p**3 + 1/3*p**4 = 0.
3, 4
Suppose -4*t - f = -8, -15*t = -18*t + 5*f + 29. Factor 0 + 4/13*b**t + 0*b + 2/13*b**4 + 0*b**2.
2*b**3*(b + 2)/13
Let f(y) be the second derivative of 1/45*y**6 + 0 + 15*y + 0*y**2 - 1/18*y**4 - 1/10*y**5 + 1/3*y**3. Factor f(m).
2*m*(m - 3)*(m - 1)*(m + 1)/3
Suppose 11*d - 6*d = 45. Let p(m) = -2*m + 20. Let l be p(d). Factor -2*i**2 - l*i**2 - 5*i + 6*i**2 + 7*i.
2*i*(i + 1)
Let c(r) be the second derivative of r**5/160 - r**4/64 + 13*r**2/2 - 15*r. Let f(m) be the first derivative of c(m). Solve f(j) = 0.
0, 1
Let q(a) = a**2 + a + 1. Suppose 3*o - o + 5*k = 19, 5*o + 2 = 4*k. Let g(r) = 5*r**o + 3 - 1 + 2 + 4*r. Let f(y) = -g(y) + 4*q(y). Factor f(v).
-v**2
Let u(l) = -l**2 - l. Let z(n) = -n**2 + 17*n + 5. Let t(m) = u(m) + z(m). Let b(c) = -c**2 + 8*c + 2. Let f(j) = 10*b(j) - 4*t(j). Factor f(q).
-2*q*(q - 8)
Let i(v) be the third derivative of -49*v**6/200 - 91*v**5/50 + 11*v**4/8 - 2*v**3/5 + 63*v**2 + 1. What is k in i(k) = 0?
-4, 1/7
Let o(g) be the first derivative of g**3/3 + 5*g**2/2 - 79. Suppose o(j) = 0. What is j?
-5, 0
Let q(m) be the second derivative of -1/40*m**5 + 0*m**2 + 0 + 1/12*m**3 + 0*m**4 + 39*m. Find u such that q(u) = 0.
-1, 0, 1
Let r(w) = 2*w**2 + 8*w + 19*w**3 + 27*w**2 - 8 + 11*w**2. Let c(h) = -104*h**3 - 220*h**2 - 44*h + 44. Let j(f) = -5*c(f) - 28*r(f). What is t in j(t) = 0?
-1, 1/3
Let j(a) be the second derivative of -1/2*a**3 + 8*a + 51/40*a**5 + 7/10*a**6 + 0 + 0*a**2 + 1/8*a**4. Determine b, given that j(b) = 0.
-1, -1/2, 0, 2/7
Suppose 100 = 2*y + 2*y + 5*w, 5*y = -w + 104. Determine h, given that 2 + 52*h**3 + 335*h - 333*h - 30*h**2 - 6*h**3 - y*h**4 = 0.
-1/5, 1/2, 1
Let k(j) = 2*j**2 + 11*j + 15. Let h be k(-3). Let n(w) be the third derivative of 0 + 0*w + 1/30*w**6 + 0*w**4 + 1/15*w**5 + h*w**3 + 7*w**2. Factor n(t).
4*t**2*(t + 1)
Let y be (1/(-2))/(-1) + 455/14. Let x be (-2)/(-3) + 77/y. Determine t so that -6/5*t**2 + 0*t + 3*t**4 + 9/5*t**x + 0 = 0.
-1, 0, 2/5
Let m(c) = -c**5 - 6*c**4 + 20*c**2 + 17*c - 2. Let t(o) = -2*o**5 - 6*o**4 + 19*o**2 + 18*o - 3. Let v(y) = -3*m(y) + 2*t(y). Factor v(z).
-z*(z - 5)*(z - 3)*(z + 1)**2
Let j(h) be the second derivative of -9*h**5/80 + 73*h**4/16 + 149*h**3/24 + 25*h**2/8 - 82*h. Factor j(z).
-(z - 25)*(3*z + 1)**2/4
Let o(f) = 3*f - 9. Let b be o(-6). Let v be (4/(-12))/(3/b). Find h, given that -4*h**2 + h**2 - v*h + 6*h**2 = 0.
0, 1
Let w(c) = -c**2 + 13*c - 9. Let x be w(12). Suppose 51*o + 24*o**x + 27*o**2 + 4*o**4 + 12 + 21*o**2 - 11*o = 0. Calculate o.
-3, -1
Let h be 7 + (-3*2)/(-3). Let q be (2 + -1)/3*h. Factor -12*n**2 - 19*n**3 + 3*n**5 + 9*n**4 + 19*n**q.
3*n**2*(n - 1)*(n + 2)**2
Determine f so that 1/10*f**4 + 0 + 3/2*f**2 - 5/2*f + 9/10*f**3 = 0.
-5, 0, 1
Suppose -2/13*f**3 + 12/13*f + 0 + 2/13*f**2 = 0. Calculate f.
-2, 0, 3
Let y = 8 - 5. Factor 10*h**5 - 20*h + 7 - 25*h**4 + 20*h**2 - 2 + 112*h**3 - 102*h**y.
5*(h - 1)**3*(h + 1)*(2*h - 1)
Let k(v) be the first derivative of v**6/18 + 2*v**5/15 - 11*v**4/12 - 4*v**3/3 + 49. Factor k(h).
h**2*(h - 3)*(h + 1)*(h + 4)/3
Let q(s) be the first derivative of -s**6/6 - 12*s**5/5 - 57*s**4/4 - 134*s**3/3 - 78*s**2 - 72*s + 259. Factor q(l).
-(l + 2)**3*(l + 3)**2
Let o(b) be the first derivative of -b**7/126 - 2*b**6/45 - b**5/12 - b**4/18 - 4*b - 8. Let k(x) be the first derivative of o(x). What is f in k(f) = 0?
-2, -1, 0
Let d be 15 - (2 - 12 - -22). Let -1/4*q - 3/2*q**d + 7/4*q**5 + 0 - 2*q**4 + 2*q**2 = 0. What is q?
-1, 0, 1/7, 1
Determine c so that -15/4*c**3 + 57 - 174*c + 321/4*c**2 = 0.
2/5, 2, 19
Let d(c) be the first derivative of -c**6/1440 + c**5/30 - 2*c**4/3 - 19*c**3/3 - 18. Let b(p) be the third derivative of d(p). Factor b(w).
-(w - 8)**2/4
Let x(k) = k**3 + 321*k**2 + 314*k. Let v(u) = 2*u**3 + 322*u**2 + 316*u. Let z(l) = -3*v(l) + 2*x(l). Determine j, given that z(j) = 0.
-80, -1, 0
Let s = 908/75 + 262/75. Factor s*y**3 - 6/5 + 9/5*y**5 + 33/5*y - 72/5*y**2 - 42/5*y**4.
3*(y - 1)**4*(3*y - 2)/5
Let r = -192051/11 + 17461. Suppose 14/11*y - r - 2/11*y**2 = 0. Calculate y.
2, 5
Let b(n) = -n**3 + 2*n**2 + 22*n - 8. Let w be b(-4). Factor -2/5*c**3 - 2/5*c**4 + 0 + w*c + 0*c**2.
-2*c**3*(c + 1)/5
Let q(s) be the second derivative of -s**5/240 - 5*s**4/96 + s**2/2 + 6*s. Let x(n) be the first derivative of q(n). Find d, given that x(d) = 0.
-5, 0
Let z be -11 + 20 + (-1417)/169. Factor -14/13*j**2 - 16/13*j + 10/13*j**3 + z.
2*(j - 2)*(j + 1)*(5*j - 2)/13
Let a(j) = -5*j**2 + 28*j - 4. Let l(y) = -14*y**2 + 84*y - 11. Let k(p) = 11*a(p) - 4*l(p). Let k(q) = 0. Calculate q.
0, 28
Let m(v) be the first derivative of v**7/168 + v**6/60 + v**5/80 + 2*v + 16. Let h(z) be the first derivative of m(z). Factor h(k).
k**3*(k + 1)**2/4
Suppose -41*s = -21*s - 40. Let k(q) be the second derivative of 0*q**s + 1/30*q**6 + 3*q + 0 - 1/12*q**4 + 1/6*q**3 - 1/20*q**5. Factor k(t).
t*(t - 1)**2*(t + 1)
Let -8 + 7/2*o**2 + 1/2*o**3 + 4*o = 0. What is o?
-4, 1
Let v = 30 - 0. Suppose -v = 2*k - 8*k. Determine p, given that 15*p**k + 0 - 12*p**5 + 0 + 3*p - 6*p**3 = 0.
-1, 0, 1
Let p(o) be the first derivative of 3/2*o**3 + o - 5/8*o**4 + 1/10*o**5 - 7/4*o**2 - 18. Factor p(a).
(a - 2)*(a - 1)**3/2
Factor -6*b + 6*b + 7*b - 4*b - 3*b**2 + 6*b.
-3*b*(b - 3)
Factor -424128*g + 1273*g**2 + 1459*g**2 + 26578688 - 654*g**2 - 4*g**3 + 178*g**2.
-4*(g - 188)**3
Suppose x - i + 6 = 3*x, x + 4 = 3*i. Suppose 4 = -v + 8. Solve -v*p**x + 6*p - 2*p**2 + 3*p**2 - 3 + 0*p**2 = 0 for p.
1
Factor -882 - 1/2*d**2 + 42*d.
-(d - 42)**2/2
Let p(s) be the third derivative of -s**8/392 + s**7/490 + 9*s**6/280 - s**5/35 - s**4/14 + s**2 - 259*s. Find g such that p(g) = 0.
-2, -1/2, 0, 1, 2
Suppose 6 = -3*u - 2*p, 0 = -u + 2*u - 2*p - 6. Suppose 9*q - 18 = -0*q. Factor -1/2*h + 3/4*h**4 + 1/4*h**5 - 3/4*h**q + 1/4*h**3 + u.
h*(h - 1)*(h + 1)**2*(h + 2)/4
Factor -34*u**3 + u**4 - 31*u**3 + 106*u**3 - 22*u**2 + 44*u - 24 - 40*u**3.
(u - 2)**2*(u - 1)*(u + 6)
Let n(p) be the first derivative of 7/2*p**2 + 4 + 0*p**3 + 1/12*p**4 + 0*p + 1/30*p**5. Let j(k) be the second derivative of n(k). Factor j(z).
2*z*(z + 1)
Let p(t) be the second derivative of -t**6/6 + 2*t**5 - 5*t**4/2 - 100*t**3/3 - 125*t**2/2 + 17*t. What is h in p(h) = 0?
-1, 5
Let h(l) = 23*l**2 + 1283*l + 81920. Let w(u) = -17*u**2 - 1282*u - 81920. Let a(b) = 2*h(b) + 3*w(b). Determine p, given that a(p) = 0.
-128
Let d(o) be the third derivative of o**5/40 + 5*o**4/4 - 11*o**3 + 30*o**2 - 4*o. Find i, given that d(i) = 0.
-22, 2
Let p be 2/4*0/(23/(276/(-72))). Determine v, given that 5/4*v**5 + 5/4*v**2 + 0*v + 15/4*v**3 + 15/4*v**4 + p = 0.
-1, 0
Suppose 0 = -5*h + 64 - 14. Let x be (-2 - 0/(-1)) + 9. Let -h*f**2 + x*f**4 + 3*f**5 - f**4 + 2*f**2 + 2*f**2 - 3*f = 0. What is f?
-1, 0, 1
Let c be (-12)/(-42)*(2 + 12 - 7). Factor 0 + 0*n - 1/4*n**c.
-n**2/4
Let n(b) be the first derivative of b**5/210 - b**4/42 + b**3/21 + 55*b**2/2 - 60. Let x(i) be the second derivative of n(i). Factor x(m).
2*(m - 1)**2/7
Let y(v) be the first derivative of 4*v**5/5 - 8*v**3/3 + 4*v + 108. Find m such that y(m) = 0.
-1, 1
Let z(f) be the first derivative of -f**6/27 + 104*f**5/45 - 338*f**4/9 - 103. Determine m, given that z(m) = 0.
0, 26
Let l = 7/197 + 563/788. Determine a so that 27/4*a - 9/4*a**4 + l*a**5 + 15/4 - 15/2*a**3 - 3/2*a**2 = 0.
-1, 1, 5
Let q(n) be the first derivative of 0*n**2 - 12*n**4 + 24/5*n**5 + 0*n - 10 - 2/3*n**6 + 32/3*n**3. Factor q(m).
-4*m**2*(m - 2)**3
Suppose 3*m - 3 - 6 = 0. Factor m*j**3 - 2 - 9*j + 1 - 5.
3*(j - 2)*(j + 1)**2
Suppose 93*k - 5*k + k**2 + 841 - 17*k - 13*k = 0. Calculate k.
-29
Let d(w) be the first derivative of -2/5*w**2 + 2/5*w**3 - 2/25*w**5 + 0*w**4 + 0*w - 6. Factor d(a).
-2*a*(a - 1)**2*(a + 2)/5
Determine a so that -4*a**5 - 31*a**4 + 21*a**4 + 6*a**3 + 4*a**4 + 4*a**2 = 0.
-2, -1/2, 0, 1
Let q(m) be the third derivative of m**9/3024 - m**7/168 - m**6/72 + 13*m**4/24 - 50*m**2. Let u(z) be the second derivative of q(z). Let u(l) = 0. What is l?
-1, 0, 2
Let u(j) be the first derivative of 0*j - 3/8*j**4 + 1 - 1/4*j**2 - 1/2*j**3 - 1/10*j**5. Factor u(m).
-m*(m + 1)**3/2
Let y = -269 + 276. Let q(k) be the second derivative of 0 + 0*k**2 - 1/3*k**3 - 2/5*k**5 + y*k - 5/6*k