**2*(t + 2)
Let n(c) be the third derivative of 11*c**6/240 + 31*c**5/120 - c**4/8 + 2*c**2 - 51. What is g in n(g) = 0?
-3, 0, 2/11
Let y(o) be the first derivative of o**4/9 + o**3/63 + 30*o - 14. Let i(t) be the first derivative of y(t). Determine x so that i(x) = 0.
-1/14, 0
Let d(y) be the first derivative of 4*y**5/3 - 4*y**4 + 4*y**3 - 4*y**2/3 - 77. Factor d(r).
4*r*(r - 1)**2*(5*r - 2)/3
Let u be 136/104*3/12. Let i = u - 1/13. Suppose 0 + 0*a + 3/2*a**4 - i*a**3 - 1/2*a**2 = 0. Calculate a.
-1/2, 0, 2/3
Let i = 17978 - 17976. Solve i*x**2 - 6/5*x - 4/5 = 0 for x.
-2/5, 1
Let n(z) be the third derivative of z**6/40 + 3*z**5/10 - 7*z**4/8 + 306*z**2. Find j such that n(j) = 0.
-7, 0, 1
Let u(d) be the second derivative of -8*d**7/21 - 14*d**6/15 - 2*d**5/5 + d**4/3 + 2*d - 22. What is m in u(m) = 0?
-1, 0, 1/4
Find m such that 0 + 34/5*m + 151/5*m**2 - 9/5*m**3 = 0.
-2/9, 0, 17
Let d = 1033 - 3097/3. Factor -1/3*m**4 + 0 + 2/3*m - d*m**3 + 1/3*m**2.
-m*(m - 1)*(m + 1)*(m + 2)/3
Suppose -h + 4*h - 5*c - 34 = 0, -5*c = h + 22. Factor -h*z**3 - 6*z + 18 - 3*z + 9 - 15*z**2.
-3*(z - 1)*(z + 3)**2
Let m(u) = u**3 + u**2. Let w(x) = -9*x**3 + 86*x**2 - 480*x + 640. Let c(p) = -4*m(p) - w(p). Determine a so that c(a) = 0.
2, 8
Let s(n) be the second derivative of -n**5/10 + 3*n**4/2 - 5*n**3 - 25*n**2 + 232*n. Find t, given that s(t) = 0.
-1, 5
Let m = -1 + 1. Suppose 0 = 73*h - 36*h - 18*h - 76. Solve m*t**3 + 0*t + 1/2*t**2 + 0 - 1/2*t**h = 0 for t.
-1, 0, 1
Suppose 4*d - n = 18, -3*d + 10 = d - 5*n. Suppose -2*j = 4, 3*a + 0*a = -5*j + d. Factor -11*v**2 + 2*v + 7*v + v**3 + a*v**2.
v*(v - 3)**2
Let y = -612950/19 + 32262. Factor -2/19*w**2 + y*w + 0.
-2*w*(w - 14)/19
Let w be ((-7)/(-42))/(2 - 46/24). Suppose 2*g**2 + 2/3*g**4 + w*g**3 + 0 + 2/3*g = 0. What is g?
-1, 0
Suppose 20/3*o**2 - 39*o - 1/3*o**3 + 54 = 0. Calculate o.
2, 9
Let o(d) be the second derivative of d**8/10920 - d**7/5460 - 25*d**3/6 + 21*d. Let q(x) be the second derivative of o(x). Factor q(h).
2*h**3*(h - 1)/13
Let s be -3*-10*188/24. Let j = s - 2111/9. Factor j*c + 2/9*c**2 + 2/9.
2*(c + 1)**2/9
Let i = 5367 - 1110977/207. Let f = i - -6/23. Factor -4/9*g + 0 + f*g**2.
2*g*(g - 2)/9
Let j be (1/(-3))/(((-150)/(-10))/(-90)). Let n(d) be the first derivative of 8 + 1/24*d**3 + 1/32*d**4 - 1/8*d - 1/16*d**j. Factor n(z).
(z - 1)*(z + 1)**2/8
Let g(n) = 31*n**2 - 69*n + 214. Let l(u) = 27*u**2 - 69*u + 216. Let b(v) = -6*g(v) + 7*l(v). Factor b(o).
3*(o - 19)*(o - 4)
Suppose c - 5*m = 21, 2*m + 4 = -4*c - 0. Let l be (-8)/(-20) - (1 - 1/c). Factor -3/5*y + 0*y**2 + 1/5*y**3 + l.
(y - 1)**2*(y + 2)/5
Let s = 147 - 139. Suppose -2*t + s = 5*w, -2*w = -3*t - 16 + 9. Factor -6 + 16*b - 44/3*b**w + 16/3*b**3 - 2/3*b**4.
-2*(b - 3)**2*(b - 1)**2/3
Let n(l) be the second derivative of 3*l**5/100 - 2*l**4/5 + 8*l**3/5 + 255*l. Factor n(r).
3*r*(r - 4)**2/5
Let u be (-20)/(-9) - 20/90. Let -7*z**2 - 4*z + 8*z**2 + 3*z**u = 0. What is z?
0, 1
Suppose 4*y - 5*j + 1 = 4, -2*y - 5*j + 9 = 0. Factor -14*x + 25*x - y*x**3 - 4*x**2 - 13*x.
-2*x*(x + 1)**2
Suppose -5*d + 15 = 35. Let y be (2 + -2)/(-5 + (-8)/d). Solve y*f - 2/5*f**2 + 0 = 0.
0
Suppose -4*l - 5*v = l + 150, 2*v + 85 = -3*l. Let u = 27 + l. What is b in 3/8*b - 1/8 - 3/8*b**3 + 1/8*b**u = 0?
-1, 1/3, 1
Let x be (0/(-21))/((-4)/(-2)). Let a(k) be the second derivative of 1/8*k**4 + 0*k**3 + 0*k**2 - 6*k - 3/10*k**5 + x. Factor a(d).
-3*d**2*(4*d - 1)/2
Let c be (-446)/1784 - 2/(-8). Solve 1/3*b**2 + 1/3*b**4 - 2/3*b**3 + c + 0*b = 0 for b.
0, 1
Suppose 5*v = -4*c - 60, -2*c + 3*c = -4*v - 15. Let k(w) = w**3 + 16*w**2 + 16*w + 17. Let b be k(c). Factor 2*h**3 - 2*h**4 - 32*h + 32*h - 2*h**5 + 2*h**b.
-2*h**2*(h - 1)*(h + 1)**2
Let i(m) be the third derivative of m**6/135 + m**5/270 - 25*m**4/27 - 25*m**3/27 + 38*m**2 - 5*m. Determine w so that i(w) = 0.
-5, -1/4, 5
Let v = 1917/5 - 381. Let k(i) be the second derivative of 4*i**3 + 3*i + 13/3*i**4 + v*i**5 + 8/15*i**6 + 2*i**2 + 0. Factor k(s).
4*(s + 1)**2*(2*s + 1)**2
Let o(y) be the first derivative of y**7/420 - y**6/180 + 10*y**3/3 + 44. Let u(w) be the third derivative of o(w). Determine j, given that u(j) = 0.
0, 1
Let u = 242 - 238. Let w(m) be the first derivative of 0*m**2 + 2/55*m**5 + 0*m + 1/33*m**6 - 2/33*m**3 - 1/22*m**u - 1. Factor w(c).
2*c**2*(c - 1)*(c + 1)**2/11
Let l = 44/63 + -2/63. Let q(m) be the first derivative of -1/3*m**2 + 3 + 1/6*m**4 + 2/9*m**3 - l*m. Let q(a) = 0. Calculate a.
-1, 1
Let o(m) = -m**5 + 2*m**4 - 6*m**3 - 20*m**2 - 17*m - 8. Let t(i) = 3*i**5 - 5*i**4 + 10*i**3 + 40*i**2 + 35*i + 18. Let z(f) = 15*o(f) + 6*t(f). Factor z(v).
3*(v - 4)*(v + 1)**4
Factor -110*l**2 + 0 + 0 - 3715*l**4 + 120*l - 2*l**3 - 133*l**3 + 3690*l**4.
-5*l*(l + 2)*(l + 4)*(5*l - 3)
Let c(z) = 8*z**3 - 14*z**2 - 18*z - 6. Let j(u) = -u**3 - u - 1. Let q(l) = c(l) + 10*j(l). Factor q(o).
-2*(o + 1)*(o + 2)*(o + 4)
Let x be 10*(-6)/(-240)*8. Suppose -2 + 0*y**x + 7/3*y - 1/3*y**3 = 0. Calculate y.
-3, 1, 2
Let m(a) be the third derivative of a**6/1020 + 27*a**5/170 + 729*a**4/68 + 6561*a**3/17 - 11*a**2 - 3*a. Solve m(n) = 0 for n.
-27
Let d(z) be the third derivative of 4*z**7/525 + 11*z**6/300 - z**5/50 - 15*z**2 + 2. Factor d(r).
2*r**2*(r + 3)*(4*r - 1)/5
Let n = 2104 - 11053/5. Let a = n + 107. Factor a*p + 0 + 2/5*p**2.
2*p*(p + 1)/5
Suppose -7*y = 5*y - 36. Factor 3*m**2 - 109*m**5 + 5*m**y - 5*m**4 + 104*m**5 + 2*m**2.
-5*m**2*(m - 1)*(m + 1)**2
Let n(i) be the second derivative of -i**6/960 - i**5/120 - 5*i**4/192 - i**3/24 - 2*i**2 + 15*i. Let p(j) be the first derivative of n(j). Factor p(h).
-(h + 1)**2*(h + 2)/8
Let r = 52/21 + -38/21. Factor -r*f**2 - 1/3*f - 1/3*f**3 + 0.
-f*(f + 1)**2/3
Factor -81*q**2 + 401*q - 11*q**2 + 314*q - 5*q**3 + 9*q**3 - 1200 - 75*q.
4*(q - 10)**2*(q - 3)
Suppose -2*a**4 + 8*a**4 + 12*a - 3*a**4 - 16*a**3 + 8*a**2 - 11*a**4 + 4*a**5 = 0. Calculate a.
-1, 0, 1, 3
Let t(f) = -4*f**2 + 2*f + 30. Let m(q) = 4*q**2 - q - 29. Let z = 60 - 54. Let d(p) = z*m(p) + 5*t(p). Factor d(u).
4*(u - 2)*(u + 3)
Let 4/5*a**5 - 336/5*a - 584/5*a**2 + 48/5*a**4 + 68/5*a**3 + 1568/5 = 0. Calculate a.
-7, -2, 2
Suppose -18/13*r + 2/13*r**2 + 36/13 = 0. What is r?
3, 6
Let t = 17 - 13. Suppose -4*w**3 - 3 + 1 + 4*w**2 + 2*w + 0 - 7*w**t + 2*w**5 + 5*w**4 = 0. What is w?
-1, 1
Let v(o) be the second derivative of -o**8/6720 + o**7/1680 + o**6/1440 - o**5/240 - 11*o**3/6 + 18*o. Let j(g) be the second derivative of v(g). Factor j(r).
-r*(r - 2)*(r - 1)*(r + 1)/4
Let m = 61 + -55. Let -9 - m*s**4 - 2*s**2 + 9*s**5 + 20*s + 7 - 29*s**3 + 10 = 0. What is s?
-1, -2/3, 1, 2
Let c(v) be the second derivative of -2/5*v**2 + 0 + 1/15*v**4 + 0*v**3 - v. Factor c(j).
4*(j - 1)*(j + 1)/5
Let x(v) be the third derivative of v**7/1470 - v**6/280 - v**5/140 + 11*v**4/168 - v**3/7 - 161*v**2. Factor x(u).
(u - 3)*(u - 1)**2*(u + 2)/7
Let j(n) be the third derivative of 0 - 1/4*n**4 - 2*n**2 + 1/80*n**6 + 0*n**3 + 0*n + 3/40*n**5. Factor j(x).
3*x*(x - 1)*(x + 4)/2
Let p(n) = -n**2. Let h(u) = -8*u**2 - 263*u + 39. Let o be h(-33). Let k(f) = 3*f**2 - 6*f. Let v = -3 + 4. Let j(w) = o*p(w) + v*k(w). Factor j(i).
-3*i*(i + 2)
Let l be (-5 - -4)*(-15)/300. Let m(d) be the third derivative of -l*d**6 + 1/3*d**4 + 1/105*d**7 + 0*d**5 + d**2 + 0 + 0*d + 0*d**3. Factor m(c).
2*c*(c - 2)**2*(c + 1)
Let a(m) = m**3 + 18*m**2 + 115*m + 154. Let p(n) = 2*n**3 + 35*n**2 + 229*n + 304. Let l(x) = -15*a(x) + 6*p(x). Determine f so that l(f) = 0.
-9, -2
Suppose 4*p - 20 = 0, 2*z - 4*p = -0*p - 10. Suppose 83 = -z*v + 93. Factor 0*m**v - 1/2*m**4 + 0*m**3 + 0 + 0*m.
-m**4/2
Let b(d) = -6*d - 190. Let k be b(-32). Solve 4/9*q**k - 4/3*q**3 + 32/9*q + 16/9 = 0.
-1, -2/3, 2
Suppose 0 = 30*f - 29*f - 5. Suppose -f*g + 9*g = 0. Factor g*n + 9/5*n**2 - 3/5*n**3 - 12/5.
-3*(n - 2)**2*(n + 1)/5
Let k(h) = -17*h + 196*h + 155*h**2 + 85 - 58*h + 104*h. Let o(a) = 11*a**2 + 16*a + 6. Let r(d) = 6*k(d) - 85*o(d). Factor r(s).
-5*s*(s + 2)
Let d(q) be the first derivative of -q**3/3 - 125*q**2/2 - 320. Factor d(g).
-g*(g + 125)
Let x(a) be the second derivative of 0 - 1/195*a**6 - 33*a - 1/26*a**4 + 2/65*a**5 + 0*a**3 + 0*a**2. Factor x(t).
-2*t**2*(t - 3)*(t - 1)/13
Let p be 92/