 16/13*h**4 + 0 - 2/13*h**5 - 42/13*h**3.
-2*h**2*(h + 2)*(h + 3)**2/13
Let s(i) be the third derivative of 0*i**3 + 1/70*i**5 + 1/140*i**6 + 0 + 1/735*i**7 - 9*i**2 + 0*i + 1/84*i**4. Determine w, given that s(w) = 0.
-1, 0
Let d(h) = 2*h**3 - h**2 + 2*h. Let m(b) = 3*b**3 - 108*b**2 - 2805*b. Let k(s) = 6*d(s) - 3*m(s). Factor k(g).
3*g*(g + 53)**2
Factor 17 + 16*h**2 - h**2 + 1178*h**3 - 33*h - 1177*h**3.
(h - 1)**2*(h + 17)
Let n(t) be the first derivative of -5/2*t**2 + 5/3*t**3 - t**5 - 8 + 0*t + 5/4*t**4. Find i, given that n(i) = 0.
-1, 0, 1
Let m(y) be the first derivative of 5*y**6/2 - 21*y**5/5 - 39*y**4/4 + 31*y**3 - 30*y**2 + 12*y + 76. Find v such that m(v) = 0.
-2, 2/5, 1
Let b = 1/501 + 166/501. Let r(m) be the second derivative of 0 + 0*m**2 + 2*m + b*m**3 - 1/12*m**4. Let r(o) = 0. What is o?
0, 2
Find j such that 0*j + 0 - 21/4*j**3 + 1/2*j**2 + 19/4*j**4 = 0.
0, 2/19, 1
Let u = -2242 + 2242. Determine w so that 5/3*w**3 - 5/3*w + u*w**2 - 5/6 + 5/6*w**4 = 0.
-1, 1
Solve 4*f**2 - f**3 - 88*f**4 + 90*f**4 + 6*f**3 + f**3 = 0 for f.
-2, -1, 0
Let q(u) be the third derivative of -u**4 + 0*u**3 + 0 + 1/15*u**5 + 0*u + 14*u**2. Factor q(a).
4*a*(a - 6)
Let c = -46369/5 - -9274. Solve -c*r**3 - 12/5*