Let f(t) be the third derivative of -t**7/2205 + t**6/630 - t**4/126 + t**3/63 + 7*t**2. Let f(b) = 0. Calculate b.
-1, 1
Let u(w) = w**2 - 11*w - 12. Let d be u(11). Let k = -12 - d. Let k + 1/5*x - 1/5*x**3 + 2/5*x**2 - 2/5*x**4 = 0. What is x?
-1, -1/2, 0, 1
Let u = 4 - 8. Let p be (u/(-10))/((-2)/(-10)). Factor -w**3 + 2*w**2 + 6*w**3 - 4*w**3 - p*w**3 - w.
-w*(w - 1)**2
Let j = -1307/6 - -65351/300. Let f(u) be the third derivative of 0*u**5 - 1/60*u**4 + 0 + j*u**6 + 2*u**2 + 0*u**3 + 0*u. Factor f(k).
2*k*(k - 1)*(k + 1)/5
Let a(y) be the first derivative of -1 - 8*y**3 + 6/5*y**5 - 3/2*y**4 - 21/2*y**2 - 6*y + 1/2*y**6. Suppose a(o) = 0. What is o?
-1, 2
Determine o so that 0*o**2 + 0 + 3/5*o**3 + 0*o = 0.
0
Let v(z) be the second derivative of -z**7/147 + z**6/105 + z**5/35 - z**4/21 - z**3/21 + z**2/7 + 17*z. Suppose v(u) = 0. Calculate u.
-1, 1
Let f(r) = -r**3 - 5*r**2 - 2*r - 7. Let v be f(-5). Factor -v - 3*u**2 + 5 + 3*u - 2.
-3*u*(u - 1)
Suppose 2*t = -m - 4, 4*t + 5 = -11. Factor 5*g**5 + 0*g**3 + g**3 + 8*g**3 - 2*g**5 + 3*g**2 + 9*g**m.
3*g**2*(g + 1)**3
Let q be 28/(-16) + (0 - (-2 + 0)). Suppose -q*o - 1/4*o**2 + 1/2 = 0. Calculate o.
-2, 1
Suppose -12*r**5 - 4*r**2 + 10*r**4 - 6*r**2 - 5*r + 17*r**5 = 0. What is r?
-1, 0, 1
Let y be -3 + 2 - (1 - 4). Suppose 0*w + y*w = 6. Factor -5 - n**4 + 3*n**2 - 7*n**3 + w + 8*n**3 - n.
-(n - 2)*(n - 1)*(n + 1)**2
Suppose 0 = -0*b + 4*b - 8. Suppose 4*c - 18 = y, -y + 3*c = b*y + 9. Factor -1/2 + 1/2*i**y - 1/2*i**3 + 1/2*i.
-(i - 1)**2*(i + 1)/2
Let t(g) be the third derivative of g**7/15 - 47*g**6/360 - g**5/45 + 11*g**4/72 - g**3/9 - 3*g**2 - 3*g. Find l, given that t(l) = 0.
-1/2, 2/7, 1/3, 1
Suppose 3*c + c + 3*u = -55, 5*c = -4*u - 70. Let i be (-12)/c - (4 + -4). Factor 0 + 8/5*r**3 - 2/5*r**2 - i*r**4 + 0*r.
-2*r**2*(r - 1)*(3*r - 1)/5
Suppose -c = -0 + 1. Let i be -2 + -2 + 7 + c. Find m such that 4/9*m**3 - 2/9*m**5 + 0*m**i + 0*m - 2/9*m**4 + 0 = 0.
-2, 0, 1
Let m(v) be the second derivative of -2*v**7/21 + 2*v**6/15 + 2*v**5/5 - 2*v**4/3 - 2*v**3/3 + 2*v**2 - 26*v. What is g in m(g) = 0?
-1, 1
Let h(o) = 44*o**5 - 35*o**4 - 54*o**3 + 35*o**2 + 11*o - 1. Let f(p) = -p**5 + p**3 + p - 1. Let j(d) = -f(d) + h(d). Suppose j(n) = 0. What is n?
-1, -2/9, 0, 1
Find c, given that -13/4*c**2 + 0 + 11/4*c**3 + c - 1/2*c**4 = 0.
0, 1/2, 1, 4
Suppose -3*d - 31 = -139. Suppose -5*j = -3*g - 10*j + 68, -5*j = -g + d. Factor 64*c - g*c**2 - 22*c**2 - 2*c**4 + 16*c**3 - 40 + 8.
-2*(c - 2)**4
Let j(t) be the first derivative of t**4/6 - 2*t**3/9 - t**2/3 + 2*t/3 - 8. Factor j(o).
2*(o - 1)**2*(o + 1)/3
Let i(b) = b**3 + 11*b**2 - 6. Let s be i(-11). Let h = -3 - s. Factor -3/5*n**4 + 1/5 + 1/5*n**5 + 2/5*n**2 - 3/5*n + 2/5*n**h.
(n - 1)**4*(n + 1)/5
Let j(n) be the third derivative of n**5/100 - n**3/10 + 4*n**2. Solve j(x) = 0.
-1, 1
Let t(r) be the first derivative of r**7/3360 + r**6/720 + r**5/480 + r**3 - 1. Let s(g) be the third derivative of t(g). Factor s(i).
i*(i + 1)**2/4
Let q(a) be the third derivative of 0 - a**2 + 0*a - 1/120*a**5 + 0*a**4 + 1/12*a**3. Factor q(f).
-(f - 1)*(f + 1)/2
Let a be 476/(-3102) + (-24)/(-132). Let l = a + 536/987. Suppose -2*m**2 + 2*m**4 + 4/7*m - l*m**3 + 0 = 0. Calculate m.
-1, 0, 2/7, 1
Let y = -10 - -15. Factor -3*g - 3*g + 6*g + 2*g**4 - 2*g**3 - 2*g**2 + 2*g**y.
2*g**2*(g - 1)*(g + 1)**2
Let j = 538/2717 + -4/247. Factor -j + 4/11*w - 2/11*w**2.
-2*(w - 1)**2/11
Let m(p) be the second derivative of -p**6/3 - 6*p**5/5 - 3*p**4/2 - 2*p**3/3 - 7*p. Factor m(h).
-2*h*(h + 1)**2*(5*h + 2)
Let t(w) = w**2 + 3*w**2 + 11 + 11*w + 0*w**2 - 5*w**2. Let u(f) = 2*f + 2. Let m(h) = 2*t(h) - 11*u(h). Find i, given that m(i) = 0.
0
Let h = -3 + 3. Let p(c) be the second derivative of 1/7*c**2 + 0*c**3 + h + c - 1/42*c**4. Let p(a) = 0. What is a?
-1, 1
Let a(v) be the second derivative of v**7/4620 - v**6/495 + v**5/165 - v**3/6 + v. Let x(j) be the second derivative of a(j). Let x(z) = 0. Calculate z.
0, 2
Let r(q) be the second derivative of q**6/15 - q**5/10 - q**4/6 + q**3/3 - 7*q. Determine n so that r(n) = 0.
-1, 0, 1
Let m(v) = v**2 - 9*v + 1. Let y = 20 - 11. Let c be m(y). Factor s**5 - 1 + 4*s**3 + 6*s**4 - c + s**5 - 4*s**2 - 6*s.
2*(s - 1)*(s + 1)**4
Let o = 4 + -4. Let b be -1 - (o + -5) - 1. Determine r so that r**2 + 3*r**3 + 0*r**2 - r**b = 0.
-1/2, 0
Suppose 0*a + 0*a**2 + 0 - 3/4*a**3 = 0. What is a?
0
Let x = -11 + 13. Let t = -37 + 40. Solve 0*a + 0*a**x + 0 - 1/3*a**4 + 0*a**t - 1/3*a**5 = 0.
-1, 0
Let p(y) be the first derivative of -1/15*y**5 + 0*y**3 + 1/3*y - 2 - 1/3*y**2 + 1/6*y**4. Factor p(v).
-(v - 1)**3*(v + 1)/3
Factor -12 + 67*b**2 + 8 - 236*b**2 - 52*b.
-(13*b + 2)**2
Let o be 6/9 + 3 + -3. Factor 1/3*t**5 - 1/3 - 1/3*t**4 + 1/3*t - o*t**3 + 2/3*t**2.
(t - 1)**3*(t + 1)**2/3
Let b(o) be the third derivative of o**8/336 - o**7/105 + o**5/30 - o**4/24 - 15*o**2. Factor b(p).
p*(p - 1)**3*(p + 1)
Solve 18/5*k**2 + 0 - 2/5*k**4 - 6/5*k**3 - 2*k = 0 for k.
-5, 0, 1
Let x be -86 + 89 + ((-27)/(-4))/(-3). Suppose -x*c**3 - 3/4*c**2 + 3/4*c + 3/4 = 0. What is c?
-1, 1
Let x be ((-2)/(-28))/((-2)/(-8)). Let o = 202 + -1410/7. Factor 2/7 + x*z**2 - o*z.
2*(z - 1)**2/7
Let g(z) = z**4 - 40*z**3 + 79*z**2 + 44*z - 88. Let m(f) = -5*f**4 + 240*f**3 - 475*f**2 - 265*f + 530. Let s(q) = -25*g(q) - 4*m(q). Factor s(t).
-5*(t - 4)**2*(t - 1)*(t + 1)
Factor -2*u**2 + 2*u**2 + 2*u**3 - 6*u**2 + 4*u**4 - 2*u + 2*u**2.
2*u*(u - 1)*(u + 1)*(2*u + 1)
Let y be 4 - (1 - (2 + -1 + 0)). Solve 2/7*f**2 + 0 + 2/7*f**y + 0*f + 4/7*f**3 = 0 for f.
-1, 0
Let f = -25 + 46. Let o be (2/(-6))/((-14)/f). Factor 0*c - 1/2*c**2 + 0 + 1/2*c**4 - 1/2*c**3 + o*c**5.
c**2*(c - 1)*(c + 1)**2/2
Suppose -3*y - g + 1 = y, 0 = y + 3*g - 3. Let v be (3/(-6))/(6/(-8)). What is m in v*m**2 + 2/3*m + y = 0?
-1, 0
Let n(w) be the second derivative of w**5/25 + 2*w**4/15 - 2*w**3/15 - 4*w**2/5 + 2*w. Solve n(d) = 0.
-2, -1, 1
Let x(c) be the first derivative of -c**3/3 + 8*c**2 - 64*c - 20. Find z such that x(z) = 0.
8
Suppose 5*x = l - 23, -4*x = 4*l + x + 33. Let i be 2/(-12)*4/l. Determine k, given that -1/6*k**3 + i*k**2 + 0*k + 0 - 2*k**4 - 3/2*k**5 = 0.
-1, -2/3, 0, 1/3
Let j(o) be the third derivative of -o**5/60 + 3*o**4/8 - 2*o**3 - 9*o**2. Let k be j(7). Factor 2/3*q - 2/3*q**k + 0.
-2*q*(q - 1)/3
Let y(m) = -5*m**3 - 9*m**2 - 8*m + 4. Let d(v) = 15*v**3 + 28*v**2 + 23*v - 12. Let l(g) = 4*d(g) + 11*y(g). Factor l(n).
(n + 1)*(n + 2)*(5*n - 2)
Let f(u) be the third derivative of -u**8/2352 + u**7/490 - u**6/420 - 27*u**2. Let f(r) = 0. Calculate r.
0, 1, 2
Suppose -84 = -2*k - 10. Let t be (-3)/12 - 13/(-4). Factor -252*l**2 - 40*l**3 + k*l - 16 - 58*l**t - 157*l.
-2*(l + 2)*(7*l + 2)**2
Factor 0*d**3 + 4/9*d**4 - 4/3*d**2 + 0 - 8/9*d.
4*d*(d - 2)*(d + 1)**2/9
Let d(l) be the third derivative of -l**8/1344 + l**7/840 + l**6/240 - l**5/120 - l**4/96 + l**3/24 + 4*l**2. Factor d(h).
-(h - 1)**3*(h + 1)**2/4
Suppose 4*k = -k. Let -6*d + k*d**2 - 14 + 5 - d**2 = 0. Calculate d.
-3
Suppose -4*y = y. Let q(h) be the second derivative of -1/36*h**4 + 0 + y*h**3 + 2*h + 1/6*h**2. Determine l, given that q(l) = 0.
-1, 1
Let y be 12411/(-10) - (-3)/(-6). Let m = y - -1246. Factor -m*k**2 + 26/5*k - 4/5.
-2*(k - 1)*(11*k - 2)/5
Determine p so that 6*p + p**2 + 5*p**2 - 3*p - 2*p**3 + 5*p**3 = 0.
-1, 0
Let v(b) = -8*b**5 + 5*b**3 - 3*b**2 + 3*b. Let u(r) = 31*r**5 + r**4 - 19*r**3 + 11*r**2 - 11*r. Let x(j) = 6*u(j) + 22*v(j). Solve x(f) = 0.
-1, 0, 2/5
Let z be 11 + -6 + -4*(-2 - -3). Suppose -2*m**3 + z + 13/2*m**2 - 11/2*m = 0. What is m?
1/4, 1, 2
Suppose -1 - 14 = -3*h. Suppose -4*p - 1 = d - 13, 18 = -p + h*d. Factor 4*z**3 + 3*z**p - 2*z**3 - z**2.
2*z**2*(z + 1)
Let z(m) = m - 8. Let x be z(4). Let q(b) = 6*b**3 - 4*b**2 + 4. Let y(n) = 5*n**3 - 4*n**2 + 3. Let j(l) = x*y(l) + 3*q(l). Suppose j(a) = 0. What is a?
0, 2
Suppose 4*h - 5*i + 18 = 0, 3*h + i + 4*i = 4. Let l(a) = -3*a**2 + 5*a - 4. Let o(s) = -s**2 + s + 1. Let m(f) = h*o(f) - l(f). Factor m(q).
(q - 1)*(5*q - 2)
Let l be 36/8*(-4)/3. Let d be l*(1 + 2)/(-3). Solve d*i**2 + i - 2*i**3 - 2*i**3 + 3*i = 0 for i.
-1/2, 0, 2
Determine a so that -7 + 60*a - 171 - 5*a**2 - 2 = 0.
6
Let z(s) be the second deri