et j(v) be the third derivative of v**5/4 - 3*v**4 + 8*v**3 + 2230*v**2. Factor j(k).
3*(k - 4)*(5*k - 4)
Let n(m) = -m**2 - 11*m + 32. Let c = 460 - 473. Let g be n(c). Factor -6*q - 12 + 45/4*q**2 + 3/4*q**4 + g*q**3.
3*(q - 1)*(q + 1)*(q + 4)**2/4
Let f(i) = -i**3 - 10*i**2 + 71*i + 700. Let g be f(-8). Factor -48/5 - 2/5*u**3 - 56/5*u - g*u**2.
-2*(u + 2)**2*(u + 6)/5
Let q(y) be the second derivative of -y**10/30240 - 149*y**4/12 - 6*y - 6. Let m(n) be the third derivative of q(n). Suppose m(r) = 0. Calculate r.
0
Factor -99/7*u**2 + 9/7*u**3 + 3/7*u**4 + 159/7*u - 72/7.
3*(u - 3)*(u - 1)**2*(u + 8)/7
Suppose -166*u + 164 = -337*u + 212*u. Determine d so that -9/8*d**3 - 9/4*d**2 + 0 + 3*d + 3/8*d**u = 0.
-2, 0, 1, 4
Suppose -3*b + 5*h = -23, -2*b + 2*h + 51 = 3*b. Let j(a) = a**2 + 5*a - 12. Let q be j(-7). Solve -q*m - 7 + b + 0*m - 1 - m**2 = 0.
-3, 1
Let u(x) be the first derivative of 3*x**4/4 - 16*x**3 - 297*x**2/2 - 378*x + 908. Factor u(c).
3*(c - 21)*(c + 2)*(c + 3)
Let i be -3 + 2 + 5 + 1086/(-4). Let l = -266 - i. Factor 3*o**2 + 3/2*o - l*o**3 - 3.
-3*(o - 2)*(o - 1)*(o + 1)/2
Let n(j) be the second derivative of -j**5/13 - j**4/2 - 12*j**3/13 + 4*j**2/13 + 1340*j. Suppose n(u) = 0. What is u?
-2, 1/10
Let a = -31/1667 + 2407303/8335. Factor 152/5*r - 4/5*r**2 - a.
-4*(r - 19)**2/5
Determine p so that 1184/11*p - 476/11*p**2 + 2/11*p**4 - 630/11 - 80/11*p**3 = 0.
-7, 1, 45
Let f(t) = 8*t**3 - 136*t**2 - 32*t - 700. Let x(s) = -3*s**3 + 45*s**2 - 9*s + 233. Let p(a) = -5*f(a) - 14*x(a). Solve p(w) = 0.
-17, -7, -1
Let o(c) = c**3 + 8*c**2 - 65*c + 27. Let w be o(-13). Let r be (-81)/36*6/w*-3. Factor r + 3/2*q**3 + 3/4*q**2 - 15/4*q.
3*(q - 1)*(q + 2)*(2*q - 1)/4
Let l(p) = -5*p**2 - 3115*p + 3095. Let g(c) = -c**2 - 778*c + 773. Let r(n) = -25*g(n) + 6*l(n). Let r(a) = 0. Calculate a.
1, 151
Determine g so that 502/9*g**2 + 0 - 2*g**3 + 56/9*g = 0.
-1/9, 0, 28
Let o(x) be the third derivative of 0*x**4 + 0*x**5 + 1/7*x**7 + 0 + 0*x**3 - 7/30*x**6 - x + 53*x**2 - 1/168*x**8. Solve o(n) = 0.
0, 1, 14
Let s(j) = -2*j**2 + 225*j + 18875. Let y be s(-56). Factor 6*m + 33/5 + 6/5*m**y - 69/5*m**2.
3*(m - 11)*(m - 1)*(2*m + 1)/5
Let h = 37/92 - 7/46. Let c(t) be the third derivative of 3/2*t**3 + 0 + 27*t**2 + 0*t - 7/8*t**4 + h*t**5 - 1/40*t**6. Solve c(p) = 0.
1, 3
Let t(w) be the second derivative of w**4/24 - 132*w**3 - 1585*w**2/4 - 6279*w. Suppose t(y) = 0. What is y?
-1, 1585
Suppose -3*c + 268 = m, 2*m - 3*c = 7*m - 1340. Let q = m + -268. What is w in -3/2*w**3 + q - 7/2*w**2 - w = 0?
-2, -1/3, 0
Let q(i) be the second derivative of i**4/22 + 160*i**3/11 - 483*i**2/11 - 2565*i. Factor q(t).
6*(t - 1)*(t + 161)/11
Let g(i) be the second derivative of -i**5/50 + i**4 + 25*i**3 - 2500*i**2 + 1201*i + 3. Factor g(u).
-2*(u - 25)**2*(u + 20)/5
Let r(j) be the first derivative of 2/9*j**3 - 38 + 0*j**2 - 50/3*j. Find t, given that r(t) = 0.
-5, 5
Suppose -46 = 10*x + 3*g, 46 = x + 30*g - 32*g. Determine b so that 1/6*b**3 + 0 + 5/6*b - b**x = 0.
0, 1, 5
Let i = 46247 + -230009/5. Let c = i + -245. Factor 2/5 - 3/5*x**2 + 1/5*x**4 - c*x**3 + 1/5*x.
(x - 2)*(x - 1)*(x + 1)**2/5
Factor 1/2*c**2 - 67 + 65/2*c.
(c - 2)*(c + 67)/2
Let y(h) = 4*h**4 - h**2 + 4*h + 1. Let x(v) = -15*v**5 - 145*v**4 + 3375*v**3 - 7685*v**2 - 15320*v - 4130. Let b(i) = x(i) - 10*y(i). Let b(c) = 0. What is c?
-23, -1, -1/3, 6
Let k be (-6)/(-18)*15/20. Let o(x) be the second derivative of 2*x + 1/6*x**6 + k*x**5 - 5/6*x**3 - 5/4*x**4 + 5*x**2 + 0. Let o(y) = 0. What is y?
-2, -1, 1
Let t(v) be the second derivative of -v**5/5 + 352*v**4/3 + 710*v**3 - 3229*v. Factor t(n).
-4*n*(n - 355)*(n + 3)
Let f(z) be the first derivative of -159 - 1/6*z**4 - 20/9*z + 4/3*z**2 + 1/45*z**5 + 1/27*z**3. Suppose f(x) = 0. Calculate x.
-2, 1, 2, 5
Let h = -93 + 96. Factor 0*w**3 - 3*w**4 + 33*w**2 - 6*w**h + 22*w - 9*w + 23*w.
-3*w*(w - 3)*(w + 1)*(w + 4)
Let -24/5 + 48/5*x - 4/15*x**3 + 2/15*x**2 = 0. What is x?
-6, 1/2, 6
Suppose 0 = -2*c - 5*y + 62, 5*y + 25 = 2*c - 37. Let d = c - 6. Find v, given that -33*v**2 + 0*v**2 + 20*v + d*v**3 - 68*v**2 + 35*v**4 + 21*v**2 = 0.
-2, 0, 2/7, 1
Suppose -61*o + 60*o - 4*c + 24 = 0, -4*o + 36 = 4*c. Let g(a) be the first derivative of 17 + 20/3*a**3 - 11/2*a**2 - o*a. Determine s so that g(s) = 0.
-1/4, 4/5
Let b = 273417 + -1367082/5. Let -39/5*k - 66/5 - b*k**2 = 0. Calculate k.
-11, -2
Let x be -2*(-436)/96 - (-22)/88. Let u(c) be the first derivative of -x*c**3 + 4*c - 12*c**2 + 12. Suppose u(i) = 0. What is i?
-1, 1/7
Let t be (-30)/4*(-672)/(-10). Let q be ((-70)/t + (-1)/(-9))*2. Factor 1/2*z**3 - z**2 - q*z + 1.
(z - 2)*(z - 1)*(z + 1)/2
Let t(f) = 4*f**2 + 9*f + 9. Let s be (-2 + (-22)/(-8))*(-3 + 7). Let x(q) = -36*q - s*q - 11*q**2 - 27 + 13*q. Let v(w) = -8*t(w) - 3*x(w). Factor v(n).
(n + 3)**2
Let v be (-2)/(-9) + 12/(-189). Let l = v - -32/63. Solve -l - 4/3*j**2 + 3*j = 0 for j.
1/4, 2
Suppose 2*t + 3 = 7. Let a(i) = -18*i + 583. Let z be a(31). Solve -13*w - 3 + z*w - 147*w**t + 30*w = 0.
1/7
Let m(c) = -c**3 - c**2 + c - 1. Let y = 68 - 70. Let g(x) = -x**3 - x**2 - 2. Let h(i) = y*m(i) + g(i). Factor h(k).
k*(k - 1)*(k + 2)
Let u be (-54)/(-1566) - 82/(-145). Factor 42/5 + 3*o - u*o**2.
-3*(o - 7)*(o + 2)/5
Let m(l) be the third derivative of l**7/630 - l**6/20 + 11*l**5/20 - 101*l**4/36 + 20*l**3/3 + 386*l**2. Let m(q) = 0. What is q?
1, 3, 4, 10
Determine p so that -40804 + 368044/3*p + 4/3*p**3 - 7276/9*p**2 = 0.
1/3, 303
Let b(p) = -3*p - 6. Let c be b(-7). Suppose -2*v + 72 = 4*u - 0*v, -u + c = -v. Factor -3*j**2 + 24*j - 10*j - u*j.
-3*j*(j + 1)
Let y(l) = -1362*l + 91254. Let z be y(67). Factor -7/2*g - 1/2*g**4 + 17/4*g**3 - 19/4*g**2 + z.
-g*(g - 7)*(g - 2)*(2*g + 1)/4
Let v(r) = -2 + 0 + 10*r + 7 - 5*r**2. Let q(o) = 75*o - 2021. Let f be q(27). Let a(k) = k**3 + 5*k**2 - 9*k - 5. Let h(t) = f*v(t) + 5*a(t). Factor h(c).
5*(c - 1)*(c + 1)**2
Let w(b) be the first derivative of -b**6/3 + 34*b**5/5 - 43*b**4/2 - 482*b**3/3 - 280*b**2 - 200*b + 8960. Factor w(t).
-2*(t - 10)**2*(t + 1)**3
Let k(t) be the second derivative of -t**7/420 + t**6/9 + 43*t**5/60 + 11*t**4/6 + 61*t**3/3 + 26*t - 2. Let l(f) be the second derivative of k(f). Factor l(s).
-2*(s - 22)*(s + 1)**2
Let y(b) be the third derivative of 0*b - 4/3*b**4 + 2/15*b**5 + 0*b**3 - 1/15*b**7 + 1/5*b**6 + 1/168*b**8 + 4 - 7*b**2. Solve y(n) = 0 for n.
-1, 0, 2, 4
Let u(m) be the first derivative of -2*m**3/15 - 77*m**2 - 768*m/5 - 1167. Factor u(c).
-2*(c + 1)*(c + 384)/5
Let s(j) be the second derivative of j**4/84 + 37*j**3/14 + 214*j**2/7 + 7115*j. Find u such that s(u) = 0.
-107, -4
Suppose 310 - 302 = -8*s. Let u(h) = h**4 - 2*h**3 - h**2 + 2. Let w(b) = 28*b**3 + 28*b**2 - 16*b - 40. Let l(j) = s*w(j) - 4*u(j). Factor l(f).
-4*(f - 1)*(f + 2)**3
Let n(z) be the second derivative of -2*z + 9 + 2*z**2 + 17/12*z**4 + 1/5*z**5 + 10/3*z**3. Factor n(k).
(k + 2)**2*(4*k + 1)
Let k = -1207/3222 + 641/1074. Factor k*p**2 + 2/3*p + 4/9.
2*(p + 1)*(p + 2)/9
Let b(s) be the first derivative of -s**3/7 + 75*s**2/7 + 171*s - 8698. Factor b(z).
-3*(z - 57)*(z + 7)/7
Let k = 120369 - 962945/8. Find q such that -7/8*q**2 - 1/4*q**3 + 0 + k*q**4 + 1/4*q = 0.
-1, 0, 2/7, 1
Let f(w) be the first derivative of w**6/21 - 204*w**5/35 + 2701*w**4/14 - 3400*w**3/7 + 2500*w**2/7 - 842. Factor f(b).
2*b*(b - 50)**2*(b - 1)**2/7
Let a(c) be the first derivative of -2/21*c**3 - 6/7*c - 4/7*c**2 + 115. Factor a(l).
-2*(l + 1)*(l + 3)/7
What is t in 0*t - 2/5*t**3 + 0 + 128/5*t**2 = 0?
0, 64
Factor -5715*s + 6375*s - 5*s**2 - 782 - 1153.
-5*(s - 129)*(s - 3)
Let o(x) = -x + 8. Let y be o(2). Suppose -a + y = 4. Suppose -16 + n**5 - 2*n**3 - 5*n**4 + a*n - 3*n**4 + 20*n**2 + 6*n - 3*n**5 = 0. Calculate n.
-2, 1
Let p = -16442 - -16445. Let z(r) be the first derivative of -24 + 0*r - 27/16*r**2 + 1/8*r**p. Determine q, given that z(q) = 0.
0, 9
Let h be 580/(-195) - (-4 - -1). Let y(r) be the second derivative of 2/13*r**2 - h*r**3 + 0 - 1/39*r**4 + 1/130*r**5 + 12*r. Factor y(l).
2*(l - 2)*(l - 1)*(l + 1)/13
Let b(p) be the first derivative of p**5/5 + 17*p**4/4 - 70*p**3 + 304*p**2 - 416*p - 4026. Factor b(z).
(z - 4)**2*(z - 1)*(z + 26)
Suppose 3*s + 4 = 3*d + 1, 