 4)/9
Let r be (-2)/(-6) - (-256)/(-30) - (-1682 + 1673). Factor r*v**2 + 0 - 4/5*v - 4/5*v**4 + 4/5*v**3.
-4*v*(v - 1)**2*(v + 1)/5
Let t be ((-2)/(-4))/(36366/928 + -39). Solve -t*c + 10/3*c**2 - 8/9 - 8/9*c**3 = 0 for c.
-1/4, 2
Let o(t) = t**3 - 18*t**2 + 3*t - 46. Let s be o(18). Determine y so that 282*y - 4 + s + 286*y - 563*y + y**2 = 0.
-4, -1
Determine l, given that -76/5*l + 74/5 + 2/5*l**2 = 0.
1, 37
Factor -20 - 279*b - 239*b - 324 - 149*b**2 - 26*b**2 - b**3.
-(b + 1)*(b + 2)*(b + 172)
Find o such that -10 - 27/5*o - 1/5*o**2 = 0.
-25, -2
Let g(t) be the third derivative of 195*t**6/8 + 16*t**5/3 - 5*t**4/6 + t**2 - 10*t + 146. Factor g(f).
5*f*(13*f + 2)*(45*f - 2)
Let w(z) = -4*z**2 - 104*z - 2808. Let x(m) = -5*m + 18*m - 7*m - 3*m**2 + 3*m - 7*m + 1. Let v(u) = -2*w(u) + 2*x(u). Factor v(f).
2*(f + 53)**2
Let x(b) be the first derivative of -16*b**4/3 - 36*b**3 + 182*b**2/3 + 8*b - 1039. Solve x(l) = 0.
-6, -1/16, 1
Let t = -27/2 + 121/6. Suppose 2*n - 559*q + 555*q = 32, -4*n + 5*q + 46 = 0. Factor -t*h**3 - 8/9*h + 2*h**n - 46/9*h**2 + 0.
2*h*(h - 4)*(3*h + 1)**2/9
Let d = -3164219/5 - -632844. Factor 0 + 17/5*b**3 - 16/5*b**2 - d*b.
b*(b - 1)*(17*b + 1)/5
Factor -224*g + 37632 + 1/3*g**2.
(g - 336)**2/3
Let s(a) be the first derivative of a**7/70 + a**6/25 + 3*a**5/100 + 87*a + 54. Let c(z) be the first derivative of s(z). Factor c(d).
3*d**3*(d + 1)**2/5
Factor -8*o - 389*o**3 - 112*o + 762*o**3 - 2*o**4 - 3*o**4 - 423*o**3 - 140*o**2.
-5*o*(o + 2)**2*(o + 6)
Let x(k) be the third derivative of k**5/30 - 79*k**4/4 + 3*k**2 - 45. Factor x(q).
2*q*(q - 237)
Let o(x) be the first derivative of -x**5/2 - 5*x**4/8 + 10*x**3/3 + 5*x**2 + 653. Let o(a) = 0. What is a?
-2, -1, 0, 2
Solve -7/3*j**4 + 0*j - 8/3*j**2 + 0 + 1/3*j**5 + 14/3*j**3 = 0.
0, 1, 2, 4
Let k(d) = 2736 - 5451 + 2728 + 6*d**2 + 17*d + 3*d**3. Let m(f) = -2*f**3 + f**2 - f - 1. Let y(q) = 4*k(q) + 4*m(q). Factor y(w).
4*(w + 2)**2*(w + 3)
Let i be (-6466)/(-4770) + 10/(-18). Let s(w) be the first derivative of -6/5*w**2 + 4/5*w**3 - 1/5*w**4 + i*w + 1. Find j such that s(j) = 0.
1
Let d(z) be the first derivative of -60*z - 2/3*z**3 + 31*z**2 + 148. Determine b, given that d(b) = 0.
1, 30
Let d be ((-6864)/64)/13 + 9. Let g(a) be the second derivative of 3/40*a**5 - 21*a + d*a**4 + 6*a**2 + 3*a**3 + 0. Factor g(m).
3*(m + 2)**3/2
Suppose -150*d - 350 = -136*d. Let o(z) = 30*z**4 - 25*z**3 + 20*z**2. Let s(f) = -f**4 - 2*f**2. Let k(g) = d*s(g) - o(g). Find y, given that k(y) = 0.
-1, 0, 6
Find f such that 621*f - 29 - 48*f**3 - 513*f - 275*f**4 - 43 + 4*f**5 + 275*f**4 + 8*f**2 = 0.
-3, -2, 1, 3
Let v(w) be the second derivative of 0*w**2 + 10/3*w**3 + 1/2*w**4 - 1/10*w**5 + 73*w + 0. Factor v(z).
-2*z*(z - 5)*(z + 2)
Suppose -y + 3*d = 2127, 15*y + 4219 = 13*y - d. Let i = -2112 - y. Suppose 2/5*a**2 + 6/5*a**3 + i - 2/5*a**4 - 6/5*a = 0. What is a?
-1, 0, 1, 3
Let g(b) be the first derivative of 2*b**3/3 - 4*b**2 - 42*b - 34. Solve g(u) = 0 for u.
-3, 7
Let p = 51947 + -259732/5. Find t such that p*t**3 + 1/5*t**5 + 0 + 1/5*t**2 + 0*t + 3/5*t**4 = 0.
-1, 0
Let g = 979542/17 - 57108. Let t = g + -512. Factor 0*u - 10/17*u**3 + t*u**5 + 6/17*u**2 + 2/17*u**4 + 0.
2*u**2*(u - 1)**2*(u + 3)/17
Let c = 5 + -13. Let h be 16/(-6)*6/c. Factor 3*q**h - 3 + 5 - 5*q - q**3 - 9*q**4 + 8*q**4 + 2*q**3.
-(q - 1)**3*(q + 2)
Let g(c) be the second derivative of -c**5/16 + 5*c**4/8 + 5*c**3/6 - 15*c**2 - 23*c + 7. Factor g(y).
-5*(y - 6)*(y - 2)*(y + 2)/4
Let x(y) be the first derivative of -3*y**5/35 + 3141*y**4/14 - 1461612*y**3/7 + 510102588*y**2/7 - 7091. Factor x(w).
-3*w*(w - 698)**3/7
Let v = -273 - -162. Let d = 114 + v. Let 16 - r**3 - 4*r**2 + 74*r - 58*r - d*r**3 = 0. What is r?
-2, -1, 2
Let l(u) = -108 + 56 - 2*u - 6*u + 2*u. Let f be l(-19). Determine q so that -f + 70 - 3*q**2 + 22*q - 70*q - 200 = 0.
-8
Let 432*d**2 - 2772*d + 1416 - 734*d + 1988*d - 3430*d - 460*d**2 = 0. What is d?
-177, 2/7
Let z(w) = -4*w + 27. Let y be z(6). Factor -201*f**5 - 10*f**y + 198*f**5 - 5*f**3 + 6*f**2 + 12*f**4.
-3*f**2*(f - 2)*(f - 1)**2
Let o(p) = -7*p**2 - 623*p + 12. Let l(g) = g**2 - 6*g - 1. Let f(i) = -12*l(i) - o(i). Factor f(j).
-5*j*(j - 139)
Let c(q) be the third derivative of -q**5/240 + 7*q**4/64 - 49*q**3/48 - 614*q**2. Factor c(d).
-(d - 7)*(2*d - 7)/8
Let q(x) = -4*x**2 + 378*x - 660. Let c(i) = 7*i**2 - 729*i + 1321. Let f(t) = 6*c(t) + 11*q(t). Factor f(w).
-2*(w - 3)*(w + 111)
Let q(k) be the third derivative of -1/6*k**3 + 0*k**4 + 1/480*k**6 + 1/80*k**5 + 0*k + 0 - 79*k**2. Factor q(b).
(b - 1)*(b + 2)**2/4
Let q(o) be the third derivative of 2/35*o**7 - 13/15*o**6 - 17*o**2 - 32/3*o**3 + 13/15*o**5 + 0*o + 1 + 13/3*o**4. Find p such that q(p) = 0.
-1, 2/3, 1, 8
Let w = 13381 + -25843/2. Let z = w - 458. Factor -3 - 11/2*k - z*k**2.
-(k + 3)*(3*k + 2)/2
Let u(v) = 449*v - 3588. Let i be u(8). Let d(h) be the third derivative of 6*h**2 + 0 + 0*h + 2*h**3 + 2/3*h**i + 1/15*h**5. Factor d(n).
4*(n + 1)*(n + 3)
Suppose -40*a + 41*a - 2 = 0. Suppose -541*w - 5*w**4 - 45*w**3 - 54*w**2 - 96*w**a - 120 + 321*w = 0. Calculate w.
-3, -2
Let s(m) = -2*m**3 - 32*m**2 - 75. Let l be s(-17). Factor -3*g + 77 - 140*g**2 + 5*g**3 + 27 - 296 + l*g - 288.
5*(g - 24)*(g - 2)**2
Suppose 2/13*v**3 + 558/13 - 18/13*v - 62/13*v**2 = 0. What is v?
-3, 3, 31
Let x(a) = 20 - 13*a**2 - 2*a**3 + 6*a**4 + 40*a + 0 + 9*a**2 + 16*a**2 + 26. Let f(q) = -q**4 - 2. Let v(k) = -35*f(k) - 5*x(k). Let v(j) = 0. Calculate j.
-2, 4
Solve 4*a**2 - 24*a**2 - 4544 - 628*a + 14*a**2 + 10*a**2 + 92*a = 0 for a.
-8, 142
Solve 756*y**2 + 351/2*y**3 + 12*y**4 + 3969/4*y + 1/4*y**5 + 0 = 0 for y.
-21, -3, 0
Let c(a) be the third derivative of 2*a**7/105 + 11*a**6/30 + 8*a**5/5 - 6*a**4 + 1076*a**2. Factor c(s).
4*s*(s - 1)*(s + 6)**2
Let z be (-269)/(-6) + 6*3/108. Suppose 4*a - 7 = -5*h, -4*h + 55 - z = a. Factor -2/7*i**2 + 2/7*i - 2/7*i**h + 2/7.
-2*(i - 1)*(i + 1)**2/7
Let t(o) be the first derivative of o**7/84 + o**6/6 + 13*o**5/40 - 5*o**4/2 + 3*o**3 + 58*o - 20. Let z(s) be the first derivative of t(s). Factor z(j).
j*(j - 1)**2*(j + 6)**2/2
Let v(s) be the third derivative of 0*s - 1/120*s**6 + 1/60*s**5 + 1/2*s**3 + 5/24*s**4 + 0 - 70*s**2. Factor v(c).
-(c - 3)*(c + 1)**2
Let r = 138 + -155. Let l be ((-50)/(-425))/((-1)/r). Factor 1/2*k - 1/2*k**l + 0.
-k*(k - 1)/2
Let j(q) be the third derivative of q**5/20 + 131*q**4/8 + 129*q**3 - 68*q**2 - 6*q. Factor j(m).
3*(m + 2)*(m + 129)
Let v be -7*(12/(-210))/((-2)/(-10)). Factor -3*m - 3*m - 3*m**v - 32 + 10 + 31.
-3*(m - 1)*(m + 3)
Let s(o) be the third derivative of -17*o**5/60 - 25*o**4/24 - o**3/6 - 126*o**2. Let b(j) = 8*j**2 + 11*j. Let k(r) = 7*b(r) + 3*s(r). Let k(p) = 0. What is p?
-1, 3/5
Solve 2/3*w**5 - 52/3*w - 22/3*w**3 + 58/3*w**2 - 2/3*w**4 + 16/3 = 0 for w.
-4, 1, 2
Let v(a) = -39*a**2 + 3858*a + 299. Let j be v(99). Factor -j*r**3 + 23/2*r**2 - 9/2 - 15*r.
-(r - 3)**2*(4*r + 1)/2
Let c(s) be the first derivative of 5*s**6/6 + 10*s**5 - 5*s**4 - 680*s**3/3 + 480*s**2 - 3026. Factor c(w).
5*w*(w - 2)**2*(w + 6)*(w + 8)
Let s(a) be the second derivative of -17*a**7/42 - 83*a**6/30 + a**5/2 + 1137*a - 2. Determine p, given that s(p) = 0.
-5, 0, 2/17
Let a(w) be the third derivative of -w**6/60 - 17*w**5/90 - w**4/3 + 32*w**3/9 - 696*w**2 + 2. Factor a(i).
-2*(i - 1)*(i + 4)*(3*i + 8)/3
Let s(w) be the second derivative of -w**5/130 - 2*w**4/39 + 5*w**3/39 - 2*w + 649. Find r, given that s(r) = 0.
-5, 0, 1
Let l(t) be the third derivative of t**6/150 - 6*t**5/25 + 23*t**4/10 + 176*t**3/15 + 314*t**2 - 2. Factor l(i).
4*(i - 11)*(i - 8)*(i + 1)/5
Let y(m) be the first derivative of -2/9*m**3 + 56 + 0*m + 0*m**4 + 1/6*m**2 - 1/18*m**6 + 2/15*m**5. Factor y(z).
-z*(z - 1)**3*(z + 1)/3
Factor -6/23*b + 0 - 2/23*b**3 - 8/23*b**2.
-2*b*(b + 1)*(b + 3)/23
What is m in 4765*m**5 - 3191*m + 1642*m**2 + 134*m**4 - 4763*m**5 + 2302*m**3 - 6049*m - 8712 = 0?
-33, -2, -1, 2
Let y = -99 - -145. Determine p, given that 72 + 3*p**2 + y*p - 24*p + 20*p = 0.
-12, -2
Let k(h) be the third derivative of 0*h - 13/72*h**4 - 1/180*h**5 + 0 + 29*h**2 - 11/9*h**3. Factor k(r).
-(r + 2)*(r + 11)/3
Let l be 44/11 - (3 + -1 + -1). Determine k, given that 