*l**3 + o*l = 0 for l.
0, 1
Let f(h) be the third derivative of -1/170*h**6 + 1/408*h**8 - 16*h**2 + 0*h + 0 - 6/17*h**3 + 44/255*h**5 + 13/68*h**4 - 2/119*h**7. Let f(m) = 0. Calculate m.
-1, 2/7, 3
Suppose -4*i = -3*k + 4*k - 194, -i + 57 = -4*k. Let g be (-133)/i + 3/1. Factor -6/7*p - g*p**3 + 2/7 + 6/7*p**2.
-2*(p - 1)**3/7
Determine a, given that -2/3*a**3 + 0*a**2 + 0*a + 0 = 0.
0
Let x(k) be the third derivative of -5*k**8/2016 + k**7/36 - 5*k**6/48 + 13*k**5/72 - 5*k**4/36 - 109*k**2 - 1. Factor x(z).
-5*z*(z - 4)*(z - 1)**3/6
Suppose 0 = 2*f - 4*i - 2, 2*f - 42*i - 3 = -39*i. Let s(o) be the first derivative of -o**6 + 3*o**2 - f*o - 6*o**4 + 2*o**3 + 4 + 21/5*o**5. Factor s(l).
-3*(l - 1)**4*(2*l + 1)
Let w be (4 + (-30)/3)/(-2). Let u be -2*10/(-4)*1. Let u - p**2 + 6*p - 3*p**w - 2*p**2 - 5 = 0. Calculate p.
-2, 0, 1
Let g be 1 + 5/(-20)*30 - -7. Solve 0*x + g*x**2 + 0 - 1/2*x**3 = 0 for x.
0, 1
Suppose 52 + 21*y + 7*y**2 - 10*y**3 + 5*y - y**2 - 72 - 2*y**4 = 0. What is y?
-5, -2, 1
Find c, given that 1/9*c**2 - 1/9*c**3 + 8/9 + 10/9*c = 0.
-2, -1, 4
Let c = -38 + 53. Let z be (-1 + 1)/(15/c). Factor -4/3*b**2 + 2*b**3 + z - 2/3*b.
2*b*(b - 1)*(3*b + 1)/3
Let u = -55 - -47. Let t = u - -19/2. Factor 3/2*g**2 + t + 3*g.
3*(g + 1)**2/2
Suppose 2*v + 14 = -2. Let g be v/(-6) - 12/(-18). Determine p, given that 1/2*p**g + 3/2 - 2*p = 0.
1, 3
Factor 80*t - 35 - 56*t - 13*t - 55*t**4 + 170*t**3 + 134*t - 230*t**2 + 5*t**5.
5*(t - 7)*(t - 1)**4
Factor 13 - 13 - 101*y + 20*y**2 - 21*y**2.
-y*(y + 101)
Let a(i) be the second derivative of i**4/60 + 13*i**3/30 + 11*i**2/5 + i + 52. Factor a(y).
(y + 2)*(y + 11)/5
Let l = -34760 - -2780881/80. Let g(q) be the second derivative of 0*q**2 - 3/16*q**4 + 0 + 1/4*q**3 - q - l*q**5. Factor g(t).
-3*t*(3*t + 1)*(9*t - 2)/4
Let f = -17675/2 + 9003. Let j = f - 165. Factor j*o**5 + 0*o**3 + 0 - 1/2*o + o**2 - o**4.
o*(o - 1)**3*(o + 1)/2
Let c(r) = 15*r**2 - 395*r - 70. Let m(k) = 105*k**2 - 2763*k - 492. Let n(w) = -27*c(w) + 4*m(w). Determine o so that n(o) = 0.
-1/5, 26
Factor -1/3*b**3 + 4 - 19/3*b + 8/3*b**2.
-(b - 4)*(b - 3)*(b - 1)/3
Let c(q) = -13*q**4 - 40*q**3 - 28*q**2 - 2*q + 5. Let j = 0 - -2. Let m(u) = 12*u**4 + 40*u**3 + 27*u**2 + 3*u - 5. Let h(f) = j*m(f) + 3*c(f). Factor h(y).
-5*(y + 1)**3*(3*y - 1)
Let g(i) be the first derivative of i**6/1800 - i**5/200 + i**4/60 + i**3/3 + 7. Let f(r) be the third derivative of g(r). Factor f(p).
(p - 2)*(p - 1)/5
Let k = 23331/38065 + -7/1655. Solve -20/23 - k*y - 2/23*y**2 = 0 for y.
-5, -2
Let s(q) = -2*q**2 - 115*q - 201. Let m(r) = -9*r**2 - 460*r - 807. Let u(p) = -3*m(p) + 11*s(p). Factor u(y).
5*(y + 2)*(y + 21)
Let h(a) = -a**2 - 7*a + 8. Let b = 77 - 79. Let r(f) be the first derivative of -f**2 + 2*f - 1. Let w(t) = b*h(t) + 9*r(t). Suppose w(o) = 0. Calculate o.
1
Let o(t) = -t**3 + 6*t**2 - 6*t + 7. Let a be o(5). Suppose -a*c + 2 + 7 = i, -3 = -5*i + 4*c. Let -8*s**3 + 10*s**i + s + 4*s**2 + s = 0. Calculate s.
-1, 0
Let z(p) = -p**3 + 11*p**2 - 10*p - 69. Let b be z(9). Solve -w**b - 1/2*w + 7/4*w**2 - 1/4 = 0 for w.
-1/4, 1
Let f(k) = k**3 + 3*k**2 + 4*k + 3. Let v be f(-2). Let s = 13 - v. Factor 2*x**4 + 2*x**2 + s*x**3 - 4*x**3 + 8*x + 14*x**2.
2*x*(x + 1)*(x + 2)**2
Let o(y) be the first derivative of -1/2*y**4 + 0*y + 1/3*y**6 - 2/3*y**3 + 0*y**2 + 2/5*y**5 - 8. Determine c so that o(c) = 0.
-1, 0, 1
Let u(j) be the third derivative of j**6/270 + 7*j**5/45 + 5*j**4/2 + 18*j**3 - 3*j**2 + 5*j. Find i such that u(i) = 0.
-9, -3
Factor 0*b - 2/5*b**5 + 0 - 2/5*b**4 + 0*b**2 + 0*b**3.
-2*b**4*(b + 1)/5
Factor -5/4*b**2 + 75/4*b + 85/2.
-5*(b - 17)*(b + 2)/4
Let a be (-96)/20 - -1*3/(-15). Let t be (-39)/(-105) + (-1)/a. Let -6/7*v + t + 2/7*v**2 = 0. What is v?
1, 2
Determine v so that -132*v + 66*v**2 + 48 + 45*v**3 - 27/2*v**4 = 0.
-2, 2/3, 4
Let s(o) = -o**4 - 2*o**3. Let u(n) = n**4 - 24*n**3 - 28*n**2. Let r(p) = 3*s(p) + u(p). Factor r(g).
-2*g**2*(g + 1)*(g + 14)
Let u = 50/3 + -344/21. Let z(d) be the first derivative of -u*d**2 + 3 + 2/21*d**3 + 0*d. Let z(l) = 0. Calculate l.
0, 2
Let s(b) = -8*b**2 + 3*b - 4. Let f be 3/2*(3 - 1). Let a(j) = 10 + 4*j - f - 4*j + 15*j**2 - 6*j. Let q(l) = 6*a(l) + 11*s(l). Suppose q(k) = 0. Calculate k.
-1/2, 2
Let o(n) be the third derivative of -n**6/24 + 5*n**5/12 + n**2 - 26. Factor o(i).
-5*i**2*(i - 5)
Let q(h) = -h**2 + h - 1. Let u(r) = r**2 - 12*r + 8. Let y(p) = -p + 1. Let s(m) = 2*u(m) - 18*y(m). Let v(k) = -2*q(k) + s(k). Solve v(z) = 0 for z.
0, 2
Let w = 8218/5 - 16431/10. Let 1/2*s**2 + w - s = 0. What is s?
1
Let u(l) = -4*l**3 - 5*l**2 + 27*l - 13. Let v(w) = 6*w**3 + 7*w**2 - 41*w + 20. Let x(m) = 8*u(m) + 5*v(m). Suppose x(o) = 0. What is o?
-4, 1/2, 1
Factor 0 + 55/4*p**2 + 0*p - 5/4*p**4 - 25/2*p**3.
-5*p**2*(p - 1)*(p + 11)/4
Let r be (-8)/(-20) - (-66)/10. Suppose 0 = r*x - 22*x + 30. Find n such that -1/2*n**3 - n**x + 1/2*n + 1 = 0.
-2, -1, 1
Let z(q) be the third derivative of 37*q**2 - 1/40*q**6 - 2/105*q**7 - 1/336*q**8 + 0*q**3 + 1/6*q**4 + 0 + 1/15*q**5 + 0*q. Suppose z(v) = 0. Calculate v.
-2, -1, 0, 1
Let y(s) = 2*s**3 - s**2 - s - 1. Let l(f) = 13*f**3 - 12*f**2 + 3*f - 10. Let b(w) = l(w) - 6*y(w). Factor b(n).
(n - 4)*(n - 1)**2
Factor -8450/17 + 8710/17*d - 262/17*d**2 + 2/17*d**3.
2*(d - 65)**2*(d - 1)/17
Let b be (-276)/345 + 368/60. Let 1/3*f**3 + b + 8/3*f - 7/3*f**2 = 0. What is f?
-1, 4
Let c = -3234 + 3236. Suppose 8/5 + 24/5*g - 54/5*g**c = 0. What is g?
-2/9, 2/3
Let w = -9 + 0. Let v be 3/w*(-4 + 1). Let -2*i**2 + 2*i**3 + v + 2 - 3 = 0. Calculate i.
0, 1
Let g be (-2)/8 - 13*2/(-8). Factor 13*v**3 - 9*v**3 - 2*v**g.
2*v**3
Let a(r) = 2*r + 51. Let y be a(-23). Suppose -5*n**3 - 13*n**4 + 4*n**y - 5*n**5 + 19*n**4 = 0. What is n?
0, 1, 5
Let -1/3*x**2 + 112/3*x - 3136/3 = 0. Calculate x.
56
Factor -10*w**2 - 1/2*w**5 + 0 - 7/2*w**4 - 9*w**3 - 4*w.
-w*(w + 1)*(w + 2)**3/2
Let n be (-5)/(-3) + (-5 - 0)/(-15). Factor -24*j - 7 - 1 + 14*j - n*j**2.
-2*(j + 1)*(j + 4)
Let c(y) be the first derivative of 55/4*y**4 + 40*y**3 + 0*y + y**5 + 19 - 90*y**2. Find h such that c(h) = 0.
-6, 0, 1
Factor 18/7*o - 10/7 - 6/7*o**2 - 2/7*o**3.
-2*(o - 1)**2*(o + 5)/7
Let k(h) = 4*h**2 + h. Let n(g) = 2*g**2 + g**2 + g - g**2. Let q = 13 + -10. Let z(u) = q*k(u) - 5*n(u). Factor z(j).
2*j*(j - 1)
Let a(y) be the first derivative of 3*y**5/25 + 6*y**4/5 - 17*y**3/5 - 18*y**2 + 324*y/5 - 248. Solve a(f) = 0.
-9, -3, 2
Let f(h) be the third derivative of h**5/20 - h**4/4 + h**3/2 + 56*h**2. Find j, given that f(j) = 0.
1
Let s be ((-2)/6)/((-2)/366). Let v = s - 181/3. Factor v*x**2 + 6 - 4*x.
2*(x - 3)**2/3
Suppose -18*b - 486 = -69*b - 111*b. Suppose -3/2*y**b + 2*y + 0 - y**4 + 1/2*y**5 + 2*y**2 = 0. What is y?
-1, 0, 2
Let h(n) = 13*n**2 + 63*n - 10. Let l be h(-5). Suppose l = -0*k + 20*k. Let 2/19*p**3 + 0 + k*p**2 + 0*p + 2/19*p**4 = 0. What is p?
-1, 0
Let 610*v + 92416 + 92*v + 1559*v**2 + 514*v - 1555*v**2 = 0. What is v?
-152
Let o(n) be the second derivative of -1/54*n**4 + 0 - 64/9*n**2 + 16/27*n**3 + 13*n. Factor o(z).
-2*(z - 8)**2/9
Let v = -523/14 + 272/7. Factor -v*c + 1 + 1/2*c**2.
(c - 2)*(c - 1)/2
Let t(v) = 139*v + 1809. Let f be t(-13). Solve 0 + 27/7*n**3 + 12/7*n + 39/7*n**f = 0 for n.
-1, -4/9, 0
Let x(a) be the third derivative of -a**6/90 + a**5/30 + 25*a**3/6 - 5*a**2. Let p(q) be the first derivative of x(q). Suppose p(u) = 0. Calculate u.
0, 1
Let b(d) be the first derivative of d**3/3 - 24*d**2 + 576*d - 255. Solve b(n) = 0.
24
Let c(r) be the second derivative of -r**8/6720 - r**7/1575 + r**6/900 + 7*r**4/6 + 2*r. Let s(g) be the third derivative of c(g). Solve s(m) = 0 for m.
-2, 0, 2/5
Factor 0*i**2 + 17*i**2 - 41*i**2 + 4*i**3 - 16 + 36*i.
4*(i - 4)*(i - 1)**2
Let p = -29/21 + 361/231. Determine y, given that -2/11*y**4 - 4/11*y**3 - p + 4/11*y**2 + 2/11*y + 2/11*y**5 = 0.
-1, 1
Factor 2/7*g**2 + 2/7*g - 12/7.
2*(g - 2)*(g + 3)/7
Let 0 + 2*u**4 + 0*u**2 - 2/3*u**5 + 0*u - 4/3*u**3 = 0. What is u?
0, 1, 2
Let j = -1979/8792 - -9/314. Let i = 3/8 - j. Solve -2/7*r**2 + i*r - 2/7 = 0.
1
Let f(t) = -8*t**2 + 10*t - 4. Let d be f(4). Let c = d + 462/5. Factor 2/5*n**2 - c*n + 0.
2*n*(n - 1)/5
Suppose 4*a - 24 = -4*d, a = d +