a = 193983/554180 - 1/27709. Let f(m) be the second derivative of 0*m**2 + 1/5*m**3 + a*m**4 + 9*m + 0 + 3/20*m**5. What is k in f(k) = 0?
-1, -2/5, 0
Let r = 6669/2 - 3333. Let s(v) be the first derivative of 3*v + 0*v**3 - 8 - r*v**4 - 3/5*v**5 + 3*v**2. Determine d so that s(d) = 0.
-1, 1
Let c(b) be the second derivative of b**8/3024 - b**7/630 + b**6/360 - b**5/540 - 43*b**2/2 + 3*b - 8. Let d(v) be the first derivative of c(v). Factor d(p).
p**2*(p - 1)**3/9
Suppose -43*j + 40*j + 5*z = -27, -z + 13 = 4*j. Let m = 11 - 8. Factor 0*p + 0 + 0*p**j + 1/5*p**m - 1/5*p**5 + 0*p**2.
-p**3*(p - 1)*(p + 1)/5
Let s = -932089/5 + 186425. Solve s*h - 4/5*h**2 - 56/5 = 0 for h.
2, 7
Let t be (-2 - -7)/((-35)/(-42)). Let q(i) be the second derivative of -3/35*i**5 + 9*i + 0*i**3 + 1/28*i**4 + 0*i**2 + 0 + 2/35*i**t. Factor q(p).
3*p**2*(2*p - 1)**2/7
Let v(p) be the third derivative of -40/9*p**3 - 1/3*p**4 + 1/360*p**6 - 34*p**2 + 1/60*p**5 + 0*p + 0. Factor v(a).
(a - 5)*(a + 4)**2/3
Let h = -247 - -253. Let s(k) = -k**2 + 63*k - 337. Let o be s(h). Let 16/9*t - 46/9*t**2 + 38/9*t**4 + 8/9 - 14/9*t**o - 2/9*t**3 = 0. What is t?
-1, -2/7, 1, 2
Let b(h) be the first derivative of 0*h + 36*h**2 - 4/3*h**3 - 58. Determine k, given that b(k) = 0.
0, 18
Suppose 8*d - 2688 = 336. Let q be (3/10)/(6 - d/70). What is b in 0 - b**3 - q*b + 3/2*b**2 = 0?
0, 1/2, 1
Let s = 478 - 253. Let g = s - 222. Factor -3/2*m**2 + 3/2*m**g - 3*m + 0.
3*m*(m - 2)*(m + 1)/2
Let s(r) be the first derivative of -4*r**6/21 - 166*r**5/35 - 255*r**4/14 + 50*r**3/21 + 419*r**2/7 - 204*r/7 + 4526. What is x in s(x) = 0?
-17, -3, -2, 1/4, 1
Let k be (-3)/21*3 + 28/(-49). Let o be 5 + ((-6)/108)/(k/(-82)). Find h, given that -8/9*h**2 + 0 - o*h - 4/9*h**3 = 0.
-1, 0
Let n(q) be the second derivative of q**4/120 - 43*q**3/20 - 13*q**2/2 - 3*q - 105. Determine w, given that n(w) = 0.
-1, 130
Let o(u) be the second derivative of -u**9/3780 - u**8/336 - 2*u**7/315 + u**4/6 + 29*u**3/6 + 15*u - 4. Let l(v) be the third derivative of o(v). Factor l(t).
-4*t**2*(t + 1)*(t + 4)
What is m in 3360*m**2 - 5084*m**4 + 732*m**3 + 5139*m**4 - 640*m + 138*m**3 = 0?
-8, 0, 2/11
Let t(v) = -6*v - 15. Let q be t(-3). What is n in 4*n**2 - 10*n**4 - n**5 - n**q - 2 + 8*n**4 - n + 3*n**3 = 0?
-2, -1, 1
Let i(y) be the second derivative of y**4/24 + 271*y**3/12 + 135*y**2/2 + 7*y - 168. Determine z, given that i(z) = 0.
-270, -1
Let f(b) be the third derivative of b**5/12 - 1615*b**4/3 + 4305*b**3/2 + 9592*b**2. Factor f(x).
5*(x - 2583)*(x - 1)
Suppose 63*u**2 - 20*u**4 + 48*u**3 + 2363*u**5 + 81*u**2 - 2367*u**5 = 0. Calculate u.
-6, -2, 0, 3
Let c(n) be the second derivative of n**4/6 + 2*n**3/3 + 5*n**2/2 - n. Let k be c(-2). Factor 3*m - 8*m + 15*m**4 - m**3 + 6*m**3 - k*m - 15*m**2 + 5*m**5.
5*m*(m - 1)*(m + 1)**2*(m + 2)
Let n(x) be the third derivative of -x**6/660 - 23*x**5/30 - 3904*x**4/33 + 16384*x**3/11 + 30*x**2 + 7*x. Factor n(q).
-2*(q - 3)*(q + 128)**2/11
Suppose -11502/5 - 12/5*v**2 - 46011/5*v = 0. Calculate v.
-3834, -1/4
Let h(r) be the third derivative of r**5/150 - 1817*r**4/30 + 3301489*r**3/15 + 133*r**2 + 43*r. Factor h(z).
2*(z - 1817)**2/5
Let i be ((-16)/36)/(48/90*(-10)/4). Let r(x) be the second derivative of 0 + i*x**4 - 12*x - 1/6*x**3 + 0*x**2 - 2/15*x**6 + 1/20*x**5. Factor r(u).
-u*(u - 1)*(u + 1)*(4*u - 1)
Suppose -2*z - 43*b + 6 = -45*b, -4*z + 5 = 3*b. Let w(n) be the second derivative of 0*n**z - 10*n + 0*n**3 + 1/36*n**4 + 0. Find h, given that w(h) = 0.
0
Let z(w) = -w - 2. Let v(x) = -x**3 - 9*x**2 + 17*x + 14. Let n be (-2)/7 + 149*(-6)/(-42). Let k(m) = n*z(m) + 3*v(m). Factor k(f).
-3*f*(f - 1)*(f + 10)
Let u be ((-5)/20)/(2/8)*-7. Suppose -x - 5*x - u*x - x**2 - 1 + 11*x = 0. What is x?
-1
Let c = -113097 - -113097. Factor c - 4/3*j**2 + 40/3*j.
-4*j*(j - 10)/3
Let t(m) = -2*m**2 + 88*m + 76. Let g be t(44). Let -65*w**3 - 16*w**5 + 79*w**2 + 36 - g*w**4 - 24*w**4 - 15*w**2 + 117*w - 87*w**3 + 51*w = 0. Calculate w.
-3, -1, -1/4, 1
Let g = -671 + 673. Let 50*x - 60 - 95 + 5*x**g + 6*x + 94*x = 0. Calculate x.
-31, 1
Let t(y) be the second derivative of -y**4/4 + 217*y**3/2 - 324*y**2 - 28*y + 21. Suppose t(s) = 0. Calculate s.
1, 216
Let r(m) be the first derivative of -m**4/4 - 5*m**3/3 + 897*m**2/2 - 891*m - 432. Factor r(g).
-(g - 27)*(g - 1)*(g + 33)
Let j(k) = -2*k**2 - 4*k + 3. Let g(b) = 2*b**2 + 2*b - 2. Let m(q) = -2*q - 48. Let u be m(-27). Let c(d) = u*g(d) + 4*j(d). Find z, given that c(z) = 0.
0, 1
Let j = -14/75 + -1097/150. Let x = 181/22 + j. Suppose 0*d - 2/11*d**2 + x = 0. What is d?
-2, 2
Factor -3/4*k**2 + 1149/4 + 573/2*k.
-3*(k - 383)*(k + 1)/4
Solve 0 - 29/4*v**2 + 5/3*v**3 - 9*v - 1/12*v**4 = 0.
-1, 0, 9, 12
What is s in -8/7*s**2 - 4/7 + 2/7*s**3 + 10/7*s = 0?
1, 2
Let l be (7/14 - (-7)/(-42))*36. Let s be (3 + (-28)/l)/(3/9). Factor -5*w + 0 + 5/2*w**3 + 5/2*w**s.
5*w*(w - 1)*(w + 2)/2
Let y(q) = -9*q**2 - 102*q + 81. Let n(d) = 25*d**2 + 304*d - 244. Let w = 562 - 579. Let t(p) = w*y(p) - 6*n(p). Factor t(k).
3*(k - 29)*(k - 1)
Suppose -2*g = -38 + 8. Let f be (9/(-90))/((-2)/g). Find r such that f*r**2 + 1/4*r**4 + r - 1 - r**3 = 0.
-1, 1, 2
Let l be 5/5 + (-8)/(-4). Suppose -2*t = -4*y + t + 18, -y = 3*t + l. Factor 105*b**3 - 18*b**2 + 102*b**3 - 12 - 27*b - 210*b**y.
-3*(b + 1)**2*(b + 4)
Let d(c) be the second derivative of -35*c + 0 + 1/54*c**3 + 2/9*c**2 - 1/180*c**5 - 1/27*c**4. Factor d(o).
-(o - 1)*(o + 1)*(o + 4)/9
Let z(g) be the first derivative of -4*g**3/15 + 154*g**2/5 - 1168*g/5 + 4225. Factor z(s).
-4*(s - 73)*(s - 4)/5
Let d = -654 - -673. Let d*f**2 + 9*f**3 + 80*f - 15*f**2 - 13*f**3 = 0. Calculate f.
-4, 0, 5
Suppose 3*o + 184 = -j + 5*j, 0 = 5*j - 20. Let q be -6 + 17 + o/7. Factor 9/2*g**2 + 3/2*g**q + 0 - 6*g.
3*g*(g - 1)*(g + 4)/2
Let u(s) = s**2 + 19713*s + 19712. Let d be u(-1). Factor 5*p**2 - 1/4*p**3 + 21/4*p + d.
-p*(p - 21)*(p + 1)/4
Let m(r) = -3*r**4 - 29*r**3 + 142*r**2 + 34*r - 144. Let a(n) = n**4 + 15*n**3 - 71*n**2 - 17*n + 72. Let g(t) = 15*a(t) + 6*m(t). Find l such that g(l) = 0.
-1, 1, 8, 9
Let y(k) be the second derivative of k**5/120 - 181*k**4/36 + 32761*k**3/36 - 5632*k. Suppose y(g) = 0. What is g?
0, 181
Let b(i) = -i**5 + i**4 + 3*i**2 + i - 1. Let j(t) = 5*t**5 + 27*t**4 + 24*t**3 - 3*t**2 - t + 1. Let n(s) = -b(s) - j(s). Factor n(l).
-4*l**3*(l + 1)*(l + 6)
Suppose 3*v - 3*i + 4*i = -4, v = 5*i + 52. Factor -16/5*z**v - 2/5 - 1/5*z**5 - 6/5*z**4 - 9/5*z - 14/5*z**3.
-(z + 1)**4*(z + 2)/5
Let f(y) be the second derivative of 0*y**3 - 168*y + 0 - 2/15*y**6 - 3/10*y**5 - 5/252*y**7 - 2/9*y**4 + 0*y**2. Factor f(n).
-n**2*(n + 2)**2*(5*n + 4)/6
Let m = 61729/10 - 30862/5. Determine d, given that 0*d + m*d**2 + 1/8*d**3 + 0 = 0.
-4, 0
Let w(x) be the third derivative of x**6/360 - 11*x**5/18 + 3025*x**4/72 - 3097*x**2. Factor w(f).
f*(f - 55)**2/3
Factor -38 - 303/2*p + 2*p**2.
(p - 76)*(4*p + 1)/2
Solve 0 - 48*o - 3/2*o**2 = 0.
-32, 0
Let x(d) be the first derivative of -189 + 0*d - 5*d**4 + 28/3*d**3 - 6*d**2 + 4/5*d**5. Let x(q) = 0. Calculate q.
0, 1, 3
Factor -28*n**2 - 7*n**3 + 121*n + 97*n - 7*n + 8*n**3 - 15*n.
n*(n - 14)**2
Let l = -33057 + 231449/7. Find s such that -6/7 + 8*s**2 - l*s = 0.
-3/28, 1
Let b(v) be the first derivative of 14*v**2 + 32 - 40*v - 4/3*v**3. Find c such that b(c) = 0.
2, 5
Factor 1532*s**3 - 88 - 4*s**2 - 76*s**2 + 124*s - 1536*s**3 + 48*s.
-4*(s - 1)**2*(s + 22)
Suppose 4371 - 8484 = 100*n - 4313. Factor -1/6*v**n + 3/2*v - 4/3.
-(v - 8)*(v - 1)/6
Let a(z) = 5*z**5 - 245*z**4 + 4045*z**3 - 18690*z**2 - 50580*z + 147395. Let w(d) = -d**4 + d**3 - 2*d**2 + d - 1. Let r(k) = a(k) + 5*w(k). Factor r(l).
5*(l - 17)**3*(l - 2)*(l + 3)
Let j be (-489)/135 - (-1064)/252. Let 375 + j*f**4 + 780*f + 156/5*f**3 + 2178/5*f**2 = 0. What is f?
-25, -1
Let o(n) be the first derivative of 0*n - 16/9*n**3 - 96 + 11/3*n**4 + 0*n**2 + 1/3*n**6 - 34/15*n**5. Let o(z) = 0. What is z?
0, 2/3, 1, 4
Let j be 19682/(-78) - (-2)/(-3). Let b = 257 + j. Factor 3/4*x**2 + 1/2 + 5/4*x - 1/4*x**b - 1/4*x**3.
-(x - 2)*(x + 1)**3/4
Find l, given that 39*l**2 + 67*l**2 - 218*l**2 + 124*l**3 = 0.
0, 28/31
Let g be (20 + -18)*(-40 - -178)*(-3)/(-63). Solve g*t**2 + 0 - 68/7*t**