3
Let v(y) be the third derivative of y**6/40 + y**5/10 - 41*y**4/8 - 21*y**3 - 7404*y**2. Determine j so that v(j) = 0.
-7, -1, 6
Let b(m) be the first derivative of m**5/15 + m**4/2 + 8*m**3/9 + 3735. Determine a, given that b(a) = 0.
-4, -2, 0
Let r = -3300662/7 - -472586. Let i = r + -1059. Solve -2/7 - c**4 - 23/7*c**3 - 13/7*c - i*c**2 = 0.
-1, -2/7
Let k(b) be the second derivative of 2*b**6/3 - 7*b**5/5 + 2*b**4/3 - 547*b. Factor k(q).
4*q**2*(q - 1)*(5*q - 2)
Let t(f) be the third derivative of 0*f - 2/385*f**7 + 1/44*f**6 + 2/11*f**3 + 25*f**2 + 0 + 0*f**5 - 5/44*f**4. Determine m, given that t(m) = 0.
-1, 1/2, 1, 2
Suppose 4*z = -5*p + 52, 2*p + 2 - 6 = 4*z. Let s be p/(5 - -19)*2. Factor 4/3*g**3 - 2/3*g + 2/3*g**4 + 2/3 - s*g**5 - 4/3*g**2.
-2*(g - 1)**3*(g + 1)**2/3
Let r = -7413 + 22247/3. Let j(t) be the second derivative of 0 - 8*t**2 - r*t**3 - 2*t - 1/3*t**4. Factor j(n).
-4*(n + 2)**2
Let g(z) be the second derivative of z**4/36 - z**3/2 - 11*z**2/3 - 1706*z. Factor g(c).
(c - 11)*(c + 2)/3
Let h(o) be the first derivative of -2*o**5/35 - 144*o**4/7 - 2017. Factor h(v).
-2*v**3*(v + 288)/7
Let w(f) be the second derivative of -f**7/35 + 4*f**6/15 - 18*f**5/25 - f**4/15 + 13*f**3/5 - 18*f**2/5 + 2255*f. Find m, given that w(m) = 0.
-1, 2/3, 1, 3
Let u be (75/(-35) + 2)*(1 + -1 + -2). Let b(z) be the second derivative of 6/7*z**2 + u*z**4 + 0 + 1/10*z**5 - 25*z - 25/21*z**3. Factor b(f).
2*(f - 1)*(f + 3)*(7*f - 2)/7
Let z = 3221/1665 - 214/185. What is u in 1/3*u**3 + 0 + z*u**2 + 2/9*u = 0?
-2, -1/3, 0
Let v be (-14 - 1314/(-78)) + (-2)/(-13). Suppose -2*p + 4*y - 12 = 0, 14 = p - 0*y + 2*y. Factor 12*f**v - 2*f**2 + f + f**p - 13*f**3 + f**2.
f*(f - 1)**2*(f + 1)
Let g(l) be the second derivative of -l**4/54 + 101*l**3/9 + 610*l**2/9 - 9248*l. Solve g(t) = 0 for t.
-2, 305
Let q(a) be the first derivative of 0*a + 43 - 2*a**2 - 7/4*a**4 + 16/3*a**3. Factor q(g).
-g*(g - 2)*(7*g - 2)
Let t = -25 + 223. Suppose t*s = 196*s + 32. Solve 27 + s*k - 54 + 28 + 13 + 2*k**2 = 0 for k.
-7, -1
Let k(r) be the second derivative of r**5/4 + 15*r**4 + 715*r**3/2 + 4235*r**2 - 772*r. Factor k(g).
5*(g + 11)**2*(g + 14)
Let i be 1*10*1 - (86 + -93). Let v(h) = 8*h**2 + 4*h + 14. Let m(u) = -23*u**2 - 13*u - 41. Let p = 2 + 4. Let w(t) = i*v(t) + p*m(t). Factor w(b).
-2*(b + 1)*(b + 4)
Let a(d) be the first derivative of d**3 - 21*d**2 + 144*d + 2222. Factor a(q).
3*(q - 8)*(q - 6)
Let n(d) be the third derivative of -1/672*d**8 - 3/140*d**7 - 1/8*d**6 - 23/60*d**5 - 3/4*d**3 + 0*d - 11/16*d**4 + 0 + 173*d**2. Determine s so that n(s) = 0.
-3, -1
Let t(x) be the third derivative of -x**6/16 - 43*x**5/240 + x**4/3 - x**3/6 + 2741*x**2 + 2. Factor t(a).
-(a + 2)*(5*a - 2)*(6*a - 1)/4
Let v(j) be the second derivative of -4096/13*j**2 - 1/78*j**4 - 4*j - 30 + 128/39*j**3. Determine h, given that v(h) = 0.
64
Let z(y) be the first derivative of -31*y**6/21 + 58*y**5/35 + 32*y**4/7 + 8*y**3/21 - 9890. Find o, given that z(o) = 0.
-1, -2/31, 0, 2
Suppose -437*k + 3514 = 1219*k + 101*k. Factor 2/3*o**4 - 2/3*o + 4/3 + 2/3*o**3 - k*o**2.
2*(o - 1)**2*(o + 1)*(o + 2)/3
Let a(k) = 46*k**2 + 2943*k - 732101. Let p(h) = 13*h**2 + 982*h - 244034. Let t(o) = -6*a(o) + 21*p(o). Factor t(b).
-3*(b - 494)**2
Let m(h) = h**2 - 48*h + 296. Let w be m(41). Let c(q) be the second derivative of 1/3*q**4 + 0*q**2 + 4/3*q**3 + 0 - w*q. Let c(t) = 0. Calculate t.
-2, 0
Let l = 77 - 48. Suppose -2*r + 3*i = -r - 15, 3*r - 5*i = l. Determine c so that 15*c**4 - 35*c**3 - r*c + 2*c**3 + 27*c**2 - 3*c**3 - 3*c = 0.
0, 2/5, 1
Let n be (-7)/(-35) - (-11)/(-165) - (-148)/240. Let p be 15*2/(-8) + (-10 - -14). Find t such that n*t**2 + 1/4 + p*t**3 + 3/4*t = 0.
-1
Let l(w) be the third derivative of 2/15*w**5 + 0 + 0*w**4 - 1/240*w**6 + 147*w**2 + 0*w + 0*w**3. What is m in l(m) = 0?
0, 16
Let b(i) = 35*i**3 + 7867*i**2 - 9759*i + 1791. Let n(z) = -8*z**3 - 1574*z**2 + 1952*z - 358. Let o(m) = 2*b(m) + 11*n(m). Find r, given that o(r) = 0.
-89, 2/9, 1
Suppose 2*m - t = 504, -m + 259 = 20*t - 24*t. Let x = -3253/13 + m. Find z, given that -x*z + 4/13 + 8/13*z**2 - 2/13*z**3 = 0.
1, 2
Let t(m) be the second derivative of m**6/180 + 21*m**5/40 - 43*m**4/24 + 65*m**3/36 + 2004*m. Factor t(l).
l*(l - 1)**2*(l + 65)/6
Find n such that 0*n - 1/3*n**4 - 15*n**3 - 86/3*n**2 + 0 = 0.
-43, -2, 0
Factor -g**3 + 33*g + 13*g**2 + 116*g**2 + 43*g + 170*g + 4*g**3.
3*g*(g + 2)*(g + 41)
Let b = 292 - -118. Factor -b*y**3 + 204*y**3 + 120*y + 207*y**3 + 100 + 21*y**2.
(y + 1)*(y + 10)**2
Let s(l) be the third derivative of -l**6/120 + 163*l**5/20 - 20169*l**4/8 + 59049*l**3/2 + 343*l**2 + l - 3. Factor s(x).
-(x - 243)**2*(x - 3)
Let s(c) = c**3 - 17*c**2 + c - 16. Let k be s(17). Let g be (-2)/k - 9/(54/(-660)). Factor -69*i**2 - 20*i**3 - 15*i**4 + 46*i**2 + 30*i + g*i**2.
-5*i*(i - 2)*(i + 3)*(3*i + 1)
Let l(m) = 109*m**2 + 12865*m - 1351. Let u(r) = 381*r**2 + 45027*r - 4728. Let a(s) = -18*l(s) + 5*u(s). Determine h so that a(h) = 0.
-113, 2/19
Let p(o) = -o**2 + 20*o + 53264. Let j be p(-221). Factor 6/5*u**4 - 42/5*u**2 - 18*u + 18/5*u**j + 108/5.
6*(u - 2)*(u - 1)*(u + 3)**2/5
Let a = 75088/21 - 18720/7. What is z in -208/3*z + a + 4/3*z**2 = 0?
26
Let w(c) be the second derivative of -3/16*c**4 - 27/8*c**2 - 38*c - 7/2*c**3 + 0. Factor w(v).
-3*(v + 9)*(3*v + 1)/4
Suppose 26*b**2 + 4*b**4 - 82*b**2 - 144*b - 232*b**3 + 228*b**3 - 40*b**2 = 0. What is b?
-3, -2, 0, 6
Let d = -62378 - -187304/3. Suppose 15*g**3 + 40/3 + 140/3*g - d*g**2 = 0. What is g?
-2/9, 2
Let g be (-4)/5 + (-568)/40. Let o = -13 - g. Factor -2*b**3 + b**2 + b**2 - b**3 - 8*b**o.
-3*b**2*(b + 2)
Suppose -4*t = 5*b + 2219, 2*t + 195 = 3*b + 1544. Let g = 6707/15 + b. Solve 4/15*l**2 + g*l**3 + 2/15*l + 0 = 0.
-1, 0
Let x = -186 + 187. Let h be (x - 1)/((-1)/(-1)). Factor -t**3 + 1/2 + h*t**2 - 1/2*t**4 + t.
-(t - 1)*(t + 1)**3/2
Let n be -20 + ((-9)/(-6) - -20). What is o in 21*o**2 - n*o**3 + 24 + 93/2*o = 0?
-1, 16
Factor 28*u**4 - 27*u**4 - 31*u**3 + 141*u**3 + 338*u - 113 - 336*u**2.
(u - 1)**3*(u + 113)
Factor 2/23*k**2 + 6/23*k**3 - 4/23*k + 0.
2*k*(k + 1)*(3*k - 2)/23
Let k(h) be the first derivative of 4*h**3/15 + 2924*h**2/5 + 2137444*h/5 - 4783. Factor k(m).
4*(m + 731)**2/5
Let w be 49/(-84)*4*(-12)/14. Let y(k) be the first derivative of w*k**2 - 4*k - 1/3*k**3 - 19. Factor y(a).
-(a - 2)**2
Let s(z) be the first derivative of 0*z + 0*z**2 - 52/15*z**3 + 70 - 1/5*z**4. Determine x, given that s(x) = 0.
-13, 0
Let 40*w**3 + 4412*w + 1545*w + 33*w**3 + 9499*w - 71*w**3 - 56448 - 344*w**2 = 0. Calculate w.
4, 84
Let f(o) = -o**2 - 15*o + 18. Let g(k) = k**3 + 26*k**2 - 54*k + 40. Let l be g(-28). Let v be f(l). What is n in -1/2*n**v + 1/2*n + 1 = 0?
-1, 2
Let t(w) = -60*w**3 + 234*w**2 + 1496*w + 2921. Let g(a) = -7*a**3 + 29*a**2 + 187*a + 365. Let n(j) = -17*g(j) + 2*t(j). Factor n(k).
-(k + 3)*(k + 11)**2
Let q(f) be the third derivative of 8*f**7/105 + 23*f**6/6 - 91*f**5/5 + 185*f**4/6 - 62*f**3/3 - 1626*f**2. Find j, given that q(j) = 0.
-31, 1/4, 1
Let 3*n**2 - 314*n - 352541 + 1176269 - 2830*n = 0. Calculate n.
524
Let n(b) be the third derivative of 0*b + 11/42*b**4 + b**3 + 1/210*b**5 + 0 + 2*b**2. Factor n(m).
2*(m + 1)*(m + 21)/7
Let q(h) = -3*h**3 + 15*h**2 - 2*h - 8. Suppose -27 = 19*b - 28*b. Let u(t) = 3*t**3 - 16*t**2 + 2*t + 8. Let j(z) = b*q(z) + 2*u(z). Factor j(n).
-(n - 4)*(n - 1)*(3*n + 2)
Let w = -16403 - -16403. Let s(m) be the second derivative of -4/3*m**4 - 27*m - 1/5*m**5 + w - 4*m**2 - 10/3*m**3. Factor s(j).
-4*(j + 1)**2*(j + 2)
Let q = 941 + -3414. Let z = 2475 + q. Factor 0*s + 3/2*s**3 + 0*s**z + 0 + 9/4*s**4 + 3/4*s**5.
3*s**3*(s + 1)*(s + 2)/4
Solve -1320*s**4 - 16817*s**3 - 19215*s**2 - 29288*s - 36*s**5 + 21938*s + 3668*s**3 = 0 for s.
-35/2, -1, -2/3, 0
Let t(j) be the third derivative of j**7/70 + 47*j**6/10 + 1767*j**5/4 - 47*j**4/2 - 4418*j**3 + 236*j**2. Let t(y) = 0. Calculate y.
-94, -1, 1
Let k = -112 - -111. Let n(f) = -4*f**2 + 28*f - 23. Let y(s) = -1. Let q(h) = k*n(h) - y(h). Factor q(p).
4*(p - 6)*(p - 1)
Solve 1380/7*c - 4/7*c**4 - 2740/7*c**2 + 392 - 1380/7*c**3 = 0 for c.
-343, -2, -1, 1
Let k be 1*-5 - (8 - (5 + 2)). Let r be k/(-9)*(78/(-16)