-2, -1, 65
Let i = 116/231 + -1/462. Let h(g) be the first derivative of 3/4*g**2 + 1/2*g + i*g**3 + 1/8*g**4 - 2. Factor h(o).
(o + 1)**3/2
Let v(j) be the first derivative of -4*j**3/3 - 226*j**2 - 448*j - 13. Factor v(y).
-4*(y + 1)*(y + 112)
Let z(f) be the second derivative of -f**6/360 + 31*f**5/120 + 4*f**4/3 + f**3/3 + 57*f**2/2 - 30*f + 4. Let o(a) be the second derivative of z(a). Factor o(b).
-(b - 32)*(b + 1)
Let z(t) be the third derivative of 104*t**2 + 0 - 1/945*t**7 - 2744/27*t**3 - 7/3*t**5 - t - 833/27*t**4 - 43/540*t**6. Determine j so that z(j) = 0.
-14, -1
Let c = 157763 + -1104340/7. What is j in 10/7*j + 9/7 + c*j**2 = 0?
-9, -1
Let k(z) be the third derivative of z**8/5040 + z**7/840 + z**6/540 + 49*z**3/3 + 16*z**2 + 3*z. Let m(t) be the first derivative of k(t). Factor m(o).
o**2*(o + 1)*(o + 2)/3
Let m(v) be the third derivative of -7/60*v**5 - v**2 + 1/105*v**7 - 1/672*v**8 + 17/48*v**4 + 0 + 0*v**6 - 115*v - 1/2*v**3. Determine x, given that m(x) = 0.
-2, 1, 3
Let m = 13 + -8. Suppose 4*r = m*n + 3520, n = -2*n. Let 880*s + 3*s**2 - r*s + s**3 = 0. Calculate s.
-3, 0
Let l(v) be the first derivative of 0*v + 4/9*v**3 + 34/3*v**2 - 150. Suppose l(t) = 0. Calculate t.
-17, 0
Let s(p) = -11*p**4 - 13*p**3 - 2*p**2 + 61*p - 9. Let k(r) = -6*r**4 - 6*r**3 - 2*r**2 + 30*r - 8. Let a(n) = -7*k(n) + 4*s(n). Factor a(q).
-2*(q - 2)*(q + 1)**2*(q + 5)
Let v(t) be the first derivative of 3*t**4/28 + 110*t**3/7 - 3*t**2/14 - 330*t/7 - 283. Factor v(o).
3*(o - 1)*(o + 1)*(o + 110)/7
Let f = -8879 - -8886. Let a(z) be the third derivative of 0*z**6 - 1/112*z**8 + 0*z**4 + 0*z**5 - 26*z**2 + 1/35*z**f + 0 + 0*z + 0*z**3. Factor a(k).
-3*k**4*(k - 2)
Let i be ((-507)/195)/(21/(-70)). Let w(a) be the second derivative of 17*a + 16/45*a**6 + 3*a**2 + i*a**3 + 0 + 52/15*a**5 + 193/18*a**4. Factor w(z).
2*(z + 3)**2*(4*z + 1)**2/3
Find q, given that 0*q**2 + 0 + 145/3*q**5 + 0*q**3 + 5*q**4 + 0*q = 0.
-3/29, 0
Let a be 1/(2 - (-10)/(-6)). Suppose -c - a = -2*c. Factor 9*l + 9*l + 65*l**2 - c*l + 20*l**3.
5*l*(l + 3)*(4*l + 1)
Let q = -1922/9 - -27493/45. Let b = q + -395. What is i in 4/5*i**3 + 28/5*i - 4*i**2 - b = 0?
1, 3
Let r = -849133/4 - -4245713/20. Factor 6/5 + 6/5*b**5 - 12/5*b**3 + 6/5*b + 6/5*b**4 - r*b**2.
6*(b - 1)**2*(b + 1)**3/5
Let w be 651/5 - 10/50. Let d = -80 + w. Suppose -18*v**3 - 20*v**4 + 10*v**2 + 3*v**3 + d*v**3 + 0*v**4 = 0. Calculate v.
-1/4, 0, 2
Factor 0 - 1/6*a**3 - 42*a - 37/6*a**2.
-a*(a + 9)*(a + 28)/6
Let h(w) be the first derivative of w**6/40 - w**5/4 + w**4/2 + w**2 + 15*w - 39. Let i(a) be the second derivative of h(a). Factor i(r).
3*r*(r - 4)*(r - 1)
Let i(z) be the second derivative of z**7/28 - 399*z**6/40 + 80193*z**5/80 - 307197*z**4/8 + 218889*z**3/2 - 107811*z**2 - 32*z + 4. What is t in i(t) = 0?
1/2, 1, 66
Let 157*t + 703*t + 535*t**2 + 340 - 5*t**5 + 55*t**3 - t**4 - 210*t**3 - 174*t**4 = 0. What is t?
-34, -1, 2
Let y = -83719/60 + 6977/5. Let a(c) be the third derivative of 0 + 2/5*c**3 + 15*c**2 + y*c**4 + 1/150*c**5 + 0*c. Factor a(z).
2*(z + 2)*(z + 3)/5
Let l be (-5)/((-35)/189) - -1. Suppose 39 = -9*m + 282. Determine r so that 4 + 11*r**3 + m*r**2 + 14*r**2 + 41*r**3 + 19*r**2 + l*r + 16*r**4 = 0.
-1, -1/4
Suppose 1333 - 460*w - 70*w**2 + 1454 - 472*w + 71*w**2 = 0. What is w?
3, 929
Let u(m) be the first derivative of 5*m**3/3 - 310*m**2 + 2974. Factor u(v).
5*v*(v - 124)
Let l(n) be the first derivative of 2/33*n**3 + 8/11*n**2 + 0*n + 87. Solve l(q) = 0 for q.
-8, 0
Let z(p) = -5*p**3 + 1530*p**2 - 3053*p + 1516. Let x(q) = -5*q**3 + 1530*q**2 - 3051*q + 1517. Let o(v) = 4*x(v) - 3*z(v). Factor o(r).
-5*(r - 304)*(r - 1)**2
Let a(d) = -400*d**3 + 7415*d**2 + 7695*d - 14135. Let j(x) = -7*x**3 + 130*x**2 + 135*x - 248. Let l(p) = 2*a(p) - 115*j(p). Factor l(o).
5*(o - 25)*(o - 1)*(o + 2)
Let k = 2372599/3 + -790865. Factor 7/3*o + 1/2 + 19/6*o**2 + k*o**3.
(o + 1)**2*(8*o + 3)/6
Let n = -177 - -176. Let q be 48/(-6) - -9 - n*2. Factor -9/2*u**3 + q*u**2 + 3 + 21/2*u.
-3*(u - 2)*(u + 1)*(3*u + 1)/2
Let -8*l**2 + 97*l**2 - 760*l - l**3 + 169*l**2 + 504 - l**3 = 0. Calculate l.
1, 2, 126
Suppose 0 = -2*t + 7*m - 9*m - 140, -4*t = 5*m + 275. Let h be 2/42*(-69 - t). Factor 10/7*w**2 + 8/7*w**3 + 4/7*w + 0 + h*w**4.
2*w*(w + 1)**2*(w + 2)/7
Let a(b) be the third derivative of -1/21*b**5 - 4*b + 0 + 4*b**2 + 1/84*b**6 - 5/21*b**4 - 8/21*b**3 + 1/245*b**7. Determine k so that a(k) = 0.
-2, -1, -2/3, 2
Suppose -5*c + 41 = 3*a, 0 = 3*c - 5*a + 50 - 27. Let d be 1 - (2759/(-15) - -2). Factor d*x + 196/5*x**2 + 56/15*x**3 + 4802/15 + 2/15*x**c.
2*(x + 7)**4/15
Determine q so that 1119/2 - 188*q**3 + 188*q - 1/2*q**4 - 559*q**2 = 0.
-373, -3, -1, 1
Let r(t) be the third derivative of -t**7/630 - t**6/72 - t**5/45 + 760*t**2. Factor r(d).
-d**2*(d + 1)*(d + 4)/3
Suppose 0 = 3*i + 5*s + 20, -12 = 7*i - 8*i + 3*s. Suppose i = -3*u - 4*z + 9, z = -u + 5*u - 12. Factor 7/3*j - 1/3*j**u + 2 + 0*j**2.
-(j - 3)*(j + 1)*(j + 2)/3
Factor 7992*k**4 + 63*k**4 + 3213*k**3 + 134141*k**5 - 134066*k**5 + 321*k**2.
3*k**2*(k + 107)*(5*k + 1)**2
Let a(h) be the third derivative of h**8/5040 + h**7/315 + h**6/60 - h**5/2 + 92*h**2. Let f(c) be the third derivative of a(c). Find l, given that f(l) = 0.
-3, -1
Let d(v) = -v**3 - 60*v**2 - 62*v - 104. Let m be d(-59). Factor 119*r**2 + r**4 - 2*r**3 + 14*r**4 + 128*r + 2*r**5 + 9*r**4 + m*r**2 + 106*r**3.
2*r*(r + 2)**2*(r + 4)**2
Let y(k) = -11*k**2 - 540*k + 4730. Let m(d) = 35*d**2 + 1620*d - 14220. Let s(q) = -3*m(q) - 10*y(q). Factor s(n).
5*(n - 8)*(n + 116)
Factor 157*d - d**3 - 5*d**2 + 157*d + 2*d**2 + 163*d - 473*d.
-d*(d - 1)*(d + 4)
Let u(v) = 60*v**2 + 245*v + 248. Let i(j) = -j**3 - 2*j**2 - j. Let q(h) = -i(h) - u(h). Factor q(o).
(o - 62)*(o + 2)**2
Suppose -5*i + 150 = 5. Determine b so that -32*b**2 + 90*b**2 + 8 - 27*b**2 - i*b**2 + 10*b = 0.
-4, -1
Let d = 537 - 534. Factor 16*b - b**2 + 32 + 0*b**2 - 3*b + 15*b - d*b**2.
-4*(b - 8)*(b + 1)
Solve 8*l**4 + 180*l**3 + 2*l**4 - 1712*l**2 + 10*l**4 + 3*l**4 - 27*l**4 + 9216 - 7680*l = 0.
-4, 1, 24
Suppose 40*p - 25*p = 210. Let t(b) be the second derivative of 0 + 0*b**2 + 0*b**3 - 1/100*b**5 + p*b - 1/60*b**4. Let t(u) = 0. Calculate u.
-1, 0
Let s(w) = -4*w**3 - 3*w**2 + 8*w + 3. Let k be s(-3). Factor k - 69*v + 0*v**2 + 29*v + 5*v**2.
5*(v - 6)*(v - 2)
Find q, given that -90*q - 627/7 - 3/7*q**2 = 0.
-209, -1
Factor 9/8*g**4 - 9/8*g**2 + 0 - 11/2*g**3 + 11/2*g.
g*(g - 1)*(g + 1)*(9*g - 44)/8
Let g be 153 + -133 + (-16)/(-7) + -22. Factor -4/7*v + 0 - g*v**2.
-2*v*(v + 2)/7
Factor 6*c**2 + 4*c**2 + c**4 - 2*c**4 - 114*c**3 + 52*c**3 + 71*c**3.
-c**2*(c - 10)*(c + 1)
Let h(k) be the first derivative of k**3/4 - 435*k**2/8 + 429*k/2 - 345. Factor h(l).
3*(l - 143)*(l - 2)/4
Let a = 63 + -65. Let s be 2 - (a + 2) - -2. Suppose -n**3 + 22*n**4 - 30*n**s + 6*n**5 + 73 - 77 + 12*n**2 + 2*n - 7*n**3 = 0. What is n?
-1, -2/3, 1
Let f be -16 - ((-6)/4)/(45/960*2). Factor -1/2*n**2 + f - 7*n.
-n*(n + 14)/2
Let w = -180 + 212. Solve 37 + w*j + j**2 + 46 + 3*j**2 - 35 = 0 for j.
-6, -2
Suppose 10*m = 21*m + 55. Let v be -1*1 + (15/m - -7). Factor -8/5*c**v - 4/5*c**2 - 4/5*c**4 + 0*c + 0.
-4*c**2*(c + 1)**2/5
Factor -25 + 4*j**5 + 95 - 348*j**4 - 8*j**2 + 708*j + 286 - 650*j**3 - 62*j**3.
4*(j - 89)*(j - 1)*(j + 1)**3
Let a(r) be the third derivative of r**8/264 + 124*r**7/1155 + 643*r**6/660 + 37*r**5/15 + 40*r**4/33 - 128*r**3/33 + r**2 + 5*r - 2. Let a(f) = 0. Calculate f.
-8, -1, 2/7
Let d(r) be the third derivative of -65*r**2 - 8/9*r**3 + 0 + 1/54*r**4 + 0*r + 1/135*r**5. Solve d(k) = 0.
-4, 3
Let s be 19/10 - (-3 - (-58)/20). Suppose 1 + u**2 - 5*u - 8*u**2 + 4*u**s - 3 = 0. What is u?
-1, -2/3
Determine o, given that 1/3*o**3 - 34/3*o + 31/3*o**2 - 64/3 = 0.
-32, -1, 2
Let p(i) be the second derivative of i**7/21 + i**6/5 - 23*i**5/10 + 11*i**4/2 - 14*i**3/3 + 65*i - 10. Solve p(d) = 0.
-7, 0, 1, 2
Suppose -1348*j - 1385*j + 2612*j + 282 = -81. Factor 0 + 2/7*n**j + 6/7*n**2 + 0*n.
2*n**2*(n + 3)/7
Let g(p) be the second derivative of -9*p**4/4 + 371*p**3/2 - 123*p**2 + p - 178. Factor g(c).
-3*(c - 41)*(9*c - 2)
Let n be (-12)/(-42) - (-380)/(-7). Let d = n + 56. Let 48*k - k**d + 192 + 