 Let m(g) = 3*o(g) + q(g). Determine l, given that m(l) = 0.
-1
Suppose -47*u**2 + 39*u + u**3 + 0*u**2 - 16*u**2 + 2*u**3 + 21*u = 0. Calculate u.
0, 1, 20
Let q = -23741/3 - -94967/12. Find f, given that 5/4*f + q*f**3 - f**2 - 1/2 = 0.
1, 2
Factor -3/2*h**3 + 9/2*h**2 + 3/2*h - 9/2.
-3*(h - 3)*(h - 1)*(h + 1)/2
Let t(o) = 2*o**3 - 40*o**2 - 68*o - 32. Let i(u) = -u**3 + 40*u**2 + 68*u + 32. Let v(g) = g - 19. Let f be v(13). Let a(w) = f*i(w) - 5*t(w). Factor a(r).
-4*(r + 1)**2*(r + 8)
Let l be 54/(-9)*(-6 - (-53)/9). Determine g, given that -1/3*g**2 - 1/3 + l*g = 0.
1
Factor 42/5*c**2 + 1/5*c**3 - 87/5*c + 44/5.
(c - 1)**2*(c + 44)/5
Suppose 2*l = -3*t + 2, 6*t - 2*l = 7*t + 2. Factor 2/5*g - 2/15*g**t - 4/15.
-2*(g - 2)*(g - 1)/15
Let c(k) = k + 2. Let v be c(-19). Let f = v - -25. Factor -8*u + 7*u - f*u**4 - 20*u**3 - 3*u - 16*u**2.
-4*u*(u + 1)**2*(2*u + 1)
Let z(h) be the third derivative of h**8/336 - 17*h**7/210 + 31*h**6/60 + 49*h**5/30 - 21*h**4/8 - 27*h**3/2 - 40*h**2. Factor z(f).
(f - 9)**2*(f - 1)*(f + 1)**2
Let n be (-2)/9 - 836/(-198). What is u in 4/3*u**2 - n*u + 8/3 = 0?
1, 2
Let o(m) be the third derivative of m**10/12600 + 5*m**9/4032 + m**8/160 + 3*m**7/560 - m**5/4 + 9*m**2. Let t(s) be the third derivative of o(s). Factor t(u).
3*u*(u + 3)**2*(4*u + 1)
Suppose -161*h = -158*h - 9. Let a(q) be the first derivative of -2 + 10/9*q**h + 8/3*q + 1/6*q**4 + 8/3*q**2. Factor a(w).
2*(w + 1)*(w + 2)**2/3
Let f(s) be the first derivative of -28 + 0*s + 55/3*s**3 + 5*s**2 + 95/4*s**4 + 5/2*s**6 + 13*s**5. Let f(t) = 0. What is t?
-2, -1, -1/3, 0
Suppose 5*r + 10 = -5*m, 2*m - 20*r = -15*r + 24. Let c be 12/(-18) + -2 + 6/m. Solve -c*f**2 + 1/3*f**4 + 2/3*f**3 + 0 - 2/3*f = 0 for f.
-2, -1, 0, 1
Let v be (-21)/(-6) + (-3)/6. Let q(g) be the third derivative of 1/3*g**4 - v*g**2 - 1/30*g**5 + 0*g + 0 + 0*g**3. Factor q(o).
-2*o*(o - 4)
Factor 565*m**3 + 6*m**2 - 282*m**3 - m - 18 - 282*m**3 - 12.
(m - 2)*(m + 3)*(m + 5)
Let j(l) be the third derivative of l**5/12 + 10*l**4/3 - 30*l**3 - 66*l**2. Determine m, given that j(m) = 0.
-18, 2
Let i be (-4 + 3)*(-3 - -3). Let -3*b**3 - 4*b**2 + i*b**3 + 3*b**3 + 4*b**3 = 0. Calculate b.
0, 1
Let d(z) be the first derivative of z**5/4 + 5*z**4/12 - 5*z + 45. Let s(m) be the first derivative of d(m). Solve s(v) = 0 for v.
-1, 0
Let i(h) be the second derivative of -1/24*h**4 + 1/60*h**6 - 5*h + 0*h**2 + 1/12*h**3 + 0 - 1/40*h**5. Let i(w) = 0. What is w?
-1, 0, 1
Determine l so that 60*l + 4*l**4 + 192*l**2 + 2*l + 82*l + 52*l**3 = 0.
-6, -1, 0
Factor 5/2*w + 1/4*w**3 - 6 + 13/4*w**2.
(w - 1)*(w + 2)*(w + 12)/4
Let x(f) be the third derivative of -14*f**2 + 0*f**4 + 1/100*f**6 + 0 + 0*f - 1/150*f**5 + 0*f**3 + 1/840*f**8 - 1/175*f**7. Factor x(i).
2*i**2*(i - 1)**3/5
Let q(r) be the third derivative of -r**8/1680 - 29*r**7/1680 - 7*r**6/240 + r**5/10 - r**3/6 + 26*r**2. Let m(o) be the third derivative of q(o). Factor m(g).
-3*(g + 7)*(4*g + 1)
Let v(r) = 3*r**2 + 18*r - 1. Let o be 7750/70 - (-2)/7. Let k(t) = 111*t - o*t + 2*t**2 - 1 - 3*t**2. Let c(z) = 10*k(z) - 2*v(z). Find d such that c(d) = 0.
-2, -1/4
Let a be (-8)/10*(-10)/4. Let y(v) be the first derivative of -24*v - 5 - 15*v**5 - 114*v**3 + 78*v**a + 285/4*v**4. Solve y(c) = 0.
2/5, 1, 2
Suppose -4*c + 16 = y, -4*c = -y + 5 + 11. Suppose 33*s = 37*s - y. Factor 0*u - 8/3*u**5 + 0 + 2/3*u**s + 0*u**3 + 0*u**2.
-2*u**4*(4*u - 1)/3
Let d(n) be the first derivative of -n**6/75 + n**4/15 - n**2/5 - 10*n + 7. Let m(k) be the first derivative of d(k). Factor m(v).
-2*(v - 1)**2*(v + 1)**2/5
Let d(c) = -2*c**2 - c + 4. Let h be d(0). Find k, given that -9 + 1 + 5 - 8*k + 2*k**h + 8*k**3 - 3 + 4*k**2 = 0.
-3, -1, 1
Let w(q) = -3*q + 21. Let y be w(7). Let k(x) be the second derivative of 0 + 1/60*x**4 + y*x**2 - x - 1/30*x**3. Factor k(r).
r*(r - 1)/5
Let u be (-49 - -9)/((-4)/6). Suppose -u = -5*f + 20. Factor -16*k + 39*k**4 + 51*k**4 - 27*k**4 - 60*k**3 - 128*k**2 + f.
(k - 2)*(3*k + 2)**2*(7*k - 2)
Let a be (-27)/(-117)*3/(-2). Let r = -1/78 - a. Factor r*g**2 - 4/3*g + 4/3.
(g - 2)**2/3
Let f(h) = -h**3 + 8*h**2 + 4*h - 12. Let p be f(8). Let o = p + -18. Find g such that 4*g + 3*g**2 + 4*g**2 + 4 - 6*g**o = 0.
-2
Let g(h) be the third derivative of -h**5/60 - 103*h**4/12 - 10609*h**3/6 - 153*h**2. Factor g(o).
-(o + 103)**2
Let q(a) be the first derivative of 2*a**3/15 + 42*a**2/5 + 882*a/5 + 9. Factor q(g).
2*(g + 21)**2/5
Let d = 4998 - 4996. Determine c so that -1/3*c + 0 + 5/3*c**2 + d*c**3 = 0.
-1, 0, 1/6
Let r be (-2 + -16)*(-4)/8. Let l be (-3)/r*-3 - 3. Let h(c) = 7*c**2 + 5*c + 3. Let b(u) = -3*u**2 - 2*u - 1. Let v(g) = l*h(g) - 5*b(g). Factor v(x).
(x - 1)*(x + 1)
Let o(f) = -2*f + 8. Let c be o(3). Let y(n) = n**2 - 2. Let r be y(c). Factor -4/7 + 0*v**r + 2/7*v**3 - 6/7*v.
2*(v - 2)*(v + 1)**2/7
Suppose -66 = -5*q - 16. Suppose -q*t = -55 + 15. Suppose -1/2*y + 1/2*y**3 - 3/2*y**2 + 1 + 1/2*y**t = 0. Calculate y.
-2, -1, 1
Let v(q) = -q**2 - q + 5. Let h be v(-2). Factor -7*d**3 + 20*d**3 + 28*d**h - 150*d**2 + 40*d - 6*d**3.
5*d*(d - 4)*(7*d - 2)
Let b(y) be the second derivative of y**7/7560 - y**6/2160 - y**5/180 - 5*y**4/2 - 2*y. Let k(w) be the third derivative of b(w). Factor k(r).
(r - 2)*(r + 1)/3
Let f(c) be the third derivative of c**10/30240 + c**9/7560 - c**8/6720 - c**7/1260 + c**4/24 - 10*c**2. Let p(d) be the second derivative of f(d). Factor p(x).
x**2*(x - 1)*(x + 1)*(x + 2)
Let s(w) be the first derivative of 17 + 3/4*w**2 + 3/2*w**3 + 1/8*w. Let s(l) = 0. Calculate l.
-1/6
Let i(c) be the third derivative of c**7/105 + c**6/60 - 8*c**5/15 + 5*c**4/3 - 8*c**2 - 3*c. Find d such that i(d) = 0.
-5, 0, 2
Let x(l) = 3 - 2*l - 2*l + 35*l**3 - 32*l**3. Let i be x(1). Factor i*c + 2/3*c**2 + 4/3.
2*(c + 1)*(c + 2)/3
Let j(a) be the first derivative of 2*a**3/3 + 8*a**2 + 14*a - 47. Factor j(m).
2*(m + 1)*(m + 7)
Suppose 2*v + 0 = -10. Let h be ((-4)/v)/((-2)/(-5)). Factor h*z + 4*z**2 - 4*z**3 + z**3 + 2*z.
-z*(z - 2)*(3*z + 2)
Let q = -64 + 69. Find i such that 3 - q*i**2 + 68*i - 63*i + 6 + 1 = 0.
-1, 2
Let d(w) be the first derivative of 0*w**2 + 2/3*w**4 + 0*w - 4/15*w**5 - 14 + 4/3*w**3. Solve d(x) = 0.
-1, 0, 3
Let u(h) be the second derivative of 21*h**5/20 - 53*h**4/2 - 97*h**3/2 + 24*h**2 + 549*h. Determine q, given that u(q) = 0.
-1, 1/7, 16
Let j(f) be the third derivative of -9/4*f**5 - 23/40*f**6 - 81/16*f**4 - 27/4*f**3 + 8*f**2 + 0 + 0*f - 11/140*f**7 - 1/224*f**8. Find o, given that j(o) = 0.
-3, -1
Let 3/4*f - 1/4*f**2 + 0 = 0. What is f?
0, 3
Let s(y) be the first derivative of 2/9*y**6 + 8/15*y**5 + 0*y + 0*y**4 - 2 - 8/9*y**3 - 2/3*y**2. Factor s(h).
4*h*(h - 1)*(h + 1)**3/3
Let g be 2 + -12 + ((-980)/168 - -16). Factor -g*q + 0 + 1/3*q**2 - 1/6*q**3.
-q*(q - 1)**2/6
Suppose 1/5*h**2 - 2*h**3 - 1/5*h**4 + 2*h + 0 = 0. Calculate h.
-10, -1, 0, 1
Let x = -6 - -9. Suppose 0*y + y = x. Factor -3*w + y*w + w + w**3 - 2*w**3.
-w*(w - 1)*(w + 1)
Let f = -711 + 12089/17. Solve -f*x**4 - 12/17*x**3 - 6/17 - 24/17*x**2 - 20/17*x = 0.
-3, -1
Factor -1/3*j**2 + 7*j - 20/3.
-(j - 20)*(j - 1)/3
Let k = -1790 - -1794. Let j(f) be the second derivative of -5/2*f**3 - 1/4*f**k - 6*f**2 + 2*f + 0. Let j(r) = 0. Calculate r.
-4, -1
Suppose -5*y + 7 = -3*d, -5*d + 41 = 4*y + 28. Let 2/5*r**4 + 0*r**3 + 0 + 0*r - 2/5*r**y = 0. Calculate r.
-1, 0, 1
Suppose -3*r + 28*g = 32*g + 20, 3*r = -3*g - 15. Factor r - 4/13*u - 2/13*u**2.
-2*u*(u + 2)/13
Let l(q) = -9*q**2 + 4*q - 4. Let g be l(1). Let t be (-34)/g - (3 + (-203)/63). Solve -1/9*b**t + 4/9 - 4/9*b**3 + 4/9*b - 1/3*b**2 = 0 for b.
-2, -1, 1
Let m be 34 - 34 - (0 - (-16)/18). Let t = m + 65/63. Determine k, given that -6/7*k**2 - t*k**3 - 8/7 - 12/7*k = 0.
-2
Let s(t) be the third derivative of t**7/1050 + 9*t**6/200 - 19*t**5/100 + 29*t**4/120 + 272*t**2. Factor s(b).
b*(b - 1)**2*(b + 29)/5
Let u(r) be the first derivative of 0*r - 11 - 2/3*r**3 + 1/2*r**4 + 0*r**2. Factor u(i).
2*i**2*(i - 1)
Let t = 41 + -23. Suppose n + s - 8 = -4*n, 5*n = 4*s + t. What is o in -o**3 + o**2 + 0*o**2 + 3*o**3 - 5*o**n = 0?
0, 2
Let f(g) be the second derivative of -5*g**4/12 + 45*g**3/2 + 236*g. Determine p, given that f(p) = 0.
0, 27
Let l(b) = -2*b**2 + 2*b.