 1)*(i + 1)**2
Let y(b) be the first derivative of 3*b**2 - 1/3*b**3 - 1/2*b**4 - 12*b + 1/10*b**5 + 8. Let a(r) be the first derivative of y(r). Factor a(z).
2*(z - 3)*(z - 1)*(z + 1)
Suppose -k + 4 = 2. Factor -4*r + 2*r - 2 - k + 10*r + 12*r**2.
4*(r + 1)*(3*r - 1)
Let t(c) be the second derivative of -c**8/11200 + c**7/2100 + c**6/400 - c**4/6 - 41*c**3/6 + 18*c - 1. Let g(x) be the third derivative of t(x). Factor g(l).
-3*l*(l - 3)*(l + 1)/5
Let a(k) be the third derivative of k**10/680400 - k**8/30240 + k**7/11340 - 3*k**5/20 - 7*k**2. Let p(h) be the third derivative of a(h). Factor p(d).
2*d*(d - 1)**2*(d + 2)/9
Suppose -3*m = 7*h - 12*h - 25, 3*h + 16 = 2*m. Let g(y) be the third derivative of 0*y**3 + 0 - 2*y**2 + 1/20*y**6 + 0*y**4 + 0*y + 1/40*y**m. Factor g(a).
3*a**2*(4*a + 1)/2
Determine b, given that -58*b + 1/2*b**2 + 1682 = 0.
58
Let 4/5*j**3 - 156/5*j - 8/5*j**2 - 288/5 = 0. What is j?
-3, 8
Let g be 2/(-4)*(0 - 0). Suppose g = -x + 2*x - 4*t, 6 = 3*t. Let 2*f - f**2 + 3 - x*f + f**2 + 3*f**2 = 0. What is f?
1
Let y(g) be the first derivative of 1/11*g**2 - 1/22*g**4 + 2/55*g**5 - 2/33*g**3 + 0*g + 25. Factor y(q).
2*q*(q - 1)**2*(q + 1)/11
Let k(g) be the second derivative of -4*g**7/21 - 7*g**6/5 + 79*g**5/10 - 71*g**4/6 + 3*g**3 + 8*g**2 - 537*g. Solve k(q) = 0 for q.
-8, -1/4, 1
Let n(k) be the first derivative of -k**5/40 + k**3/8 - k**2/8 + 97. Determine c so that n(c) = 0.
-2, 0, 1
Let n(f) be the third derivative of -f**8/168 + 2*f**7/273 + f**6/260 + 648*f**2. Factor n(l).
-2*l**3*(l - 1)*(13*l + 3)/13
Let z(y) = -6*y**2 - 2*y + 36. Let g(q) = -4*q**2 - q + 24. Suppose 0 = -4*w - 1 + 21. Let d(s) = w*z(s) - 8*g(s). Factor d(o).
2*(o - 3)*(o + 2)
Factor 60*p**2 - 27 - 37 - 24*p - 56*p**2.
4*(p - 8)*(p + 2)
Let i(s) be the third derivative of -s**5/390 - 7*s**4/52 - 18*s**3/13 - 523*s**2. Solve i(r) = 0 for r.
-18, -3
Let z(b) be the first derivative of b**4/3 + 2*b**3/3 - 15*b + 28. Let v(x) be the first derivative of z(x). Determine c so that v(c) = 0.
-1, 0
Let t(r) = 175*r + 175. Let c be t(-1). Solve 0*b**2 + 1/5*b**3 + c - 1/5*b = 0.
-1, 0, 1
Factor 8/5*g + 4/5*g**2 - 32/5.
4*(g - 2)*(g + 4)/5
Let u(q) be the second derivative of -q**6/10 + 12*q**5/5 - 29*q**4/4 + 7*q**3 - q + 438. Factor u(o).
-3*o*(o - 14)*(o - 1)**2
Let r be 510/(-25) - (-4)/10. Let y be 4*8/r - -2. Factor -y*v**2 + 2/5*v**4 - 1/5*v + 0 + 1/5*v**5 + 0*v**3.
v*(v - 1)*(v + 1)**3/5
Factor 0*k + 0 - 2/5*k**3 + 2/5*k**2.
-2*k**2*(k - 1)/5
Let z(d) be the second derivative of -d**4/42 + 13*d**3/21 - 12*d**2/7 - 153*d. Find w such that z(w) = 0.
1, 12
Let p(y) be the first derivative of y**4/16 - 11*y**3/12 + 5*y**2/4 + 205. Factor p(l).
l*(l - 10)*(l - 1)/4
Suppose -2*w + 30 = 4*c, -4*c - 3*w = -0*c - 29. Suppose -4*f + c = 2*j, 4*j - 4 - 6 = -2*f. Factor -h**4 + 3*h - 2*h**4 + h**4 - 2*h**3 + 2*h**j - h.
-2*h*(h - 1)*(h + 1)**2
Suppose 210 - 219 = -t. Let h be 3 + 44/(-8) - t/(-3). Suppose h*o**3 + 0 - 1/2*o**5 + 1/2*o**2 - 1/2*o**4 + 0*o = 0. What is o?
-1, 0, 1
Let d(a) be the second derivative of a**6/1440 + a**5/240 + a**4/96 + 10*a**3/3 - 15*a. Let w(u) be the second derivative of d(u). Solve w(f) = 0.
-1
Let n = -506/13 + 2543/65. Let p(j) be the second derivative of 12*j + 2/5*j**2 + n*j**3 + 1/30*j**4 + 0. Factor p(f).
2*(f + 1)*(f + 2)/5
Let n = 808/1089 + -36/121. Let -4/9*z**4 - 2/9*z + n*z**2 + 0 + 2/9*z**3 = 0. Calculate z.
-1, 0, 1/2, 1
Let h(v) = -v**2 - 2 - 1 + 4. Let z = -73 - -58. Let s(i) = -27*i**2 - 15*i + 12. Let c(k) = z*h(k) + s(k). Solve c(n) = 0.
-1, -1/4
Let t(p) be the third derivative of 0*p**3 + 0 - 1/48*p**4 + 0*p - 1/420*p**7 + 45*p**2 + 1/120*p**5 + 1/240*p**6. Solve t(k) = 0 for k.
-1, 0, 1
Let m be (-58)/8 + 7 + (-2)/(-8). Suppose 0 = -2*d - 3*t + 6, -3*t + m*t + 6 = -5*d. Factor 0 + 6/7*y**2 - 15/7*y**4 + d*y - 9/7*y**3.
-3*y**2*(y + 1)*(5*y - 2)/7
Let o(p) be the second derivative of 5*p**7/42 - 3*p**5/2 - 10*p**4/3 - 5*p**3/2 - p + 15. Factor o(b).
5*b*(b - 3)*(b + 1)**3
Suppose 5*o + 30 = -4*q + 77, -3*o = 5*q - 23. Let w = -5 + o. Suppose -2*n + 12*n**5 + w*n - 278*n**2 + 286*n**2 - 16*n**3 - 8*n**4 = 0. What is n?
-1, -1/3, 0, 1
Suppose 0 = -2*m + m - 1. Let z(p) = p**3 + p**2 + p + 1. Let y(q) = -9*q**3 - 3*q**2 - 6*q - 6. Let g(o) = m*y(o) - 6*z(o). Factor g(r).
3*r**2*(r - 1)
Let k(c) = 37*c**3 + 96*c**2 - 504*c - 26. Let s(o) = -6*o**3 - 16*o**2 + 84*o + 4. Let z(h) = 2*k(h) + 13*s(h). Find u, given that z(u) = 0.
-7, 0, 3
Let b = -225 + 677/3. Factor -1/3*d**2 - 1/3 - b*d.
-(d + 1)**2/3
Factor -v**2 - 6/5*v + 4/5*v**3 + 0.
v*(v - 2)*(4*v + 3)/5
Suppose -10*w + g = -9*w - 2, 5*w - 3*g = 12. Suppose 0*i = 3*i - 12. Determine o, given that 1/2*o**w - 7/4*o**2 + 0 + 7/4*o**i - 1/2*o = 0.
-1, -2/7, 0, 1
Suppose 2*s = -z - 45, 0*z - 4*z = s + 40. Let b = 23 + s. Factor -2*r**2 + 14*r**3 - 23*r**b + 13*r**3 - 2*r**2.
4*r**2*(r - 1)
Let s(l) be the third derivative of l**3 - 41*l**2 - 1/6*l**4 + 1/90*l**5 + 0*l + 0. Find f such that s(f) = 0.
3
Let i(o) = o**2 + 18*o + 3. Let n be i(-18). Factor -9*t - 10 + t**n + 29*t**2 - 32*t**2 + 5.
(t - 5)*(t + 1)**2
Let a(x) be the first derivative of 4 + 0*x + 3/2*x**2 - 1/30*x**3 - 1/300*x**5 + 1/60*x**4. Let m(s) be the second derivative of a(s). Factor m(p).
-(p - 1)**2/5
Let c(i) be the third derivative of i**5/300 + 11*i**4/60 - 32*i**2. Suppose c(r) = 0. Calculate r.
-22, 0
Let i = 137 - 133. Let p = -7 + 7. Factor -2/5*y**5 + 0 - 2/5*y**3 - 4/5*y**i + 0*y**2 + p*y.
-2*y**3*(y + 1)**2/5
Suppose 6 + 1 = -7*v. Let z(t) = t**5 + t**3 - t. Let u(a) = -a**5 + 2*a**4 - 10*a**3 + 2*a**2 + 9*a - 4. Let d(y) = v*u(y) - 2*z(y). Factor d(o).
-(o - 1)**3*(o + 1)*(o + 4)
Let r(l) be the second derivative of 0 + 162/7*l**2 - 12/7*l**3 + 1/21*l**4 + 17*l. Suppose r(p) = 0. Calculate p.
9
Let h(z) be the first derivative of -18*z**5/5 + 30*z**4 + 544*z**3/3 + 272*z**2 + 160*z - 400. What is p in h(p) = 0?
-2, -2/3, 10
Let y(l) = -l**2 - 4*l + 2. Let a be y(-4). Factor 4*o**2 - 15*o + 3*o**3 + o**a + 9 - 2*o**2.
3*(o - 1)**2*(o + 3)
Suppose 6*k - 39 = k + 4*m, -2*k = 3*m + 12. Suppose 0*d - 3/2*d**3 + k*d**2 + 0 = 0. Calculate d.
0, 2
Let k = -774 - -779. Let u(f) be the second derivative of 0 - 2*f + f**4 + 6*f**3 + 1/15*f**k + 18*f**2. Find b such that u(b) = 0.
-3
Suppose 3*u = -4*r + 2, 161*r + 2 = 159*r - 3*u. What is h in 1/4*h**r + 0 - h = 0?
0, 4
Suppose 2*l + 16/7*l**2 + 4/7*l**3 - 2/7*l**5 - 4/7*l**4 + 4/7 = 0. What is l?
-1, 2
Let w(v) be the first derivative of -v**5/20 - 11*v**4/12 - 35*v**3/6 - 25*v**2/2 - 19*v + 17. Let k(s) be the first derivative of w(s). Factor k(i).
-(i + 1)*(i + 5)**2
Suppose 2 + 28 = -5*p, -5*r - 9 = 4*p. Suppose 0 + 36/7*z**r + 48/7*z**2 + 16/7*z = 0. Calculate z.
-2/3, 0
Let i(k) = -6 + 4*k + 6. Let a be i(1). Factor 11*h**2 - 2*h**2 - 4*h - 3*h**2 - 2*h**a.
-2*h*(h - 1)**2*(h + 2)
Let h(k) be the third derivative of 0*k + 1/24*k**4 - 1/120*k**6 - 1/3*k**3 - 1/210*k**7 + 0 - 14*k**2 + 1/20*k**5. Find n, given that h(n) = 0.
-2, -1, 1
Let p(b) be the first derivative of 0*b - 4/3*b**6 + 27 + 0*b**2 + 0*b**3 - 6/5*b**5 + 0*b**4. Factor p(i).
-2*i**4*(4*i + 3)
Let v(g) = 2*g + 26. Let r be v(-12). Suppose 3*n - 6 = -4*u, -r*u - 4*n + 2*n = -2. Find b, given that b**2 + u + 2*b**2 + 3*b + 0*b - 9*b = 0.
1
Let r = -20 + 24. Suppose 18*m**4 + 50*m**r - 16*m**5 - 112*m**3 + 88*m**2 + 2 - 18*m - 14*m + 2 = 0. What is m?
1/4, 1
Let n be 3 - (54/76)/((-6)/(-12)). Let j = n - 292/209. Factor -j*c**2 + 0 + 0*c + 8/11*c**3.
2*c**2*(4*c - 1)/11
Let c(i) be the first derivative of 32/3*i**3 + 0*i**2 - 4/5*i**5 + 0*i**4 - 64*i + 10. Suppose c(r) = 0. Calculate r.
-2, 2
Let x(h) be the second derivative of -1/36*h**4 + 1/60*h**5 + 0*h**3 + 6*h + 0 + 0*h**2. Determine m so that x(m) = 0.
0, 1
Suppose -36 - 12*i + 6*i - 4*i**2 - 8*i - 10*i = 0. What is i?
-3
Let q(v) be the second derivative of 0 - 1/4*v**5 - 4*v - 20/3*v**3 + 10*v**2 + 25/12*v**4. Factor q(f).
-5*(f - 2)**2*(f - 1)
Let v = 4787 + -4785. Solve 0 - 2/15*p**3 - 2/15*p - 4/15*p**v = 0.
-1, 0
Let n be (-75)/48*(-2 - (-36)/15). Let k = -1/8 - n. Factor k*f**2 - 4*f + 8.
(f - 4)**2/2
Let m(d) = 10*d**2 - 18*d - 16. Let a(j) = -2 + 54*j - 55*j + j**2 + 2. Let c(t) = -6*a(t) + m(t). Factor c(x)