160*l + 5*l**4 + 720 - 116*l**2 + 1924*l + 105*l**3 - 380*l**3 = 0.
-5, -2/5, 6, 12
Let n be 2 - (-1 - (-2 + 4)). Suppose -5*s + 3*p + 17 = -13, 3*s + 2*p = -1. Factor -20*w**n - 95*w**3 + 20*w**s + 14*w**2 - 49*w**2 - 65*w**4 - 5*w.
-5*w*(w + 1)**3*(4*w + 1)
Suppose 11*g - 7*g - 232 = 0. Let v = 61 - g. Factor -4 + v*m**3 - 6*m**2 + 5*m**4 + 10*m - 3*m**4 - 5*m**3.
2*(m - 1)**3*(m + 2)
Let j(s) be the first derivative of -6/11*s**3 - 24/11*s**2 + 90 - 32/11*s. Let j(u) = 0. What is u?
-4/3
Let v be (9 - (-86)/(-4))*161/(-690). Let q(r) be the third derivative of 0 + 1/12*r**5 + 245/6*r**3 - v*r**4 + r**2 - 6*r. Factor q(m).
5*(m - 7)**2
Let w(n) be the second derivative of 4/57*n**3 - 9/190*n**5 - 5*n - 4 - 3/38*n**4 + 4/19*n**2. Solve w(p) = 0.
-1, -2/3, 2/3
Let o(g) = -5*g**2 + 60*g + 729. Let b(f) = 9*f**2 - 119*f - 1458. Suppose 20*j - 44 = 16*j. Let p(w) = j*o(w) + 6*b(w). Solve p(i) = 0.
-27
Let i(o) = -o**3 + 10*o**2 + 41*o - 23. Let f be i(13). Let c be (90/(-5))/(-2) - f. Solve c*a**2 + 10*a + 14/3 + 2/3*a**3 = 0 for a.
-7, -1
Suppose -4*x + 5 = 97*i - 96*i, 0 = -4*i + 3*x + 20. Suppose i*m = -m + 18. Factor -3/7 - 1/7*t + 3/7*t**2 + 1/7*t**m.
(t - 1)*(t + 1)*(t + 3)/7
What is v in 14*v**4 - 67*v**2 - 128*v**2 + v**2 - 249*v**3 + 385*v**3 + 44*v = 0?
-11, 0, 2/7, 1
Factor 2/5*n**5 + 8/5*n**4 + 12/5*n**3 + 0 + 2/5*n + 8/5*n**2.
2*n*(n + 1)**4/5
Let k(o) = 4*o**2 + o - 3. Let y(d) = 9*d**2 + 3*d - 7. Let w(v) = 7*k(v) - 3*y(v). Let f(z) = -9*z**2 + 26*z. Let u(j) = -f(j) - 5*w(j). Factor u(i).
4*i*(i - 4)
Let r(k) be the third derivative of k**8/28 + 43*k**7/70 + 33*k**6/8 + 13*k**5 + 29*k**4/2 - 24*k**3 + 2*k**2 - 1554*k. Determine s, given that r(s) = 0.
-4, -3, -2, 1/4
Let g = -15/8167 + 122535/16334. Factor 3/4*b**2 - g*b + 12.
3*(b - 8)*(b - 2)/4
Let l(f) be the second derivative of -f**4/42 - 152*f**3/21 - 151*f**2/7 - 2325*f + 2. Factor l(v).
-2*(v + 1)*(v + 151)/7
Solve -60 - 17*u**2 + 8*u**2 - 52*u + 2*u**2 - 5*u**2 + 120 + 4*u**3 = 0 for u.
-3, 1, 5
Factor -592598*d**2 + 41 + 592595*d**2 + 82 + 120*d.
-3*(d - 41)*(d + 1)
Suppose 105*x - 210*x + 22 = -94*x. Let r(c) be the first derivative of -1/10*c**4 + 9 + 1/5*c**x - 6/5*c + 2/5*c**3. Factor r(n).
-2*(n - 3)*(n - 1)*(n + 1)/5
Factor r**2 - 6366 + 6222 - 3*r**2 - 146*r.
-2*(r + 1)*(r + 72)
Let k be 149/(-3) + 92/(-69). Let m = -40 - k. Factor -9*i**3 - 16*i**3 + 30*i**3 - 9*i - m*i + 15*i**2.
5*i*(i - 1)*(i + 4)
Let m(q) be the first derivative of q**5/5 + 27*q**4/4 - 472*q**3/3 + 942*q**2 - 1440*q + 3027. Factor m(z).
(z - 6)**2*(z - 1)*(z + 40)
Let r(d) be the second derivative of -d**4/8 - 237*d**3/4 + 717*d**2/2 + 610*d. Factor r(v).
-3*(v - 2)*(v + 239)/2
Let t be (8/2)/((-366)/(-18) + -19). Suppose y - 10 + 5 = 0. Factor -y*g + 5/3*g**t - 10/3*g**2 + 0.
5*g*(g - 3)*(g + 1)/3
Let q be ((-682)/(-7502))/((-14)/(-11)). Let h(s) be the third derivative of 11*s**2 + 0*s + 8/21*s**3 - 1/105*s**5 + 0 + q*s**4. Solve h(k) = 0 for k.
-1, 4
Suppose 0*q - 28 = -3*q + 4*k, -4*k = -5*q + 36. Let t = 1092966 + -4371837/4. Find r such that 3/4*r - 9/2*r**q - t*r**5 + 6*r**3 + 9/2*r**2 + 0 = 0.
-1, -1/3, 0, 1
Let l(d) be the first derivative of -21/10*d**2 + 143 - 18/5*d - 1/5*d**3. Factor l(p).
-3*(p + 1)*(p + 6)/5
Let f be ((-3075)/2255)/(3/22)*(-1)/15. Find h, given that -260/3*h**3 + 2902*h**2 + 8192/3 + f*h**4 - 16640/3*h = 0.
1, 64
Let a be (-2 - 10/(-6))/(20/(-1140)). Factor -26*t**3 + a - 11 + 28 - 12*t**4 + 4*t**5 + 2*t**3 + 84*t + 40*t**2.
4*(t - 3)**2*(t + 1)**3
Let b(p) be the third derivative of p**6/40 + 1467*p**5/20 + 717363*p**4/8 + 116930169*p**3/2 - 6384*p**2. Suppose b(v) = 0. Calculate v.
-489
Let d(m) = -3*m**2 + 9*m + 7. Let q be d(5). Let w = 26 + q. Determine b so that -4*b**w - 44*b + b**5 + 3*b**5 + 44*b = 0.
-1, 0, 1
Find x such that 648/17*x + 2/17*x**4 + 52/17*x**3 - 1080/17 + 378/17*x**2 = 0.
-15, -6, 1
Let j(r) be the second derivative of 24389*r**5/60 - 841*r**4/4 + 87*r**3/2 - 9*r**2/2 - 2*r - 1522. Determine h so that j(h) = 0.
3/29
Let v be (9 + -3)*72/54. Suppose -4*t + r + 0*r + 16 = 0, 3*r - v = -2*t. Let 0 + 2*a**3 + 2/9*a**5 + 4/9*a - 10/9*a**t - 14/9*a**2 = 0. What is a?
0, 1, 2
Let f(i) = 7*i**3 - 14*i**2 + 35*i - 22. Let z(g) = -12*g**3 + 28*g**2 - 70*g + 44. Let k(j) = 5*f(j) + 3*z(j). Factor k(h).
-(h - 11)*(h - 2)*(h - 1)
Let n(y) be the second derivative of -y**4/90 + 286*y**3/45 - 283*y**2/5 - 5*y + 32. Solve n(l) = 0.
3, 283
Let t(k) be the third derivative of -1/180*k**5 + 0*k + 1 - 11/18*k**3 + 1/6*k**4 - 16*k**2. Factor t(x).
-(x - 11)*(x - 1)/3
Suppose 4*f = -2*t - 24, 0 = -5*t - 3*f + 2 - 41. Let z(h) = h**2 + h. Let d(k) = 8*k**2 + 14*k + 6. Let b(r) = t*z(r) + d(r). Find x, given that b(x) = 0.
-3, -1
Let z be (6108/(-4072))/((-14)/4). Factor 0 + 18/7*q - z*q**3 + 3/7*q**2.
-3*q*(q - 3)*(q + 2)/7
Factor -54*t**2 - 11*t**4 + 10*t**4 + 3125*t**3 - 3005*t**3 - 65*t**2.
-t**2*(t - 119)*(t - 1)
Suppose 17*w + 1597 = 1648. Solve -1/10*k**5 + 6859*k**2 - 361*k**w - 130321/2*k + 2476099/10 + 19/2*k**4 = 0 for k.
19
Let u be ((-5)/(-5))/((-2)/10). Let m(i) = i**2 - 6*i - 40. Let r(q) = 5*q + 40. Let j(v) = u*m(v) - 4*r(v). Factor j(y).
-5*(y - 4)*(y + 2)
Let k = -41 + 44. Suppose 3*o - 11 = -l, -3*o + 16 = k*l - l. Solve 14 + 2 + 203*w**o + 36*w**2 + 144*w + 85*w**2 = 0.
-2/9
Let a = -128057 - -128059. Find v such that -20*v - 150 - 2/3*v**a = 0.
-15
Let f(p) be the first derivative of 21*p**5/5 - 3*p**4/4 + 2250. Factor f(t).
3*t**3*(7*t - 1)
Let c = 109821/26230 - -69/5246. Factor 24/5*n + c*n**3 + 57/5*n**2 - 12/5.
3*(n + 1)*(n + 2)*(7*n - 2)/5
Let u(y) be the third derivative of y**6/810 + 16*y**5/45 + 128*y**4/3 - 107*y**3/6 - 11*y**2 + 2*y. Let d(s) be the first derivative of u(s). Factor d(k).
4*(k + 48)**2/9
Let j(p) be the second derivative of 123*p + 33/130*p**5 - 4/13*p**2 + 0*p**3 + 1/91*p**7 + 17/195*p**6 + 0 + 23/78*p**4. Let j(l) = 0. What is l?
-2, -1, 1/3
Let v be (20 - 2850/45) + 48. Factor 1/3*u**5 + v*u**2 - u**3 - 8/3*u + 0 - 4/3*u**4.
u*(u - 4)*(u - 1)**2*(u + 2)/3
Let r = -7/328 + 171/328. Factor -r*i**4 - 5/2*i**3 - 3/2*i**2 + 5/2*i + 2.
-(i - 1)*(i + 1)**2*(i + 4)/2
Let v(p) be the third derivative of p**6/1980 - p**5/30 + 97*p**3/3 + 139*p**2 + p. Let j(q) be the first derivative of v(q). Factor j(u).
2*u*(u - 22)/11
Let j(u) be the second derivative of -u**5/20 + 23*u**4/6 + 16*u**3 - 2*u + 3. Let j(l) = 0. What is l?
-2, 0, 48
Suppose 0 = -4*q + 36 - 12. Let n(g) = 5*g**2 - 5*g - 3. Let c(j) = 5*j**2 - 5*j - 4. Let s(h) = q*n(h) - 7*c(h). Factor s(b).
-5*(b - 2)*(b + 1)
Let p(v) be the third derivative of v**7/4620 + v**6/990 + 45*v**3/2 - 51*v**2 - 1. Let w(o) be the first derivative of p(o). Determine h, given that w(h) = 0.
-2, 0
Suppose -2*c - 6 + 14 = 0. Suppose 0 = -5*u + n + 11, 5*n = c*u + 2*n. Suppose -6*b**3 - 5*b**5 - 10*b**2 - b**4 + 5 + 6*b**4 + 16*b**u - 5*b = 0. What is b?
-1, 1
Let u(j) be the second derivative of -j**4/48 + 59*j**3/2 - 31329*j**2/2 - 139*j + 1. Determine d so that u(d) = 0.
354
Let d be (96/(-192))/(-1 - 0). Suppose -4*u - 104 = -116. Factor d*w**2 + u*w + 4.
(w + 2)*(w + 4)/2
Let t(b) = -115*b**3 - 3300*b**2 + 136095*b - 1113810. Let x(y) = 42*y**3 + 1200*y**2 - 49489*y + 405022. Let o(f) = -11*t(f) - 30*x(f). Factor o(s).
5*(s - 15)**2*(s + 90)
Let q(y) = 51*y**5 - y**3 + 68*y**5 - 120*y**5 - y**2 + y**4. Let z(f) = 8*f**5 - 32*f**4 - 62*f**3 - 22*f**2 + 128*f. Let u(j) = -10*q(j) - z(j). Factor u(s).
2*s*(s - 1)*(s + 4)**3
Suppose 51*a + 154 = -254. Let o be ((-1211)/(-154) + a)*-24. Factor o*x - 162/11 - 2/11*x**2.
-2*(x - 9)**2/11
Suppose 2*h = -3*q + 12, -5*q + 4 = 75*h - 77*h. Factor -20*z - 11 + 33 + 20 + 2*z**q.
2*(z - 7)*(z - 3)
Let j(z) be the first derivative of -z**5 + 200*z**4 - 34310*z**3/3 + 92400*z**2 - 266805*z + 930. Suppose j(p) = 0. Calculate p.
3, 77
Let d(v) be the second derivative of -v**5/20 + 647*v**4/12 - 17388*v**3 - 52488*v**2 + 501*v - 3. Determine x, given that d(x) = 0.
-1, 324
Let r = 597743/1419775 + 3/74725. Find y, given that -r + 2/19*y**2 - 2/19*y**3 + 8/19*y = 0.
-2, 1, 2
Let r(h) = -h**2 - h. Let q be ((-8)/(-4) + 1/(-1))*-1. Let a(d) = -6*d**2 + 4*d + 10. Let u(z) = q*a(z) + 8*r(z). Factor u(l).
-2*(l + 1)*(l + 5)
Suppose 0 = 2*v + 