third derivative of c**7/8820 - c**6/1260 + c**5/420 - c**4/3 + 13*c**2. Let v(n) be the second derivative of t(n). Factor v(q).
2*(q - 1)**2/7
Let j(d) = 5*d**4 + 45*d**3 + 15*d**2 - 40*d - 35. Let s(h) = 2*h**4 + 23*h**3 + 7*h**2 - 20*h - 18. Let v(c) = -3*j(c) + 5*s(c). Factor v(y).
-5*(y - 1)*(y + 1)**2*(y + 3)
Suppose -78 - 30 = -4*t. What is i in 3*i**2 - 12*i - 8*i**2 - 10 + t*i = 0?
1, 2
Let u(s) be the second derivative of s**4/24 - 9*s**3/4 - 7*s**2 - 26*s. Factor u(k).
(k - 28)*(k + 1)/2
Let z(s) be the third derivative of 0*s**4 + 0*s**5 + 0*s**3 + 1 + 0*s**7 - 29*s**2 + 0*s - 1/336*s**8 + 1/30*s**6. Factor z(w).
-w**3*(w - 2)*(w + 2)
Let 13*b**2 + b**3 - 11*b**2 - 2*b**3 - b**2 + 2*b = 0. What is b?
-1, 0, 2
Let i(x) be the second derivative of -x**5/30 - 65*x**4/36 - 272*x**3/9 - 128*x**2/3 + 211*x. Suppose i(u) = 0. Calculate u.
-16, -1/2
Let n(q) be the first derivative of q**4/2 - 12*q**3 + 81*q**2 - 140. What is g in n(g) = 0?
0, 9
Let r(y) = -2*y**3 - 3*y**2 + 4*y + 17. Let v be r(-5). Factor 2*i**3 - 28*i**2 - 52*i - 133 + v*i - 11.
2*(i - 6)**2*(i - 2)
Suppose -30*l - 60 = -50*l. Solve 18/7 + 3*j + 6/7*j**l - 27/7*j**2 = 0 for j.
-1/2, 2, 3
Let z(u) be the third derivative of u**5/210 + 5*u**4/42 - 8*u**3/7 + 167*u**2. Factor z(c).
2*(c - 2)*(c + 12)/7
Let b(v) = v**2 + 9*v - 11. Let y be b(-11). Let p(m) = m**3 - 11*m**2 + 2*m - 20. Let a be p(y). Factor 1/3*o**3 - 2/3 + 0*o**a - o.
(o - 2)*(o + 1)**2/3
Suppose 5*g = 4*s - 334, g - 2*s + 36 = -32. Let t = g + 66. Let t - 1/3*h**4 + 0*h**3 + 0*h + 1/3*h**2 = 0. What is h?
-1, 0, 1
Factor -181/2*h - 9 - 25/2*h**3 - 230*h**2.
-(h + 18)*(5*h + 1)**2/2
Let q(p) = p**3 + 2*p**2 - 3. Let b(r) = -r**3 + 14*r**2 + 80*r - 3. Let m(i) = -b(i) + q(i). Factor m(g).
2*g*(g - 10)*(g + 4)
Let y be 2 - (-3*1 - (-21)/7). Factor -j**y - 88*j - 1 + 168*j - 82*j.
-(j + 1)**2
Let l = 26315 - 78944/3. Factor 4*g + 4/3 + l*g**4 + 2*g**3 + 13/3*g**2.
(g + 1)**2*(g + 2)**2/3
Find m, given that 7/4*m**2 - 1/8*m**4 + 0 + 3*m - 1/8*m**3 = 0.
-3, -2, 0, 4
Let n(x) be the second derivative of 5*x + 0*x**3 + 0*x**4 + 1/120*x**6 + 1/30*x**5 + 1/2*x**2 + 0. Let u(r) be the first derivative of n(r). Factor u(y).
y**2*(y + 2)
Let c(u) be the second derivative of -u**7/14 + 4*u**6/5 - 33*u**5/10 + 6*u**4 - 9*u**3/2 + 67*u. Suppose c(o) = 0. Calculate o.
0, 1, 3
Let -7*z - 14*z**2 + 36*z - 4*z**2 + 12 + 21*z = 0. What is z?
-2/9, 3
Let p(f) be the first derivative of -5*f**6/6 + 8*f**5 + 5*f**4/4 - 40*f**3/3 - 150. Suppose p(m) = 0. What is m?
-1, 0, 1, 8
Let b(x) be the second derivative of -x**5/90 - 7*x**4/18 - 8*x**3/3 - 68*x**2/9 - 4*x - 12. Factor b(h).
-2*(h + 2)**2*(h + 17)/9
Find h, given that 6 - 12*h**3 + 30*h**2 - 50*h**4 + 27*h + 34*h**4 - 15*h**5 - 20*h**4 = 0.
-1, -2/5, 1
Suppose 3*u + 37*w - 13 = 36*w, -u + w - 5 = 0. Factor 0 - 2/5*n**5 - 2/5*n**u + 2/5*n**4 + 0*n + 2/5*n**3.
-2*n**2*(n - 1)**2*(n + 1)/5
Let y(x) be the third derivative of x**8/5040 - x**7/315 - x**6/36 - 3*x**5/20 + 5*x**2. Let a(d) be the third derivative of y(d). Let a(t) = 0. Calculate t.
-1, 5
Factor -14/23*x + 2/23*x**3 - 12/23 + 0*x**2.
2*(x - 3)*(x + 1)*(x + 2)/23
Let y(d) = 11*d + 116. Let z be y(-11). Let t be z/15*3*(0 + -2). Determine w so that 1/2*w**4 + 0 - 3/2*w - 5/2*w**t - 1/2*w**3 = 0.
-1, 0, 3
What is u in -177*u**2 + 5517*u + 132*u**3 + 21 - 5457*u - 21*u**2 - 15*u**4 = 0?
-1/5, 1, 7
Let d = 766/1143 - 4/1143. Factor 2/3*n**2 + 0*n - d.
2*(n - 1)*(n + 1)/3
Let a be (-35)/15 + (2 - 1/(-2)). Let r(s) be the first derivative of -1/4*s**2 + 0*s - 1 + a*s**3. Factor r(g).
g*(g - 1)/2
Let h(p) = p**3 + 62*p**2 + 183*p + 354. Let g be h(-59). Factor 0 + g*t - 1/3*t**2 + 7/6*t**5 + 1/2*t**3 + 2*t**4.
t**2*(t + 1)**2*(7*t - 2)/6
Let f(m) be the second derivative of m**7/5040 - m**6/360 - 9*m**4/4 + 20*m. Let h(i) be the third derivative of f(i). Let h(a) = 0. Calculate a.
0, 4
Suppose 5*w - 220 = -95. Factor -16 + 67*v**2 + w + 12*v**3 - 18 + 24*v - 22*v**2.
3*(v + 1)*(v + 3)*(4*v - 1)
Let n be (-3*4/8)/(0 + -30). Let o(g) be the first derivative of 4 - 1/4*g**2 - 1/4*g + 1/8*g**4 + 0*g**3 + n*g**5. Factor o(a).
(a - 1)*(a + 1)**3/4
Suppose -4 = -4*n + 4*p, 5 = -3*n - 5*p - 8. Let v be n + -5 + (-81)/(-9). Factor -1/3*z + 1/6*z**v + 0 - 1/6*z**2.
z*(z - 2)*(z + 1)/6
Let r(v) be the first derivative of 2*v**3/39 - 17*v**2/13 - 76*v/13 - 255. Factor r(s).
2*(s - 19)*(s + 2)/13
Let r(f) be the second derivative of f**7/84 + 5*f**6/12 + 187*f**5/40 + 359*f**4/24 - 22*f**3/3 - 121*f**2 - 7*f - 6. What is x in r(x) = 0?
-11, -2, 1
Let v(w) be the second derivative of -w**6/15 - 49*w**5/20 - 311*w**4/12 - 20*w**3 + 72*w**2 + 331*w. Determine s so that v(s) = 0.
-12, -1, 1/2
Let w(f) = -f**2 - 28*f + 32. Suppose 24 = 5*p - 1. Let s(b) = 3*b**2 + 56*b - 64. Let c(l) = p*w(l) + 3*s(l). Factor c(z).
4*(z - 1)*(z + 8)
Let i = -1/59 + 123/295. Suppose 3*g = j - 5 - 0, 0 = 5*g + 2*j - 10. Let -4/5*t + g*t**2 - i + 4/5*t**3 + 2/5*t**4 = 0. What is t?
-1, 1
Let v = -30 + 32. Factor 0*q**v + q**2 - 16 + 19*q**2 - 32*q.
4*(q - 2)*(5*q + 2)
Let o(i) = -5*i**3 - 22*i**2 - 28*i - 4. Let v(x) = -5 + 8 - 4. Let q(z) = o(z) + 4*v(z). Factor q(b).
-(b + 2)**2*(5*b + 2)
Let h(u) be the first derivative of 4*u**5 - 324*u + 20 + 0*u**3 - 15*u**4 - 1/3*u**6 + 135*u**2. Solve h(z) = 0 for z.
-2, 3
Let z(b) = b**3 - b**2. Suppose -2*u + 11*u - 45 = 0. Let d(m) = -85*m**3 - 275*m**2 - 125*m - 15. Let y(l) = u*z(l) + d(l). Factor y(t).
-5*(t + 3)*(4*t + 1)**2
Let g(l) be the second derivative of 9*l**5/4 - 37*l**4/2 + 59*l**3/2 - 18*l**2 + 82*l. Factor g(y).
3*(y - 4)*(3*y - 1)*(5*y - 3)
Let n(d) be the third derivative of -7/12*d**4 + 0 - 49/6*d**3 - 4*d**2 + 0*d - 1/60*d**5. Determine w so that n(w) = 0.
-7
Let b(w) be the second derivative of -24/5*w**2 + 8*w + 1/50*w**6 - 8/5*w**3 + 0 + 3/25*w**5 + 0*w**4. Let b(q) = 0. What is q?
-2, 2
Factor 0 - 1/3*l**2 + 1/3*l**4 + 5/3*l**3 - 5/3*l.
l*(l - 1)*(l + 1)*(l + 5)/3
Let f(d) be the third derivative of -d**6/30 + 47*d**5/5 - 2209*d**4/2 + 207646*d**3/3 - 32*d**2 + 8. Let f(z) = 0. Calculate z.
47
Let v(c) be the second derivative of c**7/210 - c**5/15 + 25*c**2/2 + 13*c. Let k(p) be the first derivative of v(p). Factor k(b).
b**2*(b - 2)*(b + 2)
Let k(z) = -12*z**3 - 9*z**2 + 225*z - 273. Let r(x) = -3*x**3 - 2*x**2 + 56*x - 68. Let l(i) = 4*k(i) - 15*r(i). What is n in l(n) = 0?
-6, 2
Let g(p) be the first derivative of 5*p**3/6 + 35*p**2/2 + 100*p - 148. Factor g(d).
5*(d + 4)*(d + 10)/2
Let a(z) be the second derivative of -5*z**4/12 - 35*z**3/6 + 75*z**2 + 2*z + 69. Factor a(w).
-5*(w - 3)*(w + 10)
Let h(c) = -5*c**3 + 260*c**2 - 148*c - 95. Let i(z) = -10*z**3 + 521*z**2 - 298*z - 193. Let d(n) = 5*h(n) - 3*i(n). Factor d(b).
(b - 52)*(b - 1)*(5*b + 2)
Let s = 3/151 + 3011/453. Factor 0 + 20/3*g**2 + 5/3*g**4 - s*g**3 + 0*g.
5*g**2*(g - 2)**2/3
Let l(y) be the first derivative of -y**3 - 108*y**2 - 3888*y - 61. Determine f, given that l(f) = 0.
-36
Let b = 40 - 37. Suppose 2*p + w = -w - 10, -b*w - 15 = 4*p. Factor -8/3*k**3 + 0 + 8/3*k**2 + p*k + 2/3*k**4.
2*k**2*(k - 2)**2/3
Suppose 0 = v - 6*v + 10. Suppose -5*q = 3*w - 25, v*q - 3*w = 2*w - 21. Factor -89 + 4*n**3 + 4*n**q - 8*n + 89.
4*n*(n - 1)*(n + 2)
Let a = -51 + 68. Factor 5*z**2 + 5 - a*z - 8*z - 15 - 15*z**2.
-5*(z + 2)*(2*z + 1)
Let s(w) be the third derivative of -w**8/1176 + 8*w**7/735 + w**6/420 - 4*w**5/105 + 169*w**2. Solve s(h) = 0 for h.
-1, 0, 1, 8
Let q be (-58096)/56*(-2)/796. Let h = q + -7/199. Factor -h*c - 27/7 - 3/7*c**2.
-3*(c + 3)**2/7
Let d(q) be the third derivative of -q**5/120 - q**4/48 + 5*q**3/3 - 5*q**2 - 7. Let d(n) = 0. What is n?
-5, 4
Suppose -2 - 22 = -6*h. Let x(z) = 6*z**4 + 4*z**3 + 2*z**2 + 3. Let m(i) = 5*i**4 + 3*i**3 + i**2 + i + 2. Let j(q) = h*x(q) - 5*m(q). What is y in j(y) = 0?
-2, 1
Let t(u) be the first derivative of -u**4/14 - 46*u**3/21 - 120*u**2/7 + 288*u/7 + 61. Suppose t(w) = 0. Calculate w.
-12, 1
Let k be -3 + (-1)/(-5) + 16/20 + 2. What is m in -1/2*m + k*m**4 + 0 + m**3 - 1/2*m**5 + 0*m**2 = 0?
-1, 0, 1
Let c(t) = -3*t**4 + 7*t**3 - 2*t**2 + t - 3. Let p(o) = 24*o**3 + 5*o**4 + 2*o**2 - 2*o - 3*o**4 - 30*o**3 + 4. Let w(y) = -4*c(y) - 3*p(y). Factor w(l).
2*l*(l - 1)**2*(