3*w**4 + 126*w**2 + 54 - 3 + 120*w = 0. What is w?
-13, -1
Let m(a) = -a**3 + 18*a**2 - 37*a - 19. Let n be m(16). Let s be (-48)/n + 2/11. Factor -s*i**2 + 2/3*i**3 + 0*i + 0 + 2/3*i**4 - 2/3*i**5.
-2*i**2*(i - 1)**2*(i + 1)/3
Let h(n) be the third derivative of -n**6/240 + 7*n**5/20 + 29*n**4/16 + 11*n**3/3 - 8*n**2 + 32. Let h(p) = 0. What is p?
-1, 44
Let r(k) be the second derivative of -k**6/50 - 9*k**5/50 + 6*k**4/5 - 13*k**3/5 + 27*k**2/10 - 357*k. Suppose r(s) = 0. What is s?
-9, 1
Let a(f) be the first derivative of -f**5/30 + f**4/9 - 15*f**2 - 4. Let g(b) be the second derivative of a(b). Let g(s) = 0. What is s?
0, 4/3
Let f(p) = -2193*p + 10967. Let l be f(5). Suppose 1/3*z**3 - 1 - 5/3*z**l + 7/3*z = 0. Calculate z.
1, 3
Let x be (-42)/(-9) - -1 - 4/(-3). Let j = 10 - x. Factor 0*b + 0 - 4/7*b**j - 2/7*b**2 - 2/7*b**4.
-2*b**2*(b + 1)**2/7
Let a(b) = -2*b**3 - 24*b**2 - 167*b - 262. Let u(m) = -2*m**3 - 26*m**2 - 168*m - 258. Let q(i) = 6*a(i) - 7*u(i). Factor q(d).
2*(d + 3)**2*(d + 13)
Let v(z) = -z**3 - 20*z**2 + 23*z - 12. Let c(m) = -2*m**2. Let s(b) = 5*c(b) - v(b). Solve s(h) = 0 for h.
-12, 1
Let x(z) = -z**3 - 2*z**2 - 3*z - 14. Let i be x(-3). Let g(w) be the first derivative of -i + 0*w - 1/4*w**3 + 3/4*w**2. Factor g(d).
-3*d*(d - 2)/4
Let i = -339 - -507. Find q such that -3*q - 4*q + i + q**2 - 162 = 0.
1, 6
Let q = -13534 + 13540. Solve -2/3*p**2 - 4*p - q = 0.
-3
Factor -30*z**2 - 167*z + 302*z - 164*z + 1.
-(z + 1)*(30*z - 1)
Let r(m) be the second derivative of 0*m**2 + 0*m**4 - 1/2340*m**6 - 1/780*m**5 + 4*m + 0 + 1/2*m**3. Let t(h) be the second derivative of r(h). Solve t(n) = 0.
-1, 0
Suppose q = -34*q - 23*q. Let o(s) be the first derivative of 1/10*s**5 + 0*s**4 + 0*s + q*s**2 - 1/6*s**3 + 2. Factor o(n).
n**2*(n - 1)*(n + 1)/2
Factor 116/5*k + 4/5*k**2 + 0.
4*k*(k + 29)/5
Suppose 8*j - 12 = 4*j. Let -2*c**4 + 2*c**2 + 2*c + 2*c + 6*c**j - 8*c - 2*c**5 = 0. What is c?
-2, -1, 0, 1
Let w(v) be the third derivative of v**7/60 - 23*v**6/240 - v**5/120 + 23*v**4/48 - v**3/2 - 4*v**2 - 2. Solve w(i) = 0 for i.
-1, 2/7, 1, 3
Let b(n) be the second derivative of n**7/42 + n**6/5 - 5*n**5/4 + 3*n**4/2 + 75*n - 2. Determine x so that b(x) = 0.
-9, 0, 1, 2
Factor l - 8*l**3 + 7*l**3 + 1 + 601*l**2 - 602*l**2.
-(l - 1)*(l + 1)**2
Let x(o) = -57*o + 342. Let c be x(6). Let g(i) be the second derivative of c*i**2 - 6*i + 7/6*i**4 - 2/3*i**3 + 0. Suppose g(r) = 0. What is r?
0, 2/7
Let q(s) be the first derivative of -s**4/14 - 10*s**3/7 - 48*s**2/7 - 88*s/7 - 133. Factor q(c).
-2*(c + 2)**2*(c + 11)/7
Factor -2/5*f**2 - 7688/5 - 248/5*f.
-2*(f + 62)**2/5
Let z(i) be the third derivative of -i**5/120 - 11*i**4/48 - 5*i**3/6 + 58*i**2. Factor z(u).
-(u + 1)*(u + 10)/2
Let l = -16850678 + 25360269176/1505. Let z = -2/301 - l. Let 2/5*t**4 + 2/5*t - 6/5*t**2 - 2/5*t**3 + z = 0. Calculate t.
-1, 1, 2
Factor -24/7*q**2 - 15/7*q**3 + 0 - 12/7*q - 3/7*q**4.
-3*q*(q + 1)*(q + 2)**2/7
Let z(b) be the second derivative of -b**6/30 + 4*b**5/15 - 2*b**4/3 - 3*b**2 + 6*b. Let u(c) be the first derivative of z(c). Factor u(w).
-4*w*(w - 2)**2
Let i be ((-1)/4)/(6/(-36)) + (-24)/32. Find u, given that -3/2*u - i*u**2 - 3/4*u**5 + 9/4*u**3 + 0 + 3/4*u**4 = 0.
-1, 0, 1, 2
Let -40/3*w + 52/9*w**2 + 8/9*w**3 - 2/9*w**4 - 50 = 0. What is w?
-3, 5
Let u = -171 - -174. Let t(x) be the second derivative of -1/6*x**4 - x + 0*x**u + 0*x**2 + 0. Determine i so that t(i) = 0.
0
Let l = 2765/3 + -5527/6. Factor 3/2*c**3 + 9 - 15/2*c + l*c**4 - 7/2*c**2.
(c - 2)*(c - 1)*(c + 3)**2/2
Let y(l) be the first derivative of -5/17*l**2 - 2/51*l**3 + 0*l + 8. Factor y(k).
-2*k*(k + 5)/17
Let k(c) be the first derivative of -c**5 + 25*c**4/4 + 35*c**3 + 115*c**2/2 + 40*c + 97. Suppose k(t) = 0. Calculate t.
-1, 8
Let i be 2/8 + 5/28. Let j = -3565 - -3567. Factor i*g**j + 0*g - 3/7*g**4 + 0*g**3 + 0.
-3*g**2*(g - 1)*(g + 1)/7
Let r = 73 - 63. Let o = r + -26/3. Determine q, given that 0*q + 0 - o*q**3 + 4/3*q**2 = 0.
0, 1
Suppose 116 - 116 = -3*c. Let x(p) be the second derivative of c - p**2 - 1/3*p**3 - 2*p + 1/10*p**5 + 1/6*p**4. Factor x(o).
2*(o - 1)*(o + 1)**2
Suppose z - 5*l = 5, -2*z + 3*l + 10 = l. Let h(m) be the second derivative of 1/30*m**z + 2/9*m**4 + 0 + 5/9*m**3 + 8*m + 2/3*m**2. Factor h(u).
2*(u + 1)**2*(u + 2)/3
Let s(r) = -11*r**2 - 295*r - 2. Let n(g) = -80*g**2 - 2065*g - 15. Let f(k) = -2*n(k) + 15*s(k). Factor f(t).
-5*t*(t + 59)
Let j be 192/(-33) - (8 + 112/(-8)). Find n such that j*n**3 + 8/11*n**2 + 8/11*n + 0 = 0.
-2, 0
Suppose -j + 6*j - 15 = 0. Suppose -i + j*i = 5*i. Determine o, given that 7/2*o**3 + 1/2*o - 3/2*o**4 - 5/2*o**2 + i = 0.
0, 1/3, 1
Let p = -111 + 255. Let n be (-32)/p - ((-26)/(-36))/(-1). Determine g so that n*g**2 - 1/2 + 0*g = 0.
-1, 1
Let a be 3/5 - (-170)/50 - 0. Let k(f) be the third derivative of 3*f**2 - 1/15*f**5 - 4/3*f**3 + 0 + 0*f - 1/2*f**a. Factor k(m).
-4*(m + 1)*(m + 2)
Let n(v) = 2*v - 6 - 4 + 7 - v. Let m be n(7). Suppose -2*y**4 + 2*y**4 + 5*y**2 - 2*y**2 - 3*y**m = 0. Calculate y.
-1, 0, 1
Let h(z) be the first derivative of 4*z**5/5 - 6*z**4 + 16*z**3 - 20*z**2 + 12*z - 258. Let h(g) = 0. Calculate g.
1, 3
Suppose 44 = -w - 35. Let d = 79 + w. Factor -2/9*u**3 - 2/3*u**2 + d*u + 0.
-2*u**2*(u + 3)/9
Let n(y) be the first derivative of -1/13*y**2 + 2/39*y**3 - 2/13*y - 10 + 1/26*y**4. Determine s so that n(s) = 0.
-1, 1
Let h = -579 + 583. Let s(f) be the second derivative of -3*f**2 - h*f - 2/3*f**3 + 0 - 1/18*f**4. Factor s(o).
-2*(o + 3)**2/3
Solve -4/5*z - 2/5 - 2/5*z**2 = 0.
-1
Factor -90 + 3/2*f**2 + 33/2*f.
3*(f - 4)*(f + 15)/2
Let p(v) be the first derivative of v**5/210 - 4*v**3/21 + v**2 - 16. Let r(u) be the second derivative of p(u). Factor r(n).
2*(n - 2)*(n + 2)/7
Determine n, given that 0*n + 0 - 3/7*n**3 + 6/7*n**2 = 0.
0, 2
Let s(r) be the first derivative of r**4/18 + 40*r**3/27 + 100*r**2/9 + 90. Solve s(w) = 0 for w.
-10, 0
Suppose -13*h = -17*h + 8. Suppose 4*b - a + 3 = 0, -4*b - 3*a + 9 = -6*b. Factor b*y**h + 0*y + 2/5*y**5 + 0*y**3 + 0 - 2/5*y**4.
2*y**4*(y - 1)/5
Let t(c) be the first derivative of 15/2*c**2 + 3*c + 10*c**3 + 1/2*c**6 - 1 + 15/2*c**4 + 3*c**5. What is n in t(n) = 0?
-1
Let j be 679/63 + (-2)/(-9). Let f be 10/55 + 31/j. Factor -2*n**3 - 3*n**2 - 4*n**2 + f*n**2 + 0*n**2.
-2*n**2*(n + 2)
Let i(p) be the first derivative of 7 + p**2 - 1/3*p**3 + 2*p. Let k(g) = 4*g**2 - 8*g - 9. Let v(z) = 9*i(z) + 2*k(z). Factor v(t).
-t*(t - 2)
Let h(f) = 19*f**3 - 20*f**2 + 31*f - 24. Let a(c) = -41*c**3 + 40*c**2 - 61*c + 49. Let l(s) = 6*a(s) + 13*h(s). Factor l(p).
(p - 18)*(p - 1)**2
Let n = 3/193 + 184/579. Let m(q) be the second derivative of 1/2*q**2 + 1/2*q**3 + 0 - q - n*q**4. Factor m(c).
-(c - 1)*(4*c + 1)
Let v(t) = t**3 - 27*t**2 + 77*t - 115. Let a be v(24). Suppose 18*x + 17/4*x**2 - 33/4*x**4 - x**a - 17*x**3 + 4 = 0. What is x?
-4, -1, -1/4, 1
Factor 3289 - q**2 - q**2 - 3287.
-2*(q - 1)*(q + 1)
Let u(k) be the second derivative of -k**8/840 + k**6/45 + 2*k**3 - 41*k. Let r(d) be the second derivative of u(d). Factor r(s).
-2*s**2*(s - 2)*(s + 2)
Factor 28/11 - 2/11*l**2 + 26/11*l.
-2*(l - 14)*(l + 1)/11
Let f(s) = -8*s**2 - 178*s - 1808. Let n(k) = -7*k**2 - 182*k - 1807. Let r(m) = -2*f(m) + 3*n(m). What is i in r(i) = 0?
-19
Let h(k) be the third derivative of k**8/192 - 23*k**7/840 + 9*k**6/160 - 13*k**5/240 + k**4/48 - 227*k**2. Factor h(m).
m*(m - 1)**3*(7*m - 2)/4
Let g be -4 + 1 - -5 - (-2)/(-4). Let z(w) be the second derivative of 0 - g*w**3 - 1/4*w**4 - 5*w - 3*w**2. Determine l, given that z(l) = 0.
-2, -1
Factor 43*s**2 - 73*s + 90 + 18*s - 38*s**2.
5*(s - 9)*(s - 2)
Factor -456/5*v + 182/5*v**2 - 16/5*v**3 - 72.
-2*(v - 6)**2*(8*v + 5)/5
Let m(y) be the first derivative of y**4/6 + 26*y**3/9 + 23*y**2/3 + 22*y/3 + 55. Factor m(s).
2*(s + 1)**2*(s + 11)/3
Let u(k) = 3*k - 1. Let q be u(-9). Let x be (-2)/(-8) - 77/q. Factor -g + 0*g**3 + 0*g**x + g**3.
g*(g - 1)*(g + 1)
Let j be (-1 - (0 + -3)) + 0. Let p be ((-1)/j)/((-6)/72). Suppose 4*i**2 - p*i + 9 - 6 - i**2 = 0. What is i?
1
Let h(d) be the second derivative of -d**5/120 + 2*d**4/9 - 20*d**3/9 + 32*d**2/3 - 86*d. Find t such that h(t) = 0.
4, 8
Factor 13*c + 105*c**2 - 19