3, -1, 1, 2
Let b = 157407/20 - 31475/4. Determine p so that 0*p - b*p**2 + 1/5*p**3 + 0 = 0.
0, 8
Let j = 165 - 156. Suppose 15*k - 18 = j*k. Suppose -16/3*q**2 + 8*q - k = 0. Calculate q.
3/4
Let n(m) be the second derivative of -m**4/30 - 49*m**3/15 + 1562*m**2/5 - 23*m - 86. Solve n(l) = 0 for l.
-71, 22
Find m, given that 235*m**2 + 785*m - 727*m**2 + 239*m**2 + 248*m**2 - 3800 = 0.
5, 152
Let s(k) be the third derivative of -k**7/42 - 10*k**6/3 - 1423*k**5/12 + 3115*k**4/2 + 7350*k**3 - 424*k**2 - k - 2. Factor s(i).
-5*(i - 5)*(i + 1)*(i + 42)**2
Let y = 13/495 - -86/495. Let c(z) be the first derivative of 0*z**4 - z**2 - z**3 + 0*z + y*z**5 - 21. Find h such that c(h) = 0.
-1, 0, 2
Let m(u) be the third derivative of u**7/1960 - u**6/210 + u**5/280 + 3*u**4/28 - 11*u**3/6 - 73*u**2. Let f(p) be the first derivative of m(p). Factor f(b).
3*(b - 3)*(b - 2)*(b + 1)/7
Let x be (-30)/(2/(-7) - 228/(-1680)). Determine w so that -1373*w**2 + 690*w**2 + 687*w**2 - x*w = 0.
0, 50
Suppose -36 = -50*b + 10 + 54. Factor -7/2*x - 1/2*x**b - 3.
-(x + 1)*(x + 6)/2
Suppose 33*h - 29*h + 1 = -3*y, 3 = -3*h - 3*y. Let k(l) be the first derivative of 0*l - 9/2*l**4 - 3/8*l**h - 9/4*l**3 - 12/5*l**5 + 8. What is u in k(u) = 0?
-1, -1/4, 0
Let q = 829 + -811. Suppose -3*u + j - 4 + 10 = 0, -4*j = 2*u - q. Factor 2/7*l**u - 8/7*l + 0*l**2 + 0.
2*l*(l - 2)*(l + 2)/7
Let m(c) = 2*c**2 - 62*c + 4. Let l = 203 - 206. Let h(p) = 2*p**2 - 61*p + 6. Let y(z) = l*m(z) + 2*h(z). Solve y(x) = 0 for x.
0, 32
What is w in -12*w**3 + 3049*w**2 - 266 - 6727*w**2 - 1054 + 4204*w + 2950*w**2 = 0?
-66, 1/3, 5
Let a(w) be the second derivative of 3*w**5/140 - 37*w**4/28 + 135*w**3/14 - 297*w**2/14 + 1779*w. Factor a(q).
3*(q - 33)*(q - 3)*(q - 1)/7
Let w be 13 + (-2509)/858 - 5/(-6). Determine h so that -2/11*h**3 + 16000/11 + w*h**2 - 2400/11*h = 0.
20
Let z be 1632/(-119) + 14 - 29/126. Let d(n) be the second derivative of z*n**4 - 2/3*n**2 + 0 - 1/9*n**3 + 17*n. Factor d(s).
2*(s - 2)*(s + 1)/3
Let a be 7 - (5/2)/((-20)/448*-8). Let s(h) be the third derivative of -25*h**2 - 7/18*h**4 + 0 + 1/45*h**5 + 4/3*h**3 + a*h. Factor s(v).
4*(v - 6)*(v - 1)/3
Let u(v) = 11 + v**3 - 7 + v - v**2 - 6. Let o(q) = 6*q**3 - 23*q**2 - 28*q - 19. Let g(x) = 5*o(x) - 20*u(x). Factor g(m).
5*(m - 11)*(m + 1)*(2*m + 1)
Let z be 1/(12/4 - 4) - -4. Suppose 16*s**z + 4*s**4 - 6935 + 12*s**2 + 6935 = 0. What is s?
-3, -1, 0
Suppose 9*k + 75 = 12*k. Suppose 5*p = k, -4 = 2*r - p - p. Suppose -9 - 5 - 4*u**2 - 5*u + 2*u**3 - 3*u**r + 12 = 0. Calculate u.
-2, -1
Let j = 10272 - 10270. Let u(s) be the first derivative of 0*s - 28 + j*s**2 + 2*s**3 + 1/2*s**4. Factor u(f).
2*f*(f + 1)*(f + 2)
Let d = -295 + 376. Factor -h**5 - 8*h**2 - 6*h**4 - 11*h**3 + d - 81 + 2*h**2.
-h**2*(h + 1)*(h + 2)*(h + 3)
Suppose i + 0*i - n + 2 = 0, 8 = 2*i + n. Suppose -i*g = 5*k - 3*g - 15, -2*k + 2*g + 14 = 0. Determine r, given that 735*r - k*r**3 - 735*r + 8*r**4 = 0.
0, 1/4
Let n(u) = 39*u**2 + 150*u - 2. Let k be n(-4). Determine v so that 66*v**2 + 277*v - 131*v - 128*v + 0*v**3 + k*v**3 + 2*v**4 - 108 = 0.
-6, -3, 1
Suppose -5*t - 4*s + 96 = 0, -s - 24 - 20 = -3*t. Suppose -21*i + t*i = -15. Solve -7*a**3 + 4*a**i + 8*a**3 - 10*a**2 = 0.
0, 2
Let s(j) be the second derivative of 0*j**2 + 2/9*j**3 - 7 - 1/45*j**6 - 6*j - 1/15*j**5 + 1/18*j**4. Factor s(y).
-2*y*(y - 1)*(y + 1)*(y + 2)/3
Let y(f) = -18 - f**2 - 3*f + 19 + f. Let d(m) = -17*m - 111. Let u be d(-7). Let i(g) = 4*g**2 + 40*g - 44. Let j(q) = u*y(q) + i(q). Solve j(r) = 0.
3
Let m = 17660 + -13015422/737. Let y = 1440/12529 - m. Solve 6/17 - 6/17*d**2 - 2/17*d**3 + y*d = 0 for d.
-3, -1, 1
Let w = 363 - 361. Factor 0*c**2 + 4*c**2 - 4*c**2 + 2*c**w + 36*c.
2*c*(c + 18)
Let c(z) = 9*z**3 + 142*z**2 - 19980. Let v(u) = -17*u**3 - 286*u**2 + 39965. Let q(f) = -7*c(f) - 4*v(f). Determine m so that q(m) = 0.
-20, 10
Let u = 126 + -118. Factor -4*w**3 - u*w**3 + 2*w**3 - 10*w**3 - 24*w**2 - 4*w.
-4*w*(w + 1)*(5*w + 1)
Let i(o) = 2*o**2 + 4*o + 25. Let l be i(0). Find g such that -52*g**2 - 6*g + 2 + l*g**2 + 6*g**3 + 22 + 3*g**4 = 0.
-4, -1, 1, 2
Let m be 8 + (12*-1 - 602/(-42)). Factor -11/3*y**2 - m*y + 2.
-(y + 3)*(11*y - 2)/3
Let o(h) be the first derivative of h**5/34 + 29*h**4/51 + 52*h**3/17 - 72*h**2/17 - 50*h - 18. Let v(k) be the first derivative of o(k). What is r in v(r) = 0?
-6, 2/5
Let d = 34477/2 - 17237. Suppose -19/4*v**2 - 2*v**3 - d*v + 0 + 5/4*v**4 = 0. What is v?
-1, -2/5, 0, 3
Let n(s) be the second derivative of 0*s**2 - 2/15*s**5 + 0 - 4/9*s**3 - 5/9*s**4 + 58*s. Factor n(h).
-4*h*(h + 2)*(2*h + 1)/3
Let i be 30*((-3864)/(-385) - (-100)/(-10)). Let m = -2/149 + 916/1639. Suppose -m*t**5 - i*t**2 + 2/11 + 10/11*t**4 + 2/11*t + 4/11*t**3 = 0. Calculate t.
-1, -1/3, 1
Let z(g) = g**2. Let w(f) be the third derivative of -f**5/10 - f**4/3 + f**2. Let u be -5 + 2 - (-4)/(-4). Let d(a) = u*z(a) - w(a). Factor d(r).
2*r*(r + 4)
Let m(w) be the second derivative of -w**5/360 - w**4/144 + 3*w**2 - 12*w. Let d(l) be the first derivative of m(l). Let d(n) = 0. What is n?
-1, 0
Let a(r) = r**2 + r - 1. Let t(u) = -10*u - 7*u**2 - 5*u + 2*u**2 + 6*u + 8. Let n(l) = -6*a(l) - t(l). Factor n(i).
-(i - 2)*(i - 1)
Factor -1/3*m**3 - 688/3*m - 252 + 67/3*m**2.
-(m - 54)*(m - 14)*(m + 1)/3
Let w(h) = h**3 - 15*h**2 - 20*h + 77. Let y be w(16). Let o(z) be the second derivative of -5/3*z**3 + 1/6*z**4 - 6*z**2 + 0 - y*z. Factor o(j).
2*(j - 6)*(j + 1)
Let x(h) be the first derivative of h**3/12 - 175*h**2 + 122500*h + 2708. Factor x(l).
(l - 700)**2/4
Let z = 2 - 2. Let j be 2 + 1/(-5) - 3570/3150. Factor -j*k**2 + 0 + z*k.
-2*k**2/3
Let b(m) be the second derivative of 5*m**3/6 - 6*m**2 - 43*m. Let y be b(3). Factor -7*n**2 + n**y - n**4 + 0*n**3 + 6*n**2 + 7*n**2.
-n**2*(n - 3)*(n + 2)
Suppose w - 15 = 66. Let k be (-8)/(-9) + 18/w*-1. Factor 4/3 - 2/3*o**2 + k*o.
-2*(o - 2)*(o + 1)/3
Let h(c) be the third derivative of c**6/480 + 169*c**5/20 + 28561*c**4/2 + 38614472*c**3/3 + 977*c**2. Determine b so that h(b) = 0.
-676
Let z(p) be the third derivative of 4/5*p**7 + 11/84*p**8 + 0 + 0*p**3 - 28*p**2 - 8/15*p**5 + 0*p**4 + 6/5*p**6 - 3*p. Factor z(n).
4*n**2*(n + 2)**2*(11*n - 2)
Suppose 432 + 991*g + 73*g**2 + 485*g - 21*g**3 - 27*g**2 - 178*g**2 = 0. What is g?
-12, -2/7, 6
Let f(a) be the second derivative of a**7/315 + 38*a**6/225 + 63*a**5/25 + 152*a**4/45 - 379*a**3/45 - 114*a**2/5 + 2994*a. What is w in f(w) = 0?
-19, -18, -1, 1
Suppose 2470 - 10504 = 26*p. Let x = 311 + p. Factor -1/5*o**x + 1/5*o + 2/5.
-(o - 2)*(o + 1)/5
Suppose 0 - 624*b**3 - 3/4*b**5 + 0*b - 2304*b**2 - 40*b**4 = 0. What is b?
-24, -16/3, 0
Let i be 2/(-5) + (-540)/(-225). Factor 243*f**i + 2*f**3 - 2*f - 247*f**2 + 0*f**3 - 4*f**3.
-2*f*(f + 1)**2
Let x(t) be the second derivative of t**5/10 - 17*t**4/3 + 59*t**3 - 252*t**2 - 1113*t. Find m such that x(m) = 0.
3, 28
Let t(y) be the first derivative of -y**4 + 40*y**3/3 - 32*y**2 + 777. Factor t(f).
-4*f*(f - 8)*(f - 2)
Let d(c) = -c**3 + 10*c**2 + 16*c - 14. Let q be d(11). Let a = 44 - q. What is g in -7 + g**a + 0 + g**2 + 2*g**2 + 3 = 0?
-2, 1
Let q = -424 + 417. Let y(f) = f**3 + 11*f**2 + 25*f - 19. Let m be y(q). Factor 0 + 3/8*x**3 + 147/8*x - 21/4*x**m.
3*x*(x - 7)**2/8
Let -5*n**3 - 321*n**2 + 1016*n**2 - 1390 + 1597*n - 1491*n**2 + 1178*n - 584*n**2 = 0. What is n?
-278, 1
Let u be ((207/45)/1 + 1 + -2)*1. Let m(h) be the second derivative of 0 - 9/5*h**4 - u*h**3 - 2/75*h**6 - 18*h + 0*h**2 - 9/25*h**5. Let m(a) = 0. Calculate a.
-3, 0
Let j(c) = 17*c**4 + c**3 - 10*c**2 - c - 7. Let g(a) = 16*a**4 - 12*a**2 - 2*a - 6. Let h(x) = 7*g(x) - 6*j(x). Factor h(d).
2*d*(d - 2)*(d + 1)*(5*d + 2)
Factor 20/7*m + 2/7*m**2 + 16/7 - 2/7*m**3.
-2*(m - 4)*(m + 1)*(m + 2)/7
Let u(v) = v**2 - 1. Let n(l) = -20*l**2 + 80*l + 228. Let i(z) = -n(z) - 24*u(z). Factor i(s).
-4*(s + 3)*(s + 17)
Let o = -709519/80 + 8869. Let p(s) be the second derivative of o*s**5 + 1/120*s**6 - 1/4*s**2 - 5/24*s**3 - 1/16*s**4 - 14*s + 0. Factor p(l).
(l - 2)*(l + 1)**3/4
Let s(t) = -t**3 + 9*t**2 - 15*t + 9. Let z = 29 + -22. Let h be s(z). Suppose 12*o**3 - 3*o + 28*o**4 - 12*o**2 + 12*o**5 - 7*o + h*o = 0. What is o?
-1, 0, 2/3
Let m(f) 