 l be 9/(-24) - (-33)/88. Let -2/5*w**2 + 1/5*w**3 + 1/5*w + l = 0. What is w?
0, 1
Suppose -5*w = -0*q - 2*q + 2, 6 = w - 2*q. Let t = w - -5. Suppose 0 + 1/4*g + 3/4*g**t + g**2 = 0. What is g?
-1, -1/3, 0
Let o be (-5 - -1) + (-1031)/(-7). Let t = o - 143. Find l such that -t*l**2 + 0 + 2/7*l = 0.
0, 1
Let w = 1 - -1. Factor 0*r**w - r**2 - 2*r**2 + r**3 + 4*r**4 - r**2 - r.
r*(r - 1)*(r + 1)*(4*r + 1)
Let x = 63 - 313/5. Factor 2/5*z**4 - x + 0*z**2 - 4/5*z**3 + 4/5*z.
2*(z - 1)**3*(z + 1)/5
Solve -16/3 + 4/3*s**2 + 8*s - 2*s**3 = 0 for s.
-2, 2/3, 2
Let h(b) be the first derivative of 27*b**4/2 + 18*b**3 + 9*b**2 + 2*b - 8. Solve h(j) = 0.
-1/3
Solve -2/11*p**3 + 24/11*p**2 + 2*p + 4/11 - 8/11*p**4 = 0 for p.
-1, -1/4, 2
Let p(s) = 39*s**3 + 60*s**2 + 9*s - 60. Let w(j) = -8*j**3 - 12*j**2 - 2*j + 12. Let y(h) = -5*p(h) - 24*w(h). Factor y(d).
-3*(d - 1)*(d + 1)*(d + 4)
Suppose -16 = -6*y + 2*y. Factor -2*k**4 + 4*k**y + 0*k**4 + 2*k**3.
2*k**3*(k + 1)
Let j(n) be the first derivative of -n**5/80 - n + 2. Let s(x) be the first derivative of j(x). Find u such that s(u) = 0.
0
Let o(n) be the second derivative of -4/5*n**6 + 3*n**3 - 5/21*n**7 + 2*n**2 + 0 - n + 5/3*n**4 - 2/5*n**5. Let o(z) = 0. Calculate z.
-1, -2/5, 1
Let p(f) = -f**3 - f**2 + f + 1. Let k(j) = 6*j**3 - 8*j**3 + 4*j**4 + 2 - 14*j**3 + 8*j**2 + 2. Let t(g) = -k(g) + 4*p(g). Find x such that t(x) = 0.
0, 1
Factor -2*i + 35*i**3 + 4*i**2 - 35*i**3 + 2*i**5 - 4*i**4.
2*i*(i - 1)**3*(i + 1)
Let p(n) be the first derivative of 0*n + 1/8*n**2 - 1/16*n**4 + 0*n**3 - 2. Find t such that p(t) = 0.
-1, 0, 1
Let t be (-18)/(-48) - 2/48. Suppose 4/3*y**3 - y**2 + 0 - t*y = 0. Calculate y.
-1/4, 0, 1
Let s(w) be the second derivative of -w**6/24 + w**5/16 + 5*w**4/16 - 25*w**3/24 + 5*w**2/4 + 34*w. Factor s(r).
-5*(r - 1)**3*(r + 2)/4
Suppose -2*j - 14 = -0. Let l = 11 + j. Factor 5*u**l + u**4 - 6*u**3 + 2*u**3.
2*u**3*(3*u - 2)
Let b(s) = 25*s**2 + 4*s. Let v(n) be the first derivative of 8*n**3 + 2*n**2 + 6. Let i(f) = -4*b(f) + 5*v(f). Suppose i(j) = 0. What is j?
-1/5, 0
Let z(s) = -s**3 + s**2. Let y(i) = 123*i**3 + 27*i**2 - 105*i - 45. Let x(r) = -y(r) + 2*z(r). Factor x(g).
-5*(g - 1)*(5*g + 3)**2
Let w(m) be the second derivative of 1/9*m**4 - 6*m + 0 - m**2 + 1/45*m**6 - 4/9*m**3 + 2/15*m**5. Factor w(c).
2*(c - 1)*(c + 1)**2*(c + 3)/3
Suppose w = -4*w + 20. Suppose -w*t + 5*y = t + 5, -y = -2*t + 1. Determine k so that k**3 + 1 - t*k**4 - 1 + k**5 = 0.
0, 1
Let g(q) be the first derivative of 2*q**3/3 - 3*q**2 - 8*q + 12. Factor g(z).
2*(z - 4)*(z + 1)
Let c(w) = -3*w + 15. Let b be c(5). Let l(v) be the first derivative of -4 + 1/2*v**4 + 2/15*v**5 + 2/3*v**3 + 1/3*v**2 + b*v. Suppose l(t) = 0. What is t?
-1, 0
Let n(g) be the third derivative of -g**7/5040 - g**6/720 - g**5/240 - g**4/144 + g**3/2 - 3*g**2. Let p(s) be the first derivative of n(s). Solve p(u) = 0.
-1
Let o(s) be the second derivative of -s**4/48 - s**3/12 + 8*s. Factor o(v).
-v*(v + 2)/4
Suppose u + 2 = -3*k, -4*k = -5*u + 16 + 12. Let x be (-3 + 1)/((-2)/u). Let 6*a**3 + 3*a**x - 6*a**2 - 3*a - 3*a**5 - a + 2*a - a + 3 = 0. What is a?
-1, 1
Let y(r) be the second derivative of r**4/4 + 13*r**3 + 507*r**2/2 - 35*r. Suppose y(n) = 0. What is n?
-13
Suppose 3*c = -3, -5*d - 1 - 20 = -4*c. Let q = d - -5. Find o such that 0 + 0*o**2 + q*o + 2/3*o**3 = 0.
0
Let q(j) be the second derivative of 5*j**7/42 + j**6/4 + j**5/8 + j. Find f such that q(f) = 0.
-1, -1/2, 0
Let p be (-8)/((0 - 2)/1). Suppose p = 3*s - s. What is r in -s - 3*r**2 + 2*r**2 + 3 = 0?
-1, 1
Let n(m) be the third derivative of 7*m**6/320 + 3*m**5/40 - 25*m**4/64 + 3*m**3/8 - 29*m**2. Let n(j) = 0. Calculate j.
-3, 2/7, 1
Let z be (-7 - 6/(-2)) + 4. Let t(q) be the second derivative of -q**2 - 1/2*q**3 + z + q + 5/12*q**4. Factor t(i).
(i - 1)*(5*i + 2)
Let y be (-8)/(-36) - 5/(180/(-64)). Determine r so that 2/3*r**y - 2*r + 4/3 = 0.
1, 2
Let t(b) be the second derivative of -2*b**5/35 - 5*b**4/14 - 8*b**3/21 + 3*b**2/7 - 18*b. Suppose t(w) = 0. What is w?
-3, -1, 1/4
Let d(k) be the first derivative of 0*k - 1/6*k**3 - 3 + 0*k**2 + 1/10*k**5 + 0*k**4. Factor d(c).
c**2*(c - 1)*(c + 1)/2
Let o(z) be the third derivative of 1/30*z**6 + 2*z**2 + 0 - 1/12*z**5 + 1/3*z**3 + 0*z - 7/24*z**4. Factor o(d).
(d - 2)*(d + 1)*(4*d - 1)
Factor -7/2*d**2 + d + 0.
-d*(7*d - 2)/2
Let c(u) = u**3 + 9*u**2 - 10*u + 2. Let y be c(-10). Suppose 2*r = m + 15, r - 3 = -m - 0*m. Find n, given that -3*n**y - r*n - 4 - 1/2*n**3 = 0.
-2
Let r(k) be the second derivative of 2/105*k**5 - k - 1/420*k**6 + 2/21*k**3 - 3/2*k**2 + 0 - 5/84*k**4. Let o(t) be the first derivative of r(t). Factor o(u).
-2*(u - 2)*(u - 1)**2/7
Let h(l) be the third derivative of -l**5/300 - l**4/30 + l**3/6 + 43*l**2. Solve h(f) = 0.
-5, 1
Let t(r) be the first derivative of 3/2*r**4 - 5*r**3 + 0*r + 6 - 9/2*r**2. Factor t(i).
3*i*(i - 3)*(2*i + 1)
Suppose -6*o + 4*o = 4. Let b be -2*(o + 44/24). Factor 1/3*x**3 + 0*x + 0*x**2 + 0*x**4 + 0 - b*x**5.
-x**3*(x - 1)*(x + 1)/3
Let o = 640/7 + -38393/420. Let n(x) be the second derivative of -1/30*x**3 + 0*x**2 + 2*x + 0 + o*x**4. Determine t so that n(t) = 0.
0, 1
Suppose -4 = -3*z - 2*l, 5*l = z - 1 + 11. Suppose 5*r = -4*d + 23 - 1, -d - 3*r + 9 = z. Factor 2*q**4 - q**2 - 2*q**3 - 2*q**3 + d*q**2.
2*q**2*(q - 1)**2
Let f be 0/(-4 + 3) + 0. Let v be 8/(-6)*(f - 3). Let -2/7*r**v + 2/7*r**2 + 0 - 4/7*r**5 + 6/7*r**3 - 2/7*r = 0. Calculate r.
-1, 0, 1/2, 1
Let p(t) be the third derivative of t**8/224 - t**7/140 - t**6/80 + t**5/40 - 8*t**2. Factor p(r).
3*r**2*(r - 1)**2*(r + 1)/2
Suppose 3*k = -4*n + 11, k + 9 = 5*n - 0. What is b in -2/3*b**n - 2/3*b**4 + 0 + 4/3*b**3 + 0*b = 0?
0, 1
Let w(q) = -q. Let f = 24 - 12. Let s(t) be the second derivative of -7*t**4/6 + 5*t**3 - 2*t**2 - 3*t. Let u(x) = f*w(x) + s(x). Let u(n) = 0. What is n?
2/7, 1
Factor -4*z**4 + 4*z + z**2 - 9*z**2 - 4*z**2 + 12*z**3.
-4*z*(z - 1)**3
Suppose 2*g**2 + 2*g**2 - 15*g + 17*g + 2*g**3 = 0. Calculate g.
-1, 0
Suppose -4*p = 98 - 18. Let v be p/(-15) - (-4)/6. Solve -3/4*l + 1/2 + 1/4*l**v = 0.
1, 2
Let r(d) be the second derivative of -9*d**5/70 + 11*d**4/42 + 16*d**3/21 - 4*d**2/7 - 14*d. Factor r(s).
-2*(s - 2)*(s + 1)*(9*s - 2)/7
Let g(c) = c. Let s(b) = 5*b**2 - 7*b + 4. Let j(p) = 15*g(p) - 3*s(p). Factor j(f).
-3*(f - 2)*(5*f - 2)
Let j be (-23)/7 - -3 - 32/(-63). What is o in j*o + 4/9 - 2/9*o**2 = 0?
-1, 2
Let h(n) = -n**3 - 9*n**2 + 3. Let f be h(-9). Suppose -f + 9 = 3*t. Factor -1/2*s - 7/4*s**t - s**3 + 1/4.
-(s + 1)**2*(4*s - 1)/4
Let u(h) be the second derivative of 2*h**6/15 - 13*h**5/20 + h**4/3 + 2*h**3 + h. Let u(r) = 0. What is r?
-3/4, 0, 2
Let t = 28737 - 200559/7. Let o = 86 - t. What is y in -8/7 - o*y**2 + 8/7*y = 0?
2
Factor 2/5*r**3 - 16/15*r - 8/15 - 2/15*r**2.
2*(r - 2)*(r + 1)*(3*r + 2)/15
Let t = 7 + -28. Let s be 32/14 - (-6)/t. Factor 2*d**s + 0*d**2 - 5*d + 0*d + 3*d.
2*d*(d - 1)
Let s = 27/76 - 2/19. Factor 0 + 0*y**4 + 0*y + s*y**5 - 3/4*y**3 + 1/2*y**2.
y**2*(y - 1)**2*(y + 2)/4
Let z(s) be the first derivative of 2/5*s**4 - 5 - 1/15*s**6 - 3/5*s**2 - 4/15*s**3 + 4/5*s + 0*s**5. Solve z(r) = 0.
-2, -1, 1
Let h be (-27)/(-30) - 22/55. Determine c so that -h*c**2 - 1/4*c**3 + 1/2 + 1/4*c = 0.
-2, -1, 1
Let z(l) be the second derivative of l**9/3024 - l**7/280 + l**6/180 - 5*l**3/6 - 4*l. Let f(q) be the second derivative of z(q). Factor f(d).
d**2*(d - 1)**2*(d + 2)
Suppose 5*a - a = 16. Suppose -k - 13 = -0*i - 4*i, -a*i = 2*k - 10. Factor d**4 + 6*d**3 - 3*d**3 - d**i.
d**3*(d + 2)
Let b be 0/7*(-2)/(-4). Suppose 2*k - g - 9 = b, -k + 4 = -3*g - 3. Factor 0*n**3 + 0 + 4/5*n**k - 4/5*n**2 - 2/5*n + 2/5*n**5.
2*n*(n - 1)*(n + 1)**3/5
Let q = 436/21645 - -1/481. Let w(y) be the second derivative of -q*y**5 + 0*y**3 - 2*y + 0*y**2 + 0*y**4 + 0 + 5/189*y**7 - 1/45*y**6. Factor w(k).
2*k**3*(k - 1)*(5*k + 2)/9
Let z(w) be the second derivative of -2*w**6/15 - w**5/5 + w**4/3 + 2*w**3/3 - 3*w. Factor z(t).
-4*t*(t - 1)*(t + 1)**2
Let k(t) = -t**3 + 6*t**2 - 6*t + 7. Let d be k(5). Suppose -4 = -q - d. Find n, given that 0*n + n**2 - 4*n**q - 2*n - 1 - n - n**3 = 0.
-1
Let n(v) be the first derivative of -v**7/420 + v**6/90 - v**5/60 + 