et m(t) be the second derivative of -8/33*t**3 + 2*t + 0 - 4/11*t**2 + 5/66*t**4. Factor m(d).
2*(d - 2)*(5*d + 2)/11
Factor 191 - 253*m**3 + 258*m**3 - 787*m**2 - 271 + 1094*m - 232.
(m - 156)*(m - 1)*(5*m - 2)
Determine f so that -202/3*f**3 - 1525/3*f - 875/3 - 23/3*f**4 - 1/3*f**5 - 830/3*f**2 = 0.
-7, -5, -1
Let r(y) = 3*y**3 - 31*y**2 - 251*y - 257. Let k(t) = 3*t**3 - 33*t**2 - 246*t - 258. Let o(q) = 5*k(q) - 6*r(q). Solve o(d) = 0.
-6, -1, 14
Suppose 0*n - 3*n = 4*m + 2488, -2503 = 3*n + m. Let v = n + 5872/7. Factor -24/7 - v*q - 4/7*q**2.
-4*(q + 2)*(q + 3)/7
Let l = 165 - 163. Determine t so that 11*t**4 - t**2 - 14*t**l - 3*t**5 - 2*t**4 + 3*t**2 = 0.
-1, 0, 2
Let k = 334 - 330. Factor 6*u**4 + 384*u - 16*u**3 - 376*u - 4*u**2 + 6*u**k.
4*u*(u - 1)**2*(3*u + 2)
Let w = -2/4915111 + 4915115/9830222. What is x in -66*x - w*x**2 - 2178 = 0?
-66
Suppose -11*r + 26*r - 40 = 5. Let g(f) be the first derivative of f**3 - 4*f + 1/5*f**5 + 5/2*f**2 + r - 5/4*f**4. Determine h so that g(h) = 0.
-1, 1, 4
Let f be 9434/(-801) - 6*-2. Let s(t) be the first derivative of 9 + 4/3*t - f*t**3 + 1/3*t**2. Factor s(w).
-2*(w - 2)*(w + 1)/3
Let z = -28955 + 28958. Factor 0*k**2 - 6/7*k + 2/7*k**z - 4/7.
2*(k - 2)*(k + 1)**2/7
Suppose 67*t = 64*t + 90. Solve 16820*h**3 - 10*h**2 + t - 16815*h**3 - 3*h - 22*h = 0 for h.
-2, 1, 3
Suppose 399 + 1771 = 7*q. Let t be 6/(-54) - q/(-1170). Factor -2/13*l**3 + 2/13*l + 2/13*l**4 - t*l**2 + 0.
2*l*(l - 1)**2*(l + 1)/13
Suppose -4*u + 154 = 34. Factor 15*v**2 - u*v**2 - 120 - 115*v + 9*v**2 + 11*v**2.
5*(v - 24)*(v + 1)
Let m(b) be the second derivative of -4225*b**2 + 0 - 271*b + 130/3*b**3 - 1/6*b**4. Solve m(r) = 0.
65
Let c(a) be the second derivative of a**6/120 + 29*a**5/20 + 2989*a**4/48 - 3721*a**3/4 - 1405*a. Factor c(q).
q*(q - 6)*(q + 61)**2/4
Let o(l) be the second derivative of -l**4/12 + 79*l**3/6 - 39*l**2 + 45*l - 50. Solve o(k) = 0 for k.
1, 78
Let l be (-157884)/1180 + 133 - 6/10*(-8)/6. Factor l + 20/3*n**2 + 0*n + 4/3*n**3.
4*n**2*(n + 5)/3
Suppose -21*k = 47 + 16. Let u be (k - -124 - -2) + -1*3. Factor -40*f**3 - u*f + 60 - 31*f**4 + 52*f + 115*f**2 - 72*f + 36*f**4.
5*(f - 3)*(f - 2)**2*(f - 1)
Suppose 2*i + 12*u + 4142 = 4400, -i - u + 24 = 0. Factor 12005/6 - 4165/2*c + 165/2*c**2 - 5/6*c**i.
-5*(c - 49)**2*(c - 1)/6
Factor -254 - 78*p + 2*p**2 + 128*p + 46*p + 54.
2*(p - 2)*(p + 50)
Let a(l) = 2018*l**2 - 23*l + 118. Let m be a(6). Determine d, given that -6*d - 4 - 2*d + m*d**2 - 72632*d**2 = 0.
-1
Let r(s) = -13*s**2 + 8*s + 5. Let t(u) = 22 - 6*u**2 - 27 + 7 + 4*u. Let q be (-33)/(-6) - (-2)/(-4). Let k(b) = q*t(b) - 2*r(b). Find z such that k(z) = 0.
0, 1
Let q(c) = -2*c. Let l(d) = d**2 + 38*d - 21. Let y(b) = -b**3 + 33*b**2 + 68*b + 52. Let i be y(35). Let f(o) = i*q(o) - 2*l(o). Suppose f(k) = 0. Calculate k.
-21, 1
Let p(i) be the second derivative of -i**7/21 - 2*i**6/15 + 171*i**5/5 + 172*i**4/3 - 341*i**3/3 - 342*i**2 - 2423*i. Solve p(q) = 0 for q.
-19, -1, 1, 18
Suppose n + 2*s = 46, 3*n - 16726*s = -16730*s + 94. Suppose -15/4*z - 1/4*z**n + 0 = 0. What is z?
-15, 0
Suppose -33*p + 31*p + 30 = 0. Factor p*v**2 - 152*v**4 + 5*v**3 + 137*v**4 - v**5 - 10*v + 6*v**5.
5*v*(v - 2)*(v - 1)**2*(v + 1)
Let d(i) be the first derivative of 1/2*i**4 - 14/3*i**3 - 65 + 24*i + 4*i**2. Factor d(a).
2*(a - 6)*(a - 2)*(a + 1)
Let i be 1/(4/(-10)*(-21)/(-42)). Let u be (-1161)/301 + i/(-1). Factor -u*n - 2/7*n**2 - 8/7.
-2*(n + 2)**2/7
Let f = -2919900/7 - -417129. Factor 57*y + 60/7*y**2 + f*y**3 + 126.
3*(y + 6)*(y + 7)**2/7
Suppose -1039 = -6*j + 5717. Let v = -1123 + j. Factor 14/3*a**2 + 2*a**4 - 16/3*a**v + 0 - 4/3*a.
2*a*(a - 1)**2*(3*a - 2)/3
Suppose -5*u + 9 = -2*u, 3*z + 3*u = 21. Let 2/21*y**3 + 0 + 0*y - 2/21*y**5 + 2/7*y**2 - 2/7*y**z = 0. What is y?
-3, -1, 0, 1
Let y = 37876 - 37873. Factor -4 - y*s - 1/2*s**2.
-(s + 2)*(s + 4)/2
Determine v, given that -2/5*v**3 + 20*v + 98/5*v**2 + 0 = 0.
-1, 0, 50
Determine n, given that -70*n**2 + 588*n + 18*n**2 + 23*n**2 + 590 + 14*n**2 + 13*n**2 = 0.
-1, 295
Let h(p) = -p**3 - 12*p**2 + 188*p - 702. Let r be h(-22). Let -4/5*o**3 - 12/5*o**r + 8*o + 0 = 0. What is o?
-5, 0, 2
Suppose -5812921/9*c**2 - 1/9 + 4822/9*c = 0. Calculate c.
1/2411
Factor 0*l**4 - 6*l**4 + 915*l**2 - 16*l - 895*l**2 + 2*l**3.
-2*l*(l - 1)*(l + 2)*(3*l - 4)
Let f(u) be the second derivative of 12 + 135/2*u**2 - 5*u**4 + 2*u + 1/2*u**5 - 15*u**3 + 1/6*u**6. Suppose f(n) = 0. What is n?
-3, 1, 3
Solve 118/3 + 358/9*u + 4/9*u**2 = 0.
-177/2, -1
Let t = -45210 - -587744/13. Determine h, given that -4/13*h**2 - 6/13 + t*h = 0.
1/2, 3
Solve 69/4*r**2 + 11/4*r**4 - 9*r - 1/4*r**5 - 43/4*r**3 + 0 = 0 for r.
0, 1, 3, 4
Suppose -8*p + l + 5 = -3*p, 15 = -5*p - 3*l. Suppose p = -4*s + v + 1698, -4*v - 428 = -s - 2*v. Let -12 - 3*m**4 + 424*m**3 + 15*m**2 - s*m**3 = 0. What is m?
-2, -1, 1, 2
Let s(q) = -3*q**3 + 76*q**2 + 9*q - 846. Let h be s(25). Factor 7/4*v**3 + 2 + 5*v + 9/2*v**2 + 1/4*v**h.
(v + 1)*(v + 2)**3/4
Let q(n) be the third derivative of 0 - 19/48*n**4 + 13/120*n**5 + 1/2*n**3 - 302*n**2 + 0*n. Factor q(l).
(l - 1)*(13*l - 6)/2
Let n(w) be the third derivative of -w**5/480 + 29*w**4/12 + 233*w**3/12 - 43*w**2 - 2*w - 8. Determine v so that n(v) = 0.
-2, 466
Suppose -7189*x = -7166*x - 46. Let h(g) be the first derivative of 169/2*g**4 - 204*g**x - 45 - 416*g**3 - 32*g. Factor h(b).
2*(b - 4)*(13*b + 2)**2
Let p = -30 + 42. Let u be ((-18)/(-10))/(p/40). Factor 2*v + 1 + 0 - 11*v**2 + u*v**2 + 6*v**2.
(v + 1)**2
Suppose 2*h = 4*g + 24, -2*h - 3*g + 4*g = -9. Let -18*p**4 - p**h + 17*p**3 - 22*p**2 + 11*p**2 + 3*p**5 + 10*p**3 = 0. Calculate p.
0, 1, 4
Let g(u) = -4*u**2 + 12*u - 2. Let i(p) = 5*p**2 - 14*p + 2. Let c = -537 - -543. Let v(y) = c*i(y) + 7*g(y). What is s in v(s) = 0?
-1, 1
Let i = -127740 + 383224/3. Suppose -5/3*z**2 + i*z + 0 + 1/3*z**3 = 0. Calculate z.
0, 1, 4
Let a(h) be the second derivative of -h**8/26880 + h**7/5040 + h**6/960 + 7*h**4/4 - 67*h + 2. Let x(w) be the third derivative of a(w). Factor x(n).
-n*(n - 3)*(n + 1)/4
Let d(u) be the first derivative of 5*u**3/3 + 475*u**2 + 8992. Factor d(r).
5*r*(r + 190)
Let h(z) be the third derivative of -z**5/75 + 206*z**4/15 - 818*z**3/5 + 9*z**2 - 44*z. Factor h(k).
-4*(k - 409)*(k - 3)/5
Let s(w) be the second derivative of w**7/35 - 61*w**6/225 - 73*w**5/30 - 37*w**4/6 - 304*w**3/45 - 44*w**2/15 + 47*w + 5. Find p, given that s(p) = 0.
-2, -1, -2/9, 11
Factor 0 - 57*a**2 + 3/5*a**3 + 0*a.
3*a**2*(a - 95)/5
Let n(h) be the third derivative of h**6/480 + 107*h**5/80 + 8533*h**4/32 - 25921*h**3/24 - h**2 + 405*h - 2. Find b, given that n(b) = 0.
-161, 1
Let z(b) = -b**2 - 1058*b - 6307. Let l be z(-6). Let -52/7*i**4 + 9/7*i**2 + 24/7*i**l - 66/7*i**3 + 6/7 + 25/7*i = 0. What is i?
-1/2, 2/3, 3
Let d = -16762 + 16765. Let g(x) be the first derivative of 0*x + 2/3*x**d + 2 + x**2. Factor g(v).
2*v*(v + 1)
Suppose 30 - 20 = 2*b. Suppose h = b*h - 12. Let 10*z**2 + 13*z + 10*z**3 + 7*z - 15*z**h - 40 = 0. What is z?
-2, 2
Let g(m) be the first derivative of -m**6/27 - 4*m**5/9 - 4*m**4/3 + 20*m**3/27 + 25*m**2/9 - 3175. Determine v, given that g(v) = 0.
-5, -1, 0, 1
Let c(z) = -z**4 - z**3 - z + 4. Let l(a) = -4*a**4 + 38*a**3 - 198*a**2 - 42*a + 208. Let n(p) = -4*c(p) + 2*l(p). Factor n(w).
-4*(w - 10)**2*(w - 1)*(w + 1)
Let q(d) = 3*d**2 - 16*d + 5. Let m be q(7). Suppose -m = y - 5*y. Solve i - 7*i**3 + 8 + 13*i + 3*i**3 + 4*i**4 - y*i - 12*i**2 = 0 for i.
-1, 1, 2
Suppose 3*h - 37 = y, 2*y = 6*y - 20. Suppose 28 - 26*i + 0*i**3 - h*i + 9*i + i**3 - 24*i + 26*i**2 = 0. What is i?
-28, 1
Let d(i) = 12*i**4 - 2*i**3 - i**2 + 7*i - 1. Let n(a) = 7*a**4 - a**3 + 4*a - 1. Let x(r) = -3*d(r) + 5*n(r). Factor x(o).
-(o - 2)*(o - 1)*(o + 1)**2
Let b(k) = -k**3 - 206 - 51*k + 58 + 61 - 27*k**2 + 64. Let i be b(-25). Let 343/6 + 7/2*h**i - 1/6*h**3 - 49/2*h = 0. What is h?
7
Let u(p) be the third derivative of -p**6/480 - 37*p**5/30 + p**4/24 + 148*p**3/3 - 3218*p**2. Find y, given that u(y) = 0.
-296, -2, 2
Let y be ((-2184)/(-140) - 16)/((-6)/115) - (-4 + 5). Factor 8 - y*f - 4/3*f**2.
-4*(f - 1)*(f + 6)/3
Let b(y) be the first derivative of y**5/5 - 22*y**3/3 + 12*y**2 + 45*y - 543. Fact