= q - 9, 5*q = -5. Let n be ((-92)/(-16) - t)/((-3)/(-8)). Find w, given that 0*w - 3/7*w**3 + 0 - 3/7*w**n = 0.
-1, 0
Let 40*h**4 - 58*h - 77*h + 324*h**4 + 10 + 261*h**4 - 1125*h**3 + 625*h**2 = 0. Calculate h.
1/5, 2/5, 1
Let q(b) be the first derivative of b**6/21 - 4*b**5/35 - 2*b**4/7 + 16*b**3/21 + 680. Factor q(f).
2*f**2*(f - 2)**2*(f + 2)/7
Factor 45*q**2 + 10*q**2 - 825*q**3 - 834*q**3 - 13 - 25*q + 1663*q**3 + 63*q.
(q + 1)*(q + 13)*(4*q - 1)
Let l(f) = f**3 - f**2 - f + 1. Let b(r) = -4 - 7*r**2 + 5 - r - r**3 + 0*r + 8. Let z(v) = -2*b(v) + 2*l(v). Factor z(p).
4*(p - 1)*(p + 2)**2
Solve 2781/5*p**2 - 859329/5*p - 3/5*p**3 + 88510887/5 = 0.
309
Let t(j) be the second derivative of j**4/60 + 241*j**3/15 + 58081*j**2/10 + 369*j. What is x in t(x) = 0?
-241
Determine t so that -3/5*t**5 + 54/5 + 63/5*t - 12*t**3 - 24/5*t**4 - 6*t**2 = 0.
-3, -2, -1, 1
Let b(m) be the third derivative of -m**9/756 + m**8/210 - m**6/45 + m**5/30 + 2*m**3 + 9*m**2. Let j(p) be the first derivative of b(p). Factor j(n).
-4*n*(n - 1)**3*(n + 1)
Let r(f) = -5*f + 4 + 13*f + 1 - 1. Let n(x) = -x**2 - 8*x - 3. Let d(g) = 4*n(g) + 3*r(g). Suppose d(i) = 0. What is i?
-2, 0
Let c(n) be the first derivative of -n**6/900 + n**5/40 - 7*n**4/120 - 9*n**3 + 21. Let o(l) be the third derivative of c(l). Suppose o(s) = 0. Calculate s.
1/2, 7
Let u(n) be the third derivative of -21*n**2 - 3/32*n**4 + 0 + 0*n - 1/4*n**3 - 1/80*n**5. Factor u(g).
-3*(g + 1)*(g + 2)/4
Let c(t) = -t + 1. Let x = 77 - 71. Let o(j) = -4*j**2 - 18*j + 46. Let r(s) = x*c(s) - o(s). Find n such that r(n) = 0.
-5, 2
Factor -12*j**2 - 8/3*j + 0 - 16/3*j**3.
-4*j*(j + 2)*(4*j + 1)/3
Let n be 3/(-6) + 17/51*6. Solve n*b**2 - 7*b - 5/2 = 0 for b.
-1/3, 5
Let k(r) = r**3 + r**2 - 179*r - 179. Let b be k(-1). Factor -10/7*a**2 + b - 2/7*a**4 + 8/7*a**3 + 4/7*a.
-2*a*(a - 2)*(a - 1)**2/7
Let o(v) be the third derivative of v**8/448 - v**7/504 - v**6/48 + v**5/24 - 5*v**4/24 - 17*v**2. Let l(j) be the second derivative of o(j). Factor l(y).
5*(y - 1)*(y + 1)*(3*y - 1)
Let h = -2 - -4. Let 31*c**3 - 9*c**2 + 3*c - 22*c**3 - 3*c**4 + 0*c**h = 0. What is c?
0, 1
Let a be (-34)/48*(-14)/21. Let x = a - 2/9. Let -1/2*z + x + 1/4*z**2 = 0. Calculate z.
1
Let p be (-4)/(-5) + (209/(-19) - -11). Factor 4/5*c**2 - p + 4/5*c**3 - 4/5*c.
4*(c - 1)*(c + 1)**2/5
Let b(l) be the first derivative of 8*l**2 - 1/2*l**4 + 43 + 24*l - 2/3*l**3. Factor b(q).
-2*(q - 3)*(q + 2)**2
What is r in 11/2 + 18*r**2 + 17*r + 1/2*r**4 + 7*r**3 = 0?
-11, -1
Let y(s) be the first derivative of 5/2*s**2 - s**5 + 15/4*s**4 + 0*s - 5*s**3 + 13. Determine r, given that y(r) = 0.
0, 1
Let o = 32 + -21. Suppose 25 = 5*h - w, -h + 20 = 3*h + 5*w. Factor 27*k**3 + 3*k + o - h + 16*k**2 - 52*k**2.
3*(k - 1)*(3*k - 2)*(3*k + 1)
Solve -4/7*f**2 + 30/7*f - 2 = 0.
1/2, 7
Suppose 0*r = 5*r. Factor 7*h**4 - 4*h - 4*h**3 + 5*h**3 + r*h**3 + 4*h**2 - 8*h**4.
-h*(h - 2)*(h - 1)*(h + 2)
Let d be 184/8 - (28 + -8). Factor 3/5*s**5 + 12/5 + 48/5*s + 15*s**2 + 57/5*s**d + 21/5*s**4.
3*(s + 1)**3*(s + 2)**2/5
Let s be (-3)/(90/65) + 1/6. Let z be s - ((-144)/21)/3. Factor z + 0*y - 2/7*y**2.
-2*(y - 1)*(y + 1)/7
Let r(s) be the second derivative of -s**4/54 + 4*s**3/9 - 35*s**2/9 - 544*s. Let r(j) = 0. What is j?
5, 7
Let v = 20/9 - 8/9. Let a = 5/3 - 1. Find j such that 0*j**2 - v - 2*j + a*j**3 = 0.
-1, 2
Suppose 0 + 12/7*s**2 + 2/7*s**3 - 2*s = 0. Calculate s.
-7, 0, 1
Suppose 117 = 105*g - 97 + 4. Factor 8/19*w**g + 2/19*w + 12/19*w**3 + 0 + 8/19*w**4 + 2/19*w**5.
2*w*(w + 1)**4/19
Let t(g) be the first derivative of 3*g**5/4 - 5*g**4/6 - 5*g**3/6 + 22*g + 4. Let m(f) be the first derivative of t(f). Solve m(d) = 0 for d.
-1/3, 0, 1
Suppose 2*i + 88 + 30 = 0. Let s = -293/5 - i. Factor 2/5 + s*y**3 - 2/5*y - 2/5*y**2.
2*(y - 1)**2*(y + 1)/5
Let v(a) be the first derivative of a**3/30 + a**2/2 + 8*a/5 + 271. Factor v(r).
(r + 2)*(r + 8)/10
Factor 6284*y - 6280*y + 71*y**2 - 2 - y**2.
2*(5*y + 1)*(7*y - 1)
Let r be 715/(-360) + (7 - 8) + 3. Let g(y) be the second derivative of 1/18*y**3 - r*y**4 + 0 + 8*y + 0*y**2. Determine u, given that g(u) = 0.
0, 2
Let y(z) be the third derivative of z**8/224 - z**7/140 - 11*z**6/80 + 29*z**5/40 - 13*z**4/8 + 2*z**3 - 24*z**2 + z. Let y(d) = 0. What is d?
-4, 1, 2
Let a(z) be the third derivative of 0*z + 85/168*z**4 + 19*z**2 + 0 + 23/140*z**5 - 37/840*z**6 + 2/735*z**7 - 25/42*z**3. Factor a(g).
(g - 5)**2*(g + 1)*(4*g - 1)/7
Let w be 192/30 - (-1 + (-7)/(-5)). Let k be (-8*(-1)/6)/(w/9). Let -2/13*r - 2/13 - 2/13*r**5 - 2/13*r**4 + 4/13*r**3 + 4/13*r**k = 0. What is r?
-1, 1
Let d(y) be the first derivative of -2*y**5/35 - y**4/14 + 2*y**3/21 + y**2/7 - 75. What is n in d(n) = 0?
-1, 0, 1
Let y(m) = 4*m**2 - 19*m - 7. Let r(n) be the second derivative of -n**4/6 + 5*n**3/3 + 2*n**2 + 3*n. Let a(o) = -11*r(o) - 6*y(o). Factor a(z).
-2*(z - 1)**2
Let w(b) = 10*b**4 + 30*b**3 + 35*b**2 - 20*b - 40. Let x(k) = k**4 - k**2 + 2*k + 1. Let u(t) = -w(t) + 5*x(t). Solve u(p) = 0 for p.
-3, -1, 1
Let w(j) be the second derivative of j**4/24 - j**3/6 - 3*j + 15. Determine y so that w(y) = 0.
0, 2
Let i(j) be the first derivative of -j**6/21 + 2*j**5/5 - 15*j**4/14 + 6*j**3/7 + 22. Solve i(q) = 0 for q.
0, 1, 3
Let h(z) be the second derivative of z**7/168 + z**6/30 - z**5/16 + 451*z. Factor h(a).
a**3*(a - 1)*(a + 5)/4
Let l be 21/((3/4)/(-1)). Let f = l + 32. Determine d, given that 2*d**3 + 6*d**4 + 2*d**3 + 4*d**5 + 2*d**f = 0.
-1, 0
Let k(u) be the third derivative of 0 + 0*u + 3*u**2 + 0*u**4 + 0*u**3 + 1/120*u**6 + 1/60*u**5. Factor k(v).
v**2*(v + 1)
Let g = -15922 + 15925. Determine t so that -2/3*t**g + 2/3 - 7/3*t + 7/3*t**2 = 0.
1/2, 1, 2
Let n(k) be the second derivative of -1/84*k**4 - 1/14*k**3 + 23*k + 0 + 0*k**2. Let n(x) = 0. What is x?
-3, 0
Let x(n) be the first derivative of 9*n**5/5 + 3*n**4/4 + n**3/12 + 40. Factor x(m).
m**2*(6*m + 1)**2/4
Let v(w) be the second derivative of -3/2*w**2 - 39/40*w**5 - 3/4*w**6 + 0 + 17/8*w**4 - 48*w + 13/4*w**3. Determine n, given that v(n) = 0.
-1, 2/15, 1
Let k(g) be the first derivative of 2*g**5/35 + 3*g**4/14 - 10*g**3/7 + 17*g**2/7 - 12*g/7 + 42. Let k(y) = 0. What is y?
-6, 1
Let w(q) be the second derivative of q**5/40 + 53*q**4/12 + 174*q. What is r in w(r) = 0?
-106, 0
Suppose 0*b = -4*b - 8. Let u be 0 - b*3/8. Find c, given that -3/2 + 9/4*c - u*c**2 = 0.
1, 2
Let l(h) be the second derivative of -h**5/90 + 7*h**4/54 + h**3/27 - 7*h**2/9 - 163*h. Determine z so that l(z) = 0.
-1, 1, 7
Let k be 18/(-6) + (-33)/15 + -2. Let p = k + 221/30. Find d, given that 0*d + 0 + p*d**2 = 0.
0
Let y(a) = -3*a**3 + a**2 + 4*a + 3. Let t be y(-1). Let o(n) be the second derivative of 0 + 1/6*n**t + 0*n**2 + 1/12*n**4 - n. Solve o(x) = 0 for x.
-1, 0
Suppose 0 = -8*w - 9 - 7. Let i be w - 28/(-20) - 19/(-15). Factor -1/3*a**3 + a**5 + 0 + 0*a + i*a**2 - 4/3*a**4.
a**2*(a - 1)**2*(3*a + 2)/3
Suppose 23*l = 19*l + 20. Let a(x) be the second derivative of 0 - 1/7*x**3 + 3*x - 2/7*x**2 + 1/70*x**l + 0*x**4. Determine k, given that a(k) = 0.
-1, 2
Let o(q) be the third derivative of -q**8/672 - q**7/70 - 7*q**6/120 - 2*q**5/15 - 3*q**4/16 - q**3/6 - 5*q**2 - 12*q. Let o(x) = 0. What is x?
-2, -1
Let r(y) be the second derivative of -y**8/1120 + y**7/168 - y**6/60 + y**5/40 - y**4/3 - 13*y. Let b(h) be the third derivative of r(h). Factor b(o).
-3*(o - 1)**2*(2*o - 1)
Let z(o) = 3*o**4 + 7*o**3 - o**2 - 9*o - 4. Let n(l) = -l**4 + l + 2. Let p(s) = -10*n(s) - 5*z(s). Suppose p(u) = 0. What is u?
-7, -1, 0, 1
Let a(b) be the second derivative of -1/2*b**4 + 0 - b**2 + 6*b - 1/30*b**5 - 3*b**3. Let h(d) be the first derivative of a(d). Factor h(z).
-2*(z + 3)**2
Let h = 30 + -27. Solve 2*n**2 + n - 1 + 1 + n**h + 0 = 0 for n.
-1, 0
Suppose -3*a - 3*s + 6 = -a, -2*s + 12 = 4*a. Let 0 - 3*c - c**3 + 2*c**a + 0*c - 2 = 0. Calculate c.
-1, 2
Suppose 2*z - 14 = -j, 0 = -3*j + 2*z + 29 - 11. Suppose a = 3*a - j. Factor -4*l**4 + 0*l**4 + 3*l**a + l**3.
-l**3*(l - 1)
Suppose -4*q + 5*l = 3*l, 3*q + 6 = 3*l. Factor -3*z**3 - 10*z - 36*z**q - 2*z**3 + 21*z**2.
-5*z*(z + 1)*(z + 2)
Suppose -25 = 4*c + 5*k, -c - 51*k = -56*k - 25. Factor 0*t**3 + 0 + c*t + 0*t**2 - 2*t**5 - 4/3*t**4.
-2