0.
-8, -1, 1
Let d(v) be the third derivative of -v**7/735 + v**6/60 + 4*v**5/105 + 376*v**2. Factor d(t).
-2*t**2*(t - 8)*(t + 1)/7
Suppose 0 = -3*y + 560 + 4. Let b be y/(-94)*6/(-4). Suppose -5*u + 0 - 21/5*u**4 + 59/5*u**3 - b*u**2 + 2/5*u**5 = 0. What is u?
-1/2, 0, 1, 5
Let g(s) be the first derivative of 23 + 475/12*s**4 + 1215/2*s + 25/6*s**5 - 2025/4*s**2 + 5/36*s**6 + 75*s**3. Factor g(f).
5*(f - 1)**2*(f + 9)**3/6
Let m(g) = -8*g**3 - 848*g**2 - 24085*g - 83245. Let k(j) = -2*j**3 - 212*j**2 - 6021*j - 20811. Let d(o) = -26*k(o) + 6*m(o). Factor d(b).
4*(b + 4)*(b + 51)**2
Factor 2*l**2 - 27*l - 4485342 + 7*l + 4485230.
2*(l - 14)*(l + 4)
What is t in 229*t + 224*t - 630*t**3 + 5*t**4 + 147 - 1387 + 1235*t**2 + 177*t = 0?
-1, 1, 2, 124
Suppose 28*q = -321 + 97. Let i be 28/q + (-4 - -2 - -7). What is o in -3*o**3 + 3/2*o**5 + 0*o**4 + 0*o**2 + 0 + i*o = 0?
-1, 0, 1
Let p = 20 - 12. Suppose p*u = 5*u. Factor 2*w**2 + 2*w**3 + u - 7 + 0*w**3 - 1 - 8*w.
2*(w - 2)*(w + 1)*(w + 2)
Let b(u) be the first derivative of u**3/3 + 146*u**2 - 293*u + 344. Suppose b(o) = 0. What is o?
-293, 1
Let i(n) be the third derivative of n**5/3 + 395*n**4/24 - 50*n**3/3 + 1542*n**2. Factor i(w).
5*(w + 20)*(4*w - 1)
Factor 188/5*v**3 + 10 + 292/5*v**2 + 198/5*v + 42/5*v**4 - 2/5*v**5.
-2*(v - 25)*(v + 1)**4/5
Let b = 665 - 629. What is y in 138*y**2 - b*y**5 - 2807*y**4 + 152*y - 41*y**3 + 8 + 2661*y**4 - 75*y**3 = 0?
-2, -1, -1/18, 1
Let d(v) be the first derivative of v**3 - 51*v**2/2 + 48*v + 130. Factor d(x).
3*(x - 16)*(x - 1)
Suppose 12*o + 22 = 9*o - 4*t, 3*o - t - 13 = 0. Let a(m) be the first derivative of -3*m - 11 + 2*m**o - 1/3*m**3. Factor a(h).
-(h - 3)*(h - 1)
Let u(c) = -2*c**2 + 14*c - 18. Let t be u(5). Solve 361*z**2 - 20*z**4 + 18*z - 83*z - 41*z**t - 235*z**3 = 0 for z.
-13, 0, 1/4, 1
Let f(d) be the first derivative of -2/9*d**3 + 0*d - 1/12*d**4 + 0*d**2 + 14. Factor f(g).
-g**2*(g + 2)/3
Let k = 33643 - 33643. Let g(r) be the first derivative of 10*r - 10/3*r**3 - 5/6*r**6 - 35 + k*r**5 + 5*r**4 - 15/2*r**2. Let g(p) = 0. Calculate p.
-2, -1, 1
Suppose 15 = 8*f - 17. Let a = 5 + 0. Find n, given that -10*n**2 + 8*n - 4*n + 8 + 2*n**3 - 6*n**3 + f*n**4 + 3*n**3 - n**a = 0.
-1, 2
Let w(b) be the first derivative of b**6/225 + b**5/50 + b**4/45 - 43*b + 234. Let t(l) be the first derivative of w(l). Factor t(n).
2*n**2*(n + 1)*(n + 2)/15
Suppose -143*j + 24705 - 24279 = 70*j. Factor 14/3*t + 2/3*t**j - 16/3.
2*(t - 1)*(t + 8)/3
Let j = 73 - 44. Factor 1632*i**2 - j*i**4 + 5*i**5 - 35*i - 1732*i**2 - 90*i**3 + 9*i**4.
5*i*(i - 7)*(i + 1)**3
Let a(v) be the third derivative of v**5/105 + 5*v**4/2 + 208*v**3/21 + 2*v**2 + 326*v. Factor a(m).
4*(m + 1)*(m + 104)/7
Let n(s) = s**2 - 129*s - 15020. Let u be n(-74). Solve 4/3*y**2 - 2/3*y - u = 0.
-1, 3/2
Let u be ((-2)/4)/(1/(-30)). Let 14*k**2 - 6*k**4 + 27 + 2*k**3 - 20 - 2*k**5 - u + 0*k**2 = 0. What is k?
-2, -1, 1
Let q(n) be the second derivative of -n**5/120 - 23*n**4/72 + 181*n**3/36 + 203*n**2/12 + 25*n + 28. Suppose q(g) = 0. What is g?
-29, -1, 7
Suppose -3*h + t + 6 = 0, -5*h + 4*h + 2 = t. Let g be h/11 + 2440/1100. Let -2/5*b**2 - g*b - 18/5 = 0. Calculate b.
-3
Factor 23/6 + 11/3*d - 1/6*d**2.
-(d - 23)*(d + 1)/6
Factor 18*h**2 + 415*h + 12*h**2 + 384 + 1926 - 34*h**2 + 9*h**2.
5*(h + 6)*(h + 77)
Let t(y) = 8*y**3 + 166*y**2 + 1114*y + 1966. Let j(r) = 10*r**3 + 167*r**2 + 1113*r + 1959. Let k(c) = 2*j(c) - 3*t(c). Find p such that k(p) = 0.
-33, -5, -3
Let z(p) = 27*p**3 + 187*p**2 + 54*p - 2. Let x(a) = -131*a**3 - 936*a**2 - 272*a + 11. Let k(l) = 2*x(l) + 11*z(l). Find s, given that k(s) = 0.
-5, -2/7, 0
Let 1/6*y**5 + 10 + 55/6*y**2 - 56/3*y + 1/2*y**3 - 7/6*y**4 = 0. Calculate y.
-3, 1, 2, 5
Suppose 16 = 3*n - 2*n. Suppose 0 = n*y - 18*y + 6. Factor -9 + 5 + 4*m**4 - 52*m**3 + 60*m**y - 8*m.
4*(m - 1)*(m + 1)**3
Let j(p) be the third derivative of -3*p**7/70 - 98*p**6/75 - 659*p**5/60 - 161*p**4/15 - 22*p**3/5 + 84*p**2 + 10. What is c in j(c) = 0?
-11, -6, -2/9, -1/5
Suppose -3*p + 7 = 1. Let b be p/(-4*(-3)/186). Factor 5*n - 2*n**3 + n + 34 - 4*n**3 - 3*n**4 - b.
-3*(n - 1)*(n + 1)**3
Suppose 347*o - 20 = 357*o. Let k be ((-128)/28)/(-8)*(-7)/o. Factor 0*c + 12/5 - 3/5*c**k.
-3*(c - 2)*(c + 2)/5
Let y(s) be the third derivative of 0 + 17/5*s**6 + 289/1155*s**7 - 229*s**2 + 0*s + 64/33*s**3 + 2042/165*s**5 - 8*s**4. Find b such that y(b) = 0.
-4, 2/17
Find n such that -48*n**4 + 25*n**4 + 1764*n**2 - 249*n**3 + 75*n**3 + 35*n**4 + 2624 - 98*n**3 - 4128*n = 0.
1, 4, 41/3
Suppose -4*x - 4 = 0, 0 = m - 2*x - 6 - 0. Suppose 3*u - 2*d - 12 = 0, -m = -u + 2*d + 4. Factor u*n**3 + 0 + 4/5*n - 14/5*n**2.
2*n*(n - 1)*(5*n - 2)/5
Let z(m) = 1705*m - 95477. Let g be z(56). Find l such that 0*l + 0 + 1/2*l**4 + 1/2*l**5 - 2*l**g - 2*l**2 = 0.
-2, -1, 0, 2
Suppose 0 = -5*q + 35 + 15. Determine v so that 5*v**4 - q*v**3 - 12*v**4 + 5*v**4 - 12*v**2 = 0.
-3, -2, 0
Find w, given that -105563*w**3 - 34*w**2 + 196 + 6*w**2 + 32 - 202*w + 105565*w**3 = 0.
-6, 1, 19
Let q(u) be the third derivative of -4*u**2 - 1/6*u**3 + 1/30*u**5 - 1 + 0*u + 7/48*u**4. What is b in q(b) = 0?
-2, 1/4
Let s = 546308 + -546306. Factor 507 - 26*t + 1/3*t**s.
(t - 39)**2/3
Let f(l) be the first derivative of -45 + 2/45*l**3 + 2/3*l + 2/5*l**2. Suppose f(v) = 0. Calculate v.
-5, -1
Let n(s) be the third derivative of 0*s - 3/160*s**6 + 0*s**3 - 9 + 1/30*s**5 + 1/96*s**4 + 8*s**2. Suppose n(r) = 0. What is r?
-1/9, 0, 1
Find y, given that 2/17*y**3 - 2/17*y + 98/17*y**2 - 98/17 = 0.
-49, -1, 1
Let h be (-136)/20 + (4 - -6). Solve 2/5*q**2 + 2/5*q**3 - h*q - 24/5 = 0 for q.
-2, 3
Let z(r) = 14*r**3 + 1705*r**2 + 1655*r + 9. Let c(j) = 2*j**3 + j**2 - 5*j + 1. Let t(a) = 9*c(a) - z(a). Let t(g) = 0. What is g?
-1, 0, 425
Let 2763184*q + q**4 - 2 - 2763194*q - 6*q**3 + 5 + 12*q**2 = 0. What is q?
1, 3
Let t(w) be the second derivative of -8*w + 1/28*w**7 - 1/10*w**6 + 0*w**5 + 0*w**2 - 1/4*w**3 - 3 + 1/4*w**4. Solve t(k) = 0 for k.
-1, 0, 1
Let w(i) = -2*i**2 + 20*i + 92. Let l(z) = z - 4. Let y(v) = -20*l(v) + 2*w(v). Factor y(g).
-4*(g - 11)*(g + 6)
Suppose 0 = 3*d - 0 - 21. Factor 30*f + 74 + 4*f**2 - 2*f**2 + 6 - d*f**2.
-5*(f - 8)*(f + 2)
Let p(l) = l**3 - 11*l**2 + 10*l + 9. Let j be p(13). Factor -4*v**4 - 4*v + 8*v**3 + 8*v**2 + j*v**5 - 4 - 953*v**5 + 472*v**5.
-4*(v - 1)**2*(v + 1)**3
Let o be ((((-1160)/(-32))/29)/(100/24))/(9/90). Factor -14*s**o - 3*s**2 + 0*s + 0 - 9/4*s**4.
-s**2*(s + 6)*(9*s + 2)/4
Let f(u) = u**3 + 2*u**2 - u - 1. Let q(g) = -16*g**3 + 14*g**2 + 84*g - 208. Let a(d) = -4*f(d) - q(d). Let m(y) be the first derivative of a(y). Factor m(o).
4*(o + 1)*(9*o - 20)
Factor 212*n**4 + 209*n**4 + 123*n**2 + 20*n**2 + 288*n + 85*n**2 + 56*n**3 - 417*n**4.
4*n*(n + 3)**2*(n + 8)
Let k(l) = -l**5 - l**3 - l**2 - l + 1. Let f(p) = -18*p**5 - 39*p**4 + 2187*p**3 - 22527*p**2 + 78705*p - 58353. Let h(m) = -f(m) + 15*k(m). Factor h(s).
3*(s - 8)**3*(s - 1)*(s + 38)
Let c(u) = u**3 + 2*u**2. Let x(j) = -10*j**3 - 43*j**2 - 16*j + 12. Let w be (-15)/(-6)*4 + 0/(-3). Let t(m) = w*c(m) + 2*x(m). What is q in t(q) = 0?
-6, -1, 2/5
Let z(t) be the second derivative of t**6/10 + 3*t**5/20 - 13*t**4/4 - t**3/2 + 18*t**2 + 845*t. Determine b so that z(b) = 0.
-4, -1, 1, 3
Suppose 3*u - 3*t + 0 = -3, -5*u - t = -1. Let w(k) be the third derivative of 0*k**3 + 1/20*k**6 + 34*k**2 + 7/30*k**5 + 1/6*k**4 + u + 0*k. Factor w(y).
2*y*(y + 2)*(3*y + 1)
Let m be 40/24 - (2 - (-695)/(-105)). Let h be ((-6)/7)/(33/(-22)). Factor -4/7*r**4 + 12/7 - m*r + 8*r**2 + h*r**5 - 24/7*r**3.
4*(r - 1)**4*(r + 3)/7
Suppose -5*h + 9*h = -j + 24, -4*j + h = -11. Factor -15*p - p**5 + 23*p + 7*p**4 - j*p**2 - 2*p**4 - 6*p**3.
-p*(p - 2)**3*(p + 1)
Suppose 5*k - 150 = -9*c, -3*k + 26*c = 25*c - 26. Factor 40/3 - 4/3*y**2 - k*y.
-4*(y - 1)*(y + 10)/3
Factor -3*l**2 - 4383 + 0*l**2 - 156*l + 4383 + 5*l**2.
2*l*(l - 78)
Let t(n) = n**2 - 12*n - 248. Let r = -1908 + 1897. Let v be t(r). Factor -9/2*l**4 + 3/2*l**3 + 73/2*l**2 + 18 + 1/2*l**v + 48*l.
(l - 6)**2*(l + 1)**3/2
Suppose -3/2*k + 3/4*k**2 - 90 = 0. What is k?
-10, 12
Let q(h) be the second derivative of -1/70*h**5 + 0*h**2 + 34*h - 2/21*h**3 - 1 - 1/14*h**4. Let q(k) 