0. Calculate p.
-1, 0, 1
Let k = -1239/20 + 62. Let u(c) be the third derivative of -k*c**4 - 2*c**2 + 1/150*c**5 + 0 + 0*c + 2/15*c**3. Determine y so that u(y) = 0.
1, 2
Let n be (211/(-4))/(0 - (-270)/(-3)). Let f = 1/72 + n. Find p, given that -f + 0*p**3 - 3/5*p**4 + 0*p + 6/5*p**2 = 0.
-1, 1
Solve -180*c - 7*c**3 - 1/3*c**4 - 216 - 54*c**2 = 0.
-6, -3
Suppose -3 = -5*v - h - 2*h, -4*v + 1 = h. Let u(f) be the third derivative of -1/40*f**6 - 5*f**2 + 0*f - 1/20*f**5 + 0*f**3 + 0 + v*f**4. Solve u(k) = 0.
-1, 0
Let v(y) = y**3 - 14*y**2 + 13*y + 3. Let x be v(13). Suppose 4*w - 3*w = x. Factor 5*m**4 - m**4 - 7*m**5 - 3*m**3 + m**w + 5*m**5.
-2*m**3*(m - 1)**2
Solve 38/3*g**2 + 2/3*g**4 - 14*g + 14*g**3 - 40/3 = 0.
-20, -1, 1
Let m(o) = -2*o**4 - 5*o**3 - 11*o**2 + 5*o + 8. Let l(z) = z**4 + 4*z**3 + 10*z**2 - 4*z - 7. Let g(h) = -5*l(h) - 4*m(h). Find n such that g(n) = 0.
-1, 1
Let u = -4 + 9. Suppose -u*p + 16 = -4. Solve -2*c**p + c**5 - 2*c**3 + 8*c + 2*c**4 - 7*c = 0.
-1, 0, 1
Suppose 5*j - 23 + 13 = 0. Factor 2*v**4 + 25*v**j - 57*v**2 + 24*v**2.
2*v**2*(v - 2)*(v + 2)
Factor 1296 - 222*o + 4*o**2 + 0*o**2 + 78*o.
4*(o - 18)**2
Let x(v) be the third derivative of v**8/1344 + v**7/504 - 5*v**4/24 + 14*v**2. Let c(i) be the second derivative of x(i). Determine o so that c(o) = 0.
-1, 0
What is z in 13/6*z**3 + 1/6*z**5 - 7/3*z - 7/6*z**4 + 4/3 - 1/6*z**2 = 0?
-1, 1, 2, 4
Let f be ((-154880)/(-271824))/((-2)/(-3)). Let k = f + 2/809. Solve 4/7 + 10/7*c - k*c**2 = 0 for c.
-1/3, 2
Let z(o) = o. Let f(u) be the second derivative of -u**4/3 + 6*u**3 - 50*u**2 + 6*u. Let p(w) = -f(w) - 4*z(w). Determine c so that p(c) = 0.
5
Let i be 3/(-9) + 14/6. Factor -2*n**2 - 8 - 6*n - i*n - 4*n**2 + 4*n**2.
-2*(n + 2)**2
Let f = 223/14 + 46/7. Determine u so that -f*u**2 - 1/10 - 3*u = 0.
-1/15
Let k(g) be the third derivative of -g**6/180 - 7*g**5/135 + 5*g**4/108 + 212*g**2. Factor k(j).
-2*j*(j + 5)*(3*j - 1)/9
What is a in 3*a**2 - 5*a**5 - 35*a**4 + 6*a**2 - 9*a**2 + 0*a**5 - 60*a**3 = 0?
-4, -3, 0
Factor -664 + 664 + 3*i**3 + 3*i**4.
3*i**3*(i + 1)
Suppose 0 = -24*o - 20 + 44. Let y(w) be the first derivative of -2/3*w**3 + 0*w + 2/5*w**4 - 2/25*w**5 + 2/5*w**2 - o. Suppose y(n) = 0. What is n?
0, 1, 2
Let g(y) be the second derivative of -y**4/42 - 22*y**3/21 - 3*y**2 + 101*y. Factor g(o).
-2*(o + 1)*(o + 21)/7
Factor -3/2*f**3 + 4*f - 3*f**2 + 0 + 1/2*f**4.
f*(f - 4)*(f - 1)*(f + 2)/2
Let q(g) be the first derivative of 3*g**3/5 + 4*g**2 + 16*g/5 + 67. Let q(n) = 0. Calculate n.
-4, -4/9
Let s(x) be the first derivative of 245*x**3/3 + 35*x**2/2 - 10*x - 130. Determine k, given that s(k) = 0.
-2/7, 1/7
Let c be (0 - (3 + -5)) + 4. Suppose 0 = o - c*o + 10. Factor -6*x**3 - 6*x**4 - 10*x**5 + x - x + 8*x**5 - 2*x**o.
-2*x**2*(x + 1)**3
Suppose 2*b - 6 = -4*y, 2*b + b = -y + 9. Suppose 6*h - 10 = b*h + 2*l, -1 = -l. Factor 0*r**5 + r**5 + 3*r**4 + h*r**3 + r**2 - r**3 + 0*r**4.
r**2*(r + 1)**3
Let p(r) = 12*r**2 - 99*r - 93. Let k(b) = 7*b**2 - 99*b - 94. Let l(i) = -3*k(i) + 2*p(i). Solve l(s) = 0.
-32, -1
Let n(p) be the second derivative of -1/6*p**2 - 1/30*p**5 + 0 + 0*p**4 - 8*p + 1/9*p**3 + 1/90*p**6. Factor n(i).
(i - 1)**3*(i + 1)/3
Let a be (27/4 + -6)/(45/48). Let k(y) be the first derivative of -5/12*y**6 - a*y**5 + 4 + 1/4*y**2 + 1/2*y**4 + 5/3*y**3 - y. Determine t so that k(t) = 0.
-1, 2/5, 1
Let i(g) be the first derivative of 2*g**5/45 - g**4/6 - 8*g**3/27 + 18. Determine s so that i(s) = 0.
-1, 0, 4
Let -20/3*p**4 + 0 + 235/3*p**3 + 140/3*p + 620/3*p**2 = 0. Calculate p.
-2, -1/4, 0, 14
Let p = -367/4 + 12119/132. Let d(f) be the first derivative of -3/22*f**4 + 3/11*f**2 - 4/11*f + p*f**3 - 6 + 2/55*f**5. Determine u so that d(u) = 0.
-1, 1, 2
Factor -3*s - 13*s - 7*s + 60 - s**2 - 636 - 25*s.
-(s + 24)**2
Let l(o) be the first derivative of o**4/20 + 212. Suppose l(j) = 0. Calculate j.
0
Let i(f) = f - 1. Let x(p) = -2*p**2 - 3*p + 5. Suppose 35*a - 40*a + 10 = 0. Let u(m) = a*x(m) + 10*i(m). Let u(w) = 0. What is w?
0, 1
Let m(g) be the third derivative of -g**6/100 - 177*g**5/50 - 10443*g**4/20 - 205379*g**3/5 - 90*g**2 + g. Factor m(d).
-6*(d + 59)**3/5
Let h(y) be the third derivative of -5*y**8/84 + 46*y**7/105 - y**6/6 - 31*y**5/15 + 5*y**4/3 + 16*y**3/3 - 13*y**2 + 4*y. Solve h(u) = 0 for u.
-1, -2/5, 1, 4
Let b = 1453 + -966. Factor -3*k + 6*k**2 - 3*k**3 + b - 487.
-3*k*(k - 1)**2
Let f(h) be the second derivative of 1/2*h**3 - 3/20*h**4 - 13*h + 5/2*h**2 + 0 + 1/100*h**5. Factor f(w).
(w - 5)**2*(w + 1)/5
Let t be 216/(-22)*1/(-4) - 3. Let o = 41/55 + t. Factor -2/5 + o*h**2 + 1/5*h**4 - 3/5*h**3 + 3/5*h.
(h - 2)*(h - 1)**2*(h + 1)/5
Let l = -287/4 - -72. Solve 1/4*c**3 + 3/4*c - 3/4*c**2 - l = 0.
1
Let c(q) be the third derivative of -q**8/3360 + q**7/420 - q**5/15 + 5*q**4/6 + 27*q**2. Let u(n) be the second derivative of c(n). Factor u(t).
-2*(t - 2)**2*(t + 1)
Let h be ((-6)/5)/(9/(-60)). Suppose 3*o - 1 = h. Factor y**3 + 15*y + o*y**3 - 2 + 2*y**2 - y**5 - 18*y.
-(y - 2)*(y - 1)*(y + 1)**3
What is v in 2*v**3 + 1/3*v**5 - 13*v - 2*v**4 + 20/3*v**2 + 6 = 0?
-2, 1, 3
Let h(s) be the second derivative of s**4/66 + 4*s**3/11 - 28*s**2/11 - s + 6. Factor h(m).
2*(m - 2)*(m + 14)/11
Factor 68*n**5 + 65*n**5 - 129*n**5 + 9*n**3 - 108*n - n**3 + 24*n**4 - 80*n**2 - 40.
4*(n - 2)*(n + 1)**3*(n + 5)
Let w(y) be the second derivative of -y**10/151200 + y**8/33600 + 7*y**4/12 + 12*y. Let k(l) be the third derivative of w(l). Solve k(v) = 0 for v.
-1, 0, 1
Let t = -121 - -10165/84. Let i(k) be the second derivative of t*k**4 - 2/21*k**3 - 4*k + 2/7*k**2 + 0. Suppose i(p) = 0. What is p?
2
Let a(t) = t - 2*t**3 - 4*t**3 - 8*t**2 + 3*t - 1 - t**3. Let h(q) = -6*q**3 - 7*q**2 + 5*q. Let l(d) = -2*a(d) + 3*h(d). Factor l(n).
-(n - 1)*(n + 2)*(4*n + 1)
Let j(c) = 1567*c + 1571. Let i be j(-1). What is k in -5/2*k**i + 1/2*k**2 + 7/2*k**3 - 4*k + 1/2*k**5 + 2 = 0?
-1, 1, 2
Let d(b) be the first derivative of -b**6/15 - 4*b**5/25 + 3*b**4/10 + 8*b**3/15 - 4*b**2/5 - 186. Let d(k) = 0. What is k?
-2, 0, 1
Let s(t) be the first derivative of 5/4*t**2 - 5/12*t**3 - 5/8*t**4 + 5/4*t - 8. Find r such that s(r) = 0.
-1, -1/2, 1
Let j be (-13)/(-455)*-49 - (-147)/55. Let a = 2399/4378 + -1/398. Factor j*p - 4/11*p**2 - a.
-2*(p - 3)*(2*p - 1)/11
Let q be -1*(-27)/(11 - 2). Factor -1/4*w**q - 3/8*w**4 + 0 + 0*w**2 + 0*w - 1/8*w**5.
-w**3*(w + 1)*(w + 2)/8
Let s be 3*(-4)/60 - 1668/(-1140). Factor s*x - 2/19*x**2 - 72/19.
-2*(x - 6)**2/19
Let a be (-22)/264 + -3*177/(-324). Let c = -45/46 + 865/414. What is s in 2/9*s**3 + 2/3 + a*s + c*s**2 = 0?
-3, -1
Let b(g) be the first derivative of g**3/7 + g**2/7 - g/7 + 44. Determine z so that b(z) = 0.
-1, 1/3
Let i(d) be the third derivative of d**6/120 - 7*d**5/60 - 5*d**4/12 + 8*d**3/3 + 439*d**2. Suppose i(q) = 0. What is q?
-2, 1, 8
Let w(k) be the third derivative of k**7/35 + 7*k**6/30 + 19*k**5/30 + k**4/3 - 4*k**3/3 - 3*k**2 - 4. Let w(o) = 0. What is o?
-2, -1, 1/3
Suppose 2*j = 27 - 5. Factor j*f**2 + 2*f + 2*f**2 - 3*f**2 + 2*f.
2*f*(5*f + 2)
Let j(y) be the second derivative of -y**5/10 - 5*y**4/8 - y**3 + 13*y**2 + 9*y. Let b(z) be the first derivative of j(z). Solve b(a) = 0.
-2, -1/2
Let d(x) be the first derivative of -4*x**5/15 + x**4/3 + 4*x**3/3 - 2*x**2/3 - 8*x/3 - 104. Solve d(b) = 0 for b.
-1, 1, 2
Let x(v) be the first derivative of 0*v**4 + 0*v - 3/20*v**5 + 3 - v**2 - 1/40*v**6 + 0*v**3. Let b(y) be the second derivative of x(y). Factor b(s).
-3*s**2*(s + 3)
Let l(o) = -o**3 + 9*o**2 - 9*o + 6. Let r be l(8). Let t be -2 + 8/2 + r. Factor 16*m - 16*m + 2*m**3 + t*m**3 + 8 - 6*m**2.
2*(m - 2)**2*(m + 1)
Let s(f) be the second derivative of 0*f**5 - 35*f + 0*f**6 + 0*f**2 + 0 - 1/63*f**7 + 0*f**4 + 0*f**3. Factor s(j).
-2*j**5/3
Let g(s) be the second derivative of 23*s + 6/35*s**5 + 2/49*s**7 + 0 - 2/21*s**3 - 16/105*s**6 + 0*s**2 + 0*s**4. Solve g(v) = 0 for v.
-1/3, 0, 1
Suppose -8/5*j - 14/5*j**4 + 0 - 16/5*j**2 + 38/5*j**3 = 0. Calculate j.
-2/7, 0, 1, 2
Let p(v) be the first derivative of -14 + 5/6*v**2 + 1/9*v**3 + 2*v. Find x such that p(x) = 0.
-3, -2
Let b(q) = 4*q**3 + 2*q**2 - q + 1. Let z(y) = 5*y**3 + 3*y**2. Let l be -1 + 0 + (6 - 8 - 0). Let o(m) = 