t = 0.
1
Suppose 4*m + 4 = -4. Let f be ((-1)/(-3)*-2)/m. Let -f - 1/3*r**4 + 0*r + 0*r**3 + 2/3*r**2 = 0. Calculate r.
-1, 1
Suppose 6 = 2*c - 0. Solve c*t**4 + 3*t**3 + 2*t**3 - 5*t**3 = 0.
0
Let r = -11/27 - -97/216. Let u(c) be the second derivative of 1/4*c**2 + 3*c + 0 - r*c**4 + 0*c**3. Factor u(v).
-(v - 1)*(v + 1)/2
Determine b so that -5*b - 40*b + 25*b**2 - 10 + 30*b**2 + 0 = 0.
-2/11, 1
Find i, given that 19/4*i**3 + 1/4*i**5 - 1 - 25/4*i**2 + 4*i - 7/4*i**4 = 0.
1, 2
Let q(j) be the second derivative of j**6/40 + 9*j**5/20 + 27*j**4/8 + 27*j**3/2 - 2*j**2 - 6*j. Let o(l) be the first derivative of q(l). Factor o(c).
3*(c + 3)**3
Let z(j) be the third derivative of -j**7/1365 + j**6/130 - 4*j**5/195 - j**4/26 + 3*j**3/13 - 23*j**2 + 2. Suppose z(s) = 0. What is s?
-1, 1, 3
Factor -5*k + 1/3*k**4 + k**3 - 7/3*k**2 + 6.
(k - 2)*(k - 1)*(k + 3)**2/3
Let b(v) be the third derivative of -v**8/1008 + v**7/210 - v**6/120 + v**5/180 + 6*v**2. Determine t, given that b(t) = 0.
0, 1
Factor -3/5*d**3 + 0*d - 1/5*d**5 + 4/5*d**4 + 0*d**2 + 0.
-d**3*(d - 3)*(d - 1)/5
Let f(a) = 5*a**3 - 5*a. Let s(m) = m**3 - m. Let t = -6 + 7. Let p(l) = t*f(l) - 6*s(l). Let p(k) = 0. What is k?
-1, 0, 1
Let b(i) be the second derivative of i**5/130 - i**4/26 + 4*i**2/13 - 14*i. What is k in b(k) = 0?
-1, 2
Let m(v) be the second derivative of 14*v**6/45 + 43*v**5/60 + 17*v**4/36 + v**3/9 - 2*v. Suppose m(w) = 0. What is w?
-1, -2/7, -1/4, 0
Let r(b) be the third derivative of 3*b**5/40 + 29*b**4/48 + b**3/2 + 36*b**2. Factor r(k).
(k + 3)*(9*k + 2)/2
Factor -1/7*w**2 + 0*w + 0 + 1/7*w**4 + 0*w**3.
w**2*(w - 1)*(w + 1)/7
Suppose -h + 2*h - 8 = 2*l, l + 3 = 0. Let d(q) be the first derivative of -1/4*q**2 + 1/8*q**4 - 1/4*q + 1/20*q**5 - h + 0*q**3. What is r in d(r) = 0?
-1, 1
Let j(s) = 2*s**3 - 5*s**2 - 3*s + 3. Let r(m) = 3*m**3 - 9*m**2 - 5*m + 5. Let h(o) = -5*j(o) + 3*r(o). Factor h(g).
-g**2*(g + 2)
Let k = 3/113 - -163/2373. Let i(p) be the second derivative of 1/70*p**5 + 0 + 0*p**2 + 1/14*p**4 + 2*p + k*p**3. Factor i(z).
2*z*(z + 1)*(z + 2)/7
Let s(i) be the third derivative of -i**8/224 - i**7/70 - i**6/320 + i**5/32 + i**4/64 - i**3/16 - 4*i**2. Solve s(w) = 0.
-1, 1/2
Let s be ((-20)/6)/((-6)/9). Determine g so that -s*g**2 + 3 + g + 4*g**3 - 3 = 0.
0, 1/4, 1
Solve 2*v + 0*v**2 - 2*v**2 - 2*v + 2*v**3 = 0 for v.
0, 1
Let n(g) be the third derivative of g**5/150 + g**4/30 - 2*g**2. Factor n(m).
2*m*(m + 2)/5
Let k(y) be the first derivative of -y**4/14 - 2*y**3/21 + 2. Let k(q) = 0. What is q?
-1, 0
Let j be 0 - 0*7/42. Factor j - 2/9*d**2 + 0*d.
-2*d**2/9
Determine x, given that 12*x**2 - x**3 - 12*x - 5*x**3 + 3*x**3 = 0.
0, 2
Suppose b + 2*i = 30, b = -4*b + 4*i + 150. Let f be (-10)/12*(-9)/b. Factor -f - 1/2*v**2 + 3/4*v.
-(v - 1)*(2*v - 1)/4
Let p(m) = -191*m**3 + 469*m**2 - 271*m + 51. Let s(w) = 38*w**3 - 94*w**2 + 54*w - 10. Let h(f) = -2*p(f) - 11*s(f). Solve h(d) = 0 for d.
1/3, 2
Determine u so that -2/13*u**5 + 2/13*u**2 + 2/13*u**3 - 2/13*u**4 + 0*u + 0 = 0.
-1, 0, 1
Let w(u) = -4*u**2 + 3*u - 5. Suppose 3*l - 48 = -l. Let n(j) = -10*j**2 + 8*j - 12. Let q(m) = l*w(m) - 5*n(m). What is y in q(y) = 0?
0, 2
Let j(n) be the first derivative of n**4/6 - n**3/3 - 2*n**2 - n + 4. Let u(a) be the first derivative of j(a). Factor u(q).
2*(q - 2)*(q + 1)
Let f(k) be the first derivative of -k**3/18 - 26. Suppose f(y) = 0. What is y?
0
Let i(k) = -k**3 - k**2 + k + 1. Let d(f) = -3*f**3 - 6*f**2 + 4*f + 5. Let h(w) = 2*d(w) - 10*i(w). Solve h(b) = 0 for b.
-1/2, 0, 1
Let l = 6 + -2. Let p be (-28)/(-45) - l/18. Factor 2/5*i**3 + p*i + 0 + 4/5*i**2.
2*i*(i + 1)**2/5
Let v(g) be the third derivative of -3*g**8/448 - g**7/140 + 11*g**6/480 + g**5/60 - g**4/24 + 12*g**2. Factor v(q).
-q*(q + 1)**2*(3*q - 2)**2/4
Suppose -19*v + 22*v - 18 = 0. Let n(t) be the third derivative of -1/30*t**5 + 0*t + 2*t**2 + 1/60*t**v + 0*t**3 + 0 + 0*t**4. What is z in n(z) = 0?
0, 1
Let j be (-3)/(-15) + (-3)/(-10). Let b(l) be the first derivative of -1/2*l + 2 + j*l**3 + 1/2*l**2. Factor b(o).
(o + 1)*(3*o - 1)/2
Suppose 46 = 40*d - 114. Factor 3/4*s**d + 3/2*s**3 + 0*s**2 + 0*s + 0.
3*s**3*(s + 2)/4
Let k(d) be the second derivative of d**6/35 + d**5/7 + 2*d**4/21 - 8*d**3/21 + 7*d. Determine j, given that k(j) = 0.
-2, 0, 2/3
Factor 2*l**2 + 11*l + l**2 - 2 - 12*l**2.
-(l - 1)*(9*l - 2)
Let c(h) = 3*h**2 - 6*h - 3. Let y(w) = w - 1. Let b(u) = c(u) + 3*y(u). Suppose b(s) = 0. What is s?
-1, 2
Let k = -1093/3 - -365. Determine d so that 56/3*d**5 + 0 - 2/3*d**4 + k*d**2 - 20*d**3 + 4/3*d = 0.
-1, -1/4, 0, 2/7, 1
Let y be 24/12*26/4. Let r = 15 - y. Suppose -1/2*d - 1/2*d**r + 0 = 0. What is d?
-1, 0
Let o(y) be the first derivative of y**4/4 - 5*y**3/9 + y**2/6 + y/3 - 30. Determine p so that o(p) = 0.
-1/3, 1
Let j(a) be the first derivative of -a**5/25 + 11*a**3/15 + 9*a**2/5 + 8*a/5 + 47. Suppose j(z) = 0. Calculate z.
-2, -1, 4
Let o(k) be the third derivative of k**8/4320 + k**7/3780 + k**5/20 - k**2. Let m(n) be the third derivative of o(n). Determine p, given that m(p) = 0.
-2/7, 0
Let q be (3/(-2))/((-1)/2). Let a(i) be the third derivative of 0*i - 1/60*i**5 + 1/12*i**4 - 3*i**2 - 1/120*i**6 + 0 + 0*i**q. Determine f so that a(f) = 0.
-2, 0, 1
Let n = -54 + 54. Let b be 1/(-3) + -1 + 2. Let n + 2/3*s**5 + 0*s + b*s**4 + 0*s**3 + 0*s**2 = 0. What is s?
-1, 0
Let d(c) = -7*c**3 - 2*c**2 - c. Let t(y) = 6*y**3 + 3*y**2. Let a(k) = 4*d(k) + 5*t(k). Let a(j) = 0. Calculate j.
-4, 0, 1/2
Let l(t) be the third derivative of -7*t**8/48 - 5*t**7/6 - 47*t**6/24 - 29*t**5/12 - 5*t**4/3 - 2*t**3/3 + 10*t**2. Suppose l(z) = 0. What is z?
-1, -2/7
Let y = 16 - 13. Suppose l = y*l - 6. Factor 1/4*r - 1/4*r**5 + 0*r**l + 0 + 1/2*r**2 - 1/2*r**4.
-r*(r - 1)*(r + 1)**3/4
Let l(j) be the third derivative of -j**7/525 + j**6/100 - j**5/150 - j**4/20 + 2*j**3/15 - 5*j**2. What is g in l(g) = 0?
-1, 1, 2
Suppose 3*o**2 - 12*o - 24 + 15*o + 3*o = 0. Calculate o.
-4, 2
Let l(d) be the third derivative of 3*d**7/140 - d**6/40 - 5*d**2. Factor l(i).
3*i**3*(3*i - 2)/2
Let a = -535/3 - -181. Factor -1/3 + 7/3*i - 16/3*i**3 - a*i**2.
-(i + 1)*(4*i - 1)**2/3
Suppose 2*v + 1 = -1. Let y = 2 - v. Factor -g**2 + 3*g**y + 4*g**2 + g**3 - g.
g*(g + 1)*(4*g - 1)
Suppose -8*b + 0 - 4*b - 3*b**2 - 9 = 0. Calculate b.
-3, -1
Suppose -2/3*g + 4/9 - 40/9*g**2 = 0. Calculate g.
-2/5, 1/4
Let c = -9 + 13. Find z, given that -2*z**3 - c*z**2 + 2*z + 0*z + 2*z**2 + 2 = 0.
-1, 1
Factor -1/4*v**5 - 1 + 1/4*v**4 - 2*v + 5/4*v**3 - 1/4*v**2.
-(v - 2)**2*(v + 1)**3/4
Let w(k) be the third derivative of k**5/240 - k**4/48 + k**2. Find m, given that w(m) = 0.
0, 2
Suppose 0*h**2 + 3/7*h**4 + 0 + 9/7*h**3 - 12/7*h = 0. What is h?
-2, 0, 1
Let w(s) = -4*s**3 + 5*s**2 - 6*s - 6. Let r(l) = -3*l**3 - 7 - 5*l + 2*l**2 - 2*l**2 + 5*l**2. Let m(p) = -3*r(p) + 2*w(p). Factor m(f).
(f - 3)**2*(f + 1)
Suppose -w - 4*v - 18 = 0, -w - 7*v + 7 = -8*v. Factor 23/4*u**3 + 5*u + u**4 - w + 21/2*u**2.
(u + 2)**3*(4*u - 1)/4
Let f(r) be the third derivative of -r**8/16800 - r**7/8400 - r**5/15 - 5*r**2. Let j(u) be the third derivative of f(u). Let j(i) = 0. Calculate i.
-1/2, 0
Let d(n) be the first derivative of 4/7*n + 1 + 2/21*n**3 - 3/7*n**2. Let d(q) = 0. Calculate q.
1, 2
Let t(c) = 21*c**3 - 27*c**2 - 288*c - 336. Let v(z) = 5*z**3 - 7*z**2 - 72*z - 84. Let f(y) = 2*t(y) - 9*v(y). Solve f(u) = 0.
-2, 7
Let a = -5 - -6. Let w(s) = s**3 - s**2. Let n(i) = 8*i**3 - 6*i**2 + 2*i - 4. Let c(r) = a*n(r) - 10*w(r). Solve c(u) = 0 for u.
-1, 1, 2
Let a = 22618/3 + -3166271/420. Let v = a - 3/140. Find o, given that v - 2/7*o**2 - 2/7*o = 0.
-2, 1
Let d = -2/2711 + 97610/18977. What is r in 2*r**4 + 6/7 + 2/7*r**5 + 26/7*r + d*r**3 + 44/7*r**2 = 0?
-3, -1
Suppose -2*o + 7 = -1. Factor f**2 + 0*f**2 - 2 - 3*f + o.
(f - 2)*(f - 1)
Let u be (0 - -2) + 84/(-63). Determine s, given that -1/3*s - u*s**4 + 1/3*s**5 + 0*s**3 + 0 + 2/3*s**2 = 0.
-1, 0, 1
Solve 13*x**3 + 5*x**3 + 2*x**2 - 28*x**3 + 5*x**3 + 3*x**4 = 0.
0, 2/3, 1
Suppose -2*q = 22 - 8. Let v(b) = -b**3 - 6*b**2 + 6*b - 4. Let o be v(q). Solve 10/11*r**2 + 0 - 6/11*r**o - 4/11*r = 0.
0, 2/3, 1
Solve -3*c + 40*c**2 - c - 41*c**2 - 4 = 0.
-2
What is p in 5*p**3 + 