 5*t - 170 = 4*f - 130. Find k, given that 20/3 - 25/3*k**2 + 0*k**3 + 5/3*k**t + 0*k = 0.
-2, -1, 1, 2
Let r(t) be the third derivative of 3*t**6/80 - 7*t**5/20 - 5*t**4/12 + 50*t**3/3 + 62*t**2. Find l such that r(l) = 0.
-2, 10/3
Find y, given that 2*y**2 + 2392 + 4909 - 3920 + 308*y + 2121 + 6356 = 0.
-77
Factor -973 - 3*u**4 + 405 + 72*u**2 + 15*u**3 + 472 + 12*u.
-3*(u - 8)*(u - 1)*(u + 2)**2
Let 7*t**2 + t**3 + 8*t**2 + 2*t**3 + 15*t + 3*t = 0. What is t?
-3, -2, 0
Let q be (15/12)/((-15)/(-6))*6. Suppose -8/5 - 68/5*f - 126/5*f**2 + 81/5*f**q = 0. What is f?
-2/9, 2
Let v(b) be the first derivative of -12/7*b**3 - 32/7*b + 76/7*b**2 - 30. Determine s so that v(s) = 0.
2/9, 4
Let p(k) be the second derivative of k**5/20 + 7*k**4/10 + 8*k**3/15 - 17*k. Factor p(q).
q*(q + 8)*(5*q + 2)/5
Find j, given that 28/9 - 10/3*j + 2/9*j**2 = 0.
1, 14
Let h(y) be the third derivative of 0*y - 1/4*y**3 + 24*y**2 + 5/96*y**4 - 1/240*y**5 + 0. Factor h(t).
-(t - 3)*(t - 2)/4
Let v be ((-3)/(-15))/(3/45). Let q(y) be the third derivative of -1/96*y**4 + 0*y - 1/240*y**5 + 0 + y**2 + 1/12*y**v. Factor q(l).
-(l - 1)*(l + 2)/4
Suppose 99 = 2*q + 3*y, 3*q + y - 123 = 5*y. What is n in 0*n**2 - 3*n - 3*n**2 + n + n**5 + q*n**3 - 44*n**3 + 3*n**4 = 0?
-2, -1, 0, 1
Let v(w) be the first derivative of -w**6/15 - 18*w**5/25 - 19*w**4/10 + 14*w**3/5 + 56*w**2/5 - 96*w/5 + 405. What is c in v(c) = 0?
-4, -3, 1
Factor 15*h**2 - 3*h**2 + 26*h - 4*h**2 - 12*h**2 - 48 + 26*h.
-4*(h - 12)*(h - 1)
Let b(o) be the first derivative of -7*o**3/24 + 55*o**2/8 + 4*o + 70. Factor b(f).
-(f - 16)*(7*f + 2)/8
Let l be (0 + 0)*-3*4/24. Factor 0 + 6/5*q**3 + 2/5*q**2 + l*q.
2*q**2*(3*q + 1)/5
Let y(n) = n - 1. Suppose -v + 4 = 2. Suppose -h + 0*q - 7 = -3*q, v*q = 4. Let f(s) = -36*s**2 - 36*s + 8. Let j(d) = h*f(d) - 12*y(d). Factor j(c).
4*(3*c + 1)**2
Suppose -4*g + 368 = -4*m + 380, 0 = 5*m - 3*g - 15. Let x(j) be the first derivative of 0*j**2 - 8/13*j + 2/39*j**m - 10. Factor x(s).
2*(s - 2)*(s + 2)/13
Let u(r) = 46*r**3 - 462*r**2 + 26426*r + 26912. Let x(t) = -2*t**3 + t. Let b(p) = -2*u(p) - 44*x(p). Factor b(s).
-4*(s - 116)**2*(s + 1)
Let a be (-14)/((-3)/(-174)*4). Let l be (-1)/(-5) - a/35. Factor -4*u + 4*u - l*u**2 + 3*u**3 + u + 2*u.
3*u*(u - 1)**2
Let w(x) be the third derivative of -7*x**9/2160 - x**8/40 - x**7/21 - 2*x**6/45 - 11*x**5/60 - 19*x**2. Let g(d) be the third derivative of w(d). Factor g(k).
-4*(k + 2)*(7*k + 2)**2
Let f(b) be the first derivative of -6*b**5/25 - 11*b**4/10 - 2*b**3/3 + 11*b**2/5 + 16*b/5 - 81. Find i, given that f(i) = 0.
-8/3, -1, 1
Let f(d) = d**5 + d**4 + d - 1. Let z = 9 - 18. Let j(v) = 6*v**5 + 30*v**4 - 54*v**3 + 66*v**2 - 30*v. Let c(y) = z*f(y) + j(y). Factor c(h).
-3*(h - 3)*(h - 1)**4
Let m(s) be the second derivative of 3*s**5/20 + 7*s**4/12 + s**3/3 - 5*s + 7. Factor m(r).
r*(r + 2)*(3*r + 1)
Determine y, given that 44/5*y + 4/5 + 41/5*y**2 + 2*y**3 = 0.
-2, -1/10
Suppose 11*g - 6*g + 155 = 0. Let q = g - -31. Factor i**2 + 0 - 5/2*i**4 - 3/2*i**3 + q*i.
-i**2*(i + 1)*(5*i - 2)/2
Suppose -15 = 3*p - 24. Suppose -234 = -5*b + 3*s, -2*b = -5*s + 21 - 107. What is n in -9*n**2 - n**p - 48*n**3 + 10*n**3 + b*n - 12*n**4 + 12 = 0?
-2, -1/4, 1
Let l be 2 - 282/48 - -4. Let b(a) be the second derivative of -4*a + 0*a**2 + 0 + 1/6*a**3 + 1/40*a**5 - l*a**4. Factor b(t).
t*(t - 2)*(t - 1)/2
Solve 24/5*v + 36/5 + 4/5*v**2 = 0 for v.
-3
Suppose 19*z - 18 = z. Let g(t) = 5. Let i(c) = 1. Let h(n) = g(n) - 4*i(n). Let m(o) = 2*o**2 + 4*o + 5. Let a(j) = z*m(j) - 3*h(j). Let a(x) = 0. Calculate x.
-1
Suppose 1/7*f**2 - 8/7 - f = 0. Calculate f.
-1, 8
Let b(j) be the first derivative of -j**6/60 + 3*j**5/20 - 3*j**4/8 + 19*j + 15. Let c(k) be the first derivative of b(k). Factor c(z).
-z**2*(z - 3)**2/2
Let c(n) be the second derivative of -n**5/20 + 8*n**4/3 - 128*n**3/3 + 160*n. Factor c(h).
-h*(h - 16)**2
Let f = -5 - -7. Let h = 1078 - 1075. Factor -3*g**2 - h - 4*g + 0*g**f + g - 3*g.
-3*(g + 1)**2
Determine m so that -15*m**2 + 20*m**3 + 303*m**2 + 26*m**2 - 80*m - 39*m**2 + 10*m = 0.
-14, 0, 1/4
Determine c, given that 405*c - 142 - 103 - 11 + 90*c**2 - 144 - 95*c**2 = 0.
1, 80
Let l(v) be the second derivative of 21*v**4/8 + 17*v**3/4 - 3*v**2 + 12*v - 5. Factor l(w).
3*(w + 1)*(21*w - 4)/2
Let g(w) be the first derivative of 9*w**4/16 - w**3/4 - 172. Find q such that g(q) = 0.
0, 1/3
Suppose -5*a + 99 = y, 4*y = -a + 6*a - 79. Suppose 6*v = a - 7. Factor 6/5*z**v - 2/5*z**3 - 4/5*z + 0.
-2*z*(z - 2)*(z - 1)/5
Suppose -4*b + 3*q + 149 = -2*b, 2*q - 2 = 0. Let r be (-1)/(-5) + b/20. Factor -19*z**2 - 4*z**4 + 22*z**2 + z**r.
-3*z**2*(z - 1)*(z + 1)
Let f(a) = -a**3 + 37*a**2 - 101*a + 67. Let z(q) = q**3 - 19*q**2 + 50*q - 34. Let g(y) = -2*f(y) - 5*z(y). Factor g(t).
-3*(t - 3)*(t - 2)**2
Let h(m) = 3*m**3 - 32*m**2 + 158*m - 232. Let f(t) = -2*t**3 + 21*t**2 - 105*t + 155. Let c(x) = 7*f(x) + 5*h(x). Factor c(o).
(o - 5)**2*(o - 3)
Factor 56/5*f + 4/5*f**2 + 52/5.
4*(f + 1)*(f + 13)/5
Let k(w) = w**3 - 63*w - 6. Let t be k(8). Find c such that -3/8*c**3 - 3/2*c**t + 0 - 9/8*c = 0.
-3, -1, 0
Let x(s) be the first derivative of -9 + 0*s - 4/35*s**5 + 0*s**3 + 1/21*s**6 + 0*s**2 + 1/14*s**4. Find d such that x(d) = 0.
0, 1
Suppose 24 = -0*q + 3*q. Factor -3*a - 10 - q - 15*a**2 + 54*a.
-3*(a - 3)*(5*a - 2)
Let t(x) be the third derivative of x**9/20160 + x**8/3360 - x**7/560 + 13*x**5/60 + 15*x**2. Let u(g) be the third derivative of t(g). Let u(w) = 0. What is w?
-3, 0, 1
Let q be 1 + -3 - 90/(-18). Find b, given that 2*b**2 - 879 + 5*b - 2*b**3 + 871 + q*b = 0.
-2, 1, 2
Let g(l) be the third derivative of 3*l**7/280 + 31*l**6/160 + 7*l**5/80 - 31*l**4/32 - 5*l**3/4 - 829*l**2. Find o, given that g(o) = 0.
-10, -1, -1/3, 1
Suppose -4*i = 6 - 46. Let w be (256/(-140))/((-4)/i). Factor -w*k**3 - 22/7*k**2 - 4/7*k - 2*k**4 + 0.
-2*k*(k + 1)**2*(7*k + 2)/7
Let l(k) be the first derivative of 20*k**3/3 + 26*k**2 + 24*k - 112. Determine a so that l(a) = 0.
-2, -3/5
Let c(p) be the third derivative of p**6/80 - 3*p**5/40 + 2*p**2 + 35*p. Factor c(f).
3*f**2*(f - 3)/2
Let l = 44 + -42. Suppose 0 = -5*s + 2*v + 2*v + 27, -l*v - 18 = -4*s. Factor s*k**2 + 36/5*k + 12/5.
3*(k + 2)*(5*k + 2)/5
Let x(y) be the second derivative of y**6/30 - y**4/12 + 2*y + 44. Solve x(t) = 0.
-1, 0, 1
Let p(b) be the second derivative of b**10/15120 - b**9/7560 - b**8/3360 + b**7/1260 - b**4/3 - 14*b. Let g(v) be the third derivative of p(v). Factor g(a).
2*a**2*(a - 1)**2*(a + 1)
Let r(t) be the second derivative of -t**5/70 + 13*t**4/21 + 9*t**3/7 + 124*t - 2. Factor r(f).
-2*f*(f - 27)*(f + 1)/7
Suppose 2*t = 12*t. Let s(y) be the third derivative of -19/300*y**6 + t - y**2 + 1/15*y**4 - 1/35*y**7 + 0*y + 0*y**3 + 0*y**5. Let s(f) = 0. Calculate f.
-1, -2/3, 0, 2/5
Let q(j) be the second derivative of -j**10/10080 - j**9/2520 + j**7/420 + j**6/240 - 23*j**4/12 + 30*j. Let y(n) be the third derivative of q(n). Factor y(m).
-3*m*(m - 1)*(m + 1)**3
Let w = 2012 - 10057/5. Find d, given that w*d + 6/5*d**2 + 0 + 3/5*d**3 = 0.
-1, 0
Let y be 125/15 + (-2)/6. Suppose -10*x + 6*x = -y. Factor -4 + 2*k**2 - k + 3*k + 0*k + 0*k**x.
2*(k - 1)*(k + 2)
Solve -3/2*s**3 + 3/4*s**2 + 3/8*s - 3/4*s**4 + 0 + 9/8*s**5 = 0 for s.
-1, -1/3, 0, 1
Let d(u) = -u**2 - 612*u + 31216. Let g(k) = 12*k**2 + 6120*k - 312162. Let s(n) = -21*d(n) - 2*g(n). Factor s(f).
-3*(f - 102)**2
Factor 1/2*n**3 - 27/2*n**2 + 51/2*n - 25/2.
(n - 25)*(n - 1)**2/2
Let k = 12 + -7. Suppose 0 = 4*h - k*h + 10. Suppose -14*v**2 - 2*v + 0*v + h*v**2 + 2*v**2 = 0. What is v?
-1, 0
Let m(x) be the third derivative of x**8/112 - 9*x**7/70 + x**6/5 + 118*x**2. Determine k so that m(k) = 0.
0, 1, 8
Let h(u) be the second derivative of 1/10*u**4 + 3/100*u**5 + 0*u**2 + 0 - 1/50*u**6 + 0*u**3 + 3*u. Solve h(k) = 0 for k.
-1, 0, 2
Find j, given that 2*j**2 + 0*j**2 + 39*j + j**2 + 0*j = 0.
-13, 0
Let n be 63/12 + -5 - (3 + -3). Let h(s) be the third derivative of -n*s**4 + 0*s - 2/3*s**3 + 0 - 2*s**2 - 1/30*s**5. Let h(l) = 0. What is l?
-2, -1
Let s = 4 + 1. Let u = s - 3. Factor -6*q - 12*q**3 - 8*q**u - 5*q**2 + 12*q**4 - 8*q**2.
3*q*(q - 2)*(2*q + 1)**2
Suppose -2*s = -x - 3*s - 29, -62 = 3*x - 2*s.