(j) = -3*j**2 - 82 + 4*j**2 - 9*j - 61 + 163. Let q be f(5). Factor q + 3/11*b**2 - 4/11*b + 1/11*b**3.
b*(b - 1)*(b + 4)/11
Let q be 403270/125919 + (-18)/(-51). Factor q + 2/9*s**2 + 34/9*s.
2*(s + 1)*(s + 16)/9
Let p = -2524 + 53008/21. Let q(y) be the second derivative of 0 + 35*y + 0*y**2 - p*y**4 + 2/7*y**3. Factor q(m).
-4*m*(4*m - 3)/7
Factor 18 - 74*c - 2*c**5 - 21*c**3 - 40*c**3 - 23*c**3 + 7*c**4 + 116*c**2 + 19*c**4.
-2*(c - 9)*(c - 1)**4
Let d(c) be the second derivative of c**6/30 - 3*c**5/5 + 29*c**4/12 - 3*c**3 + 2615*c. Find k, given that d(k) = 0.
0, 1, 2, 9
Let p(u) = u**3 + 6*u**2 - 8*u + 10. Let n be p(-8). Let l = -48 - n. Solve -20*g**3 + 3*g**2 + g**2 + 8*g**3 + 22*g**3 + l*g**4 = 0.
-1, -2/3, 0
Suppose -699*q = -701*q + 108. Let o be (-45)/q*(-9)/60. Factor 1/4*g - o*g**2 + 0.
-g*(g - 2)/8
Let c(x) = -19*x + 3. Let s be c(3). Let m = -47 - s. Determine d so that -m*d**2 - 10*d - d**2 + 5*d**2 - 5*d - 18 = 0.
-3, -2
Let l = -755/4 + 191. Let d(z) = z**3 - 89*z**2 + 500*z - 164. Let s be d(83). Solve l*j - 3/4*j**3 - 3/2 + 0*j**s = 0 for j.
-2, 1
Let o(t) be the first derivative of -2*t**5/115 - 143*t**4/46 - 10366*t**3/69 - 5041*t**2/23 - 327. Factor o(s).
-2*s*(s + 1)*(s + 71)**2/23
Let d(u) = -12*u**3 + 2*u**2 - 36*u + 16. Let b(v) = -27*v**3 + 5*v**2 - 74*v + 32. Let y(r) = -6*b(r) + 13*d(r). Factor y(p).
2*(p - 2)*(p + 2)*(3*p - 2)
Let h = -5065/2 + 2534. Let s(b) be the second derivative of 20*b**3 + 3*b + 0 - h*b**5 - 1/6*b**6 - 40*b**2 - 5/12*b**4. Factor s(y).
-5*(y - 1)**2*(y + 4)**2
Suppose v + 2 = -w, 374*w - 370*w = -5*v - 12. Let g(p) = -p**3 + 15*p**2 - 13*p - 14. Let a be g(14). What is k in -1/5*k**w + 7/5*k + a = 0?
0, 7
Solve -2/17*h**2 - 668/17 - 670/17*h = 0.
-334, -1
Let r(p) be the second derivative of -p**5/30 + 11*p**4/12 + 4*p**3 - 29*p**2/2 + 2*p - 42. Let u(d) be the first derivative of r(d). Factor u(y).
-2*(y - 12)*(y + 1)
Suppose 343*g - 687*g + 3 = -347*g + 3*t, 0 = -5*t + 5. Factor 0*p + 5/4*p**4 + g*p**2 + 5/4*p**3 + 0.
5*p**3*(p + 1)/4
Factor 261*x**2 + 18*x**3 + 9*x**3 + 7*x**4 - 6*x**3 + 351*x - 4*x**4 + 36*x**3.
3*x*(x + 3)**2*(x + 13)
Let q(a) be the first derivative of 46/5*a**4 + 25 + 0*a + 4/15*a**6 + 62/5*a**3 + 66/25*a**5 + 18/5*a**2. Suppose q(j) = 0. What is j?
-3, -2, -1/4, 0
Let t(b) = -5*b**4 + b**3 + b. Let u(g) = 18*g**4 - 45*g**3 - 267*g**2 - 345*g. Let n(d) = 3*t(d) + u(d). Factor n(i).
3*i*(i - 19)*(i + 2)*(i + 3)
Let g(d) be the second derivative of 1/4*d**5 - 35/6*d**3 - 180*d + 0 - 5/2*d**4 + 0*d**2. Determine c, given that g(c) = 0.
-1, 0, 7
Let c(s) be the first derivative of 0*s**3 - 73 + 0*s**2 - 4/25*s**5 - 3/5*s**4 + 0*s. Let c(t) = 0. What is t?
-3, 0
Let n(p) = 3*p**2 - 87*p - 625. Let a be n(35). Let l(s) be the first derivative of 1/20*s**a + 1/8*s**4 + 0*s**3 + 32 + 0*s**2 + 0*s. Solve l(w) = 0.
-2, 0
Let x(h) = 4*h - 160. Let q be x(44). Suppose 4*l**3 + 2*l**3 - 11*l**3 - q - 35*l**2 + 67*l - 17 + 6*l**3 = 0. What is l?
1, 33
Let z(j) be the second derivative of -1/28*j**4 - 11*j + 0 + 17/7*j**3 - 867/14*j**2. Factor z(y).
-3*(y - 17)**2/7
Let t = 43549/12 - 217709/60. Factor t*s**2 - 3/5 - 3/5*s + 3/5*s**3.
3*(s - 1)*(s + 1)**2/5
Let m(f) = -f**2 + 378*f - 54300. Let b(a) = -8*a - 1. Let c(s) = -22*b(s) + 2*m(s). Factor c(x).
-2*(x - 233)**2
Suppose -3*p + v - 256 = 0, -3*p - 256 = -4*v + 12. Let x be (-14)/p*(1 - -9). Find l such that -x*l**2 + 2 + 13/3*l = 0.
-2/5, 3
Let i be 6555/8740*12/130*8/18. Let r(f) be the first derivative of -i*f**5 + 0*f**2 + 4/39*f**3 + 0*f**4 + 6 - 2/13*f. Factor r(m).
-2*(m - 1)**2*(m + 1)**2/13
Let k = -245 - -372. Let o = k + -74. Factor -15*f**2 - 5 + 5 + 15*f**3 + 5*f - o*f**4 + 48*f**4.
-5*f*(f - 1)**3
Let p(m) be the first derivative of 3*m**4/28 - 10*m**3 + 3051*m**2/14 - 12636*m/7 + 2477. Factor p(y).
3*(y - 52)*(y - 9)**2/7
Suppose -2*g - 3*f = -g - 11, 0 = -g - 4*f + 10. Factor 30*k - 12*k**2 - g*k + 15*k**4 - 6 - 13*k**4.
2*(k - 1)**3*(k + 3)
Let z(m) = -4*m**2 - 3*m + 6. Let k(n) = -3*n**2 - 2*n + 4. Let q(d) = 6*k(d) - 5*z(d). Let f(j) = 2*j**2 + 4*j - 8. Let o(p) = -3*f(p) + 4*q(p). Factor o(i).
2*i**2
Let q be 3 - 62/(-13)*(-6498)/36. Let r = q - -858. Solve 2/13*m - r*m**2 + 12/13 = 0 for m.
-2, 3
Let q(h) be the first derivative of 2*h**4 + 370*h**3/3 - 542*h**2 - 294*h - 553. Factor q(s).
2*(s - 3)*(s + 49)*(4*s + 1)
Let h(p) = 35*p**2 - 2373*p + 2316. Let q(y) = -405*y**2 + 28475*y - 27795. Let u(a) = -25*h(a) - 2*q(a). Determine b, given that u(b) = 0.
1, 462/13
Factor 0 - 44/9*i**3 + 4/9*i**4 - 76/3*i**2 - 20*i.
4*i*(i - 15)*(i + 1)*(i + 3)/9
Suppose -6*a = 9 - 39. Suppose -p - 3*p - 176 = -a*o, -5*o + 5*p + 175 = 0. Factor -o*z**4 + 49*z**3 + 64*z**2 - 8*z**4 + 6*z**5 - 34*z**3 + 49*z**3.
2*z**2*(z - 4)**2*(3*z + 2)
Let t(v) = 297*v - 194. Let i be t(6). Determine m, given that m**2 - 4*m**2 - i*m + 1585*m + 90 = 0.
-6, 5
Determine c so that -374 - 124/3*c - 2/3*c**2 = 0.
-51, -11
Let l(u) = -u**3 - 7*u**2 - 9*u - 15. Let p be l(-6). Factor -4*f**4 - 11*f**5 - 3*f**4 - 22*f**2 + 10*f**5 - 24*f**p - 3*f**4 - 7*f.
-f*(f + 1)**3*(f + 7)
Let q(v) = v**2 - 16*v + 51. Let b be q(12). Factor -3*s**3 + 9*s + s**b + 3*s**2 + s + s**3.
-s*(s - 5)*(s + 2)
Factor 145 - 5/4*i**2 - 575/4*i.
-5*(i - 1)*(i + 116)/4
Factor 111/5*z - 3/5*z**3 + 558/5 - 18*z**2.
-3*(z - 3)*(z + 2)*(z + 31)/5
Let l(p) be the first derivative of -2*p**6/21 - 4*p**5/7 - 10*p**4/7 - 40*p**3/21 - 10*p**2/7 - 4*p/7 + 1164. Factor l(u).
-4*(u + 1)**5/7
Let l be (-1 + (-26)/(-10))*70/4. Let q(h) = 2*h - 1. Let x(b) = -2*b**2 - 30*b - 70. Let u(p) = l*q(p) - 2*x(p). Factor u(c).
4*(c + 1)*(c + 28)
Let q = 368 + -363. Determine p so that 15*p**4 + 3*p**5 - 2426*p**3 + q*p**2 + 2447*p**3 + 4*p**2 = 0.
-3, -1, 0
Let d(q) be the third derivative of -q**5/180 + 191*q**4/36 - 379*q**3/6 - 4172*q**2. Let d(i) = 0. What is i?
3, 379
Let z(c) be the third derivative of -c**6/180 - 37*c**5/90 - 31*c**4/6 + 925*c**2. Let z(t) = 0. What is t?
-31, -6, 0
Let o = 3032 - 9088/3. Let r(h) be the first derivative of -1/9*h**3 + 1/3*h**2 + o*h + 2. Suppose r(u) = 0. Calculate u.
-2, 4
Let a(f) be the third derivative of 8*f**7/245 + 121*f**6/35 + 16657*f**5/140 + 1089*f**4 + 4536*f**3 + 1942*f**2. Let a(d) = 0. What is d?
-28, -9/4
Let i(s) be the second derivative of 14*s - 49/6*s**7 - 42/5*s**5 - 8/21*s**3 - 8/3*s**4 - 196/15*s**6 + 0*s**2 + 0. Solve i(z) = 0.
-2/7, 0
Solve 480 - 97*g - 94*g - 97*g - 4*g**2 + 280*g = 0 for g.
-12, 10
Let i be -9*3/(-9) - (-3 - 4). Let z be (-6)/(-63)*((-45)/i - -9). Let -12/7 + z*x**2 + 0*x = 0. What is x?
-2, 2
Let i(b) = -5*b**2 + 15*b + 1. Let r(d) = d**2 - 3*d. Let p(x) = -11*x + 11. Let q be p(4). Let c(h) = q*r(h) - 6*i(h). Factor c(o).
-3*(o - 2)*(o - 1)
Let q(i) be the first derivative of -i**4/3 - 104*i**3/9 - 272*i**2/3 + 512*i - 5009. What is h in q(h) = 0?
-16, -12, 2
Factor 15*m - 3*m**2 - 136*m + 54*m - 134*m - 24*m.
-3*m*(m + 75)
Let q(w) = -12*w**3 + 151*w**2 - 543*w + 706. Let c(k) = -16*k**3 + 201*k**2 - 725*k + 942. Let b(u) = 7*c(u) - 9*q(u). Find z, given that b(z) = 0.
3, 4, 5
Let o(f) = -5*f**4 + 29*f**3 + 40*f**2 - 76*f + 8. Let b(r) = -9*r**4 + 60*r**3 + 80*r**2 - 152*r + 14. Let j(y) = -4*b(y) + 7*o(y). Let j(u) = 0. Calculate u.
-2, 0, 1, 38
Let g(p) be the second derivative of 5/6*p**3 + 0*p**2 + 3/8*p**4 + 17/80*p**5 + 0 + 7/240*p**6 - 13*p. Let o(z) be the second derivative of g(z). Factor o(q).
3*(q + 2)*(7*q + 3)/2
Let h(w) = 4*w**2 + 540*w + 540. Let n be h(-134). Let s = -87 - -613/7. Factor -8/7*d**3 + s*d**5 + 0*d**2 + 0*d + 0 + 4/7*d**n.
4*d**3*(d - 1)*(d + 2)/7
Let x(t) be the second derivative of -15/2*t**2 - 269*t + 0 - 25/6*t**3 + 5/6*t**4. Factor x(g).
5*(g - 3)*(2*g + 1)
Let x be ((-80)/24 - (-2 + (-33)/(-9)))/(-1). Let z(k) be the first derivative of 2/45*k**x + 2/9*k**2 - 6 + 0*k**4 - 2/9*k**3 + 0*k. Factor z(j).
2*j*(j - 1)**2*(j + 2)/9
Let k(s) be the first derivative of 5*s**4/16 + 75*s**3/4 + 415*s**2/8 - 645*s/4 - 2621. What is h in k(h) = 0?
-43, -3, 1
Factor -3645 - 135*c - 5/4*c**2.
-5*(c + 54)**2/4
Let p be 6/3 + -4 - -4. Find m such that 5*m + 2*m**p - 2 - 57*m**5 + 58*m**5 - 2*m - 4*m**3 = 0.
-2, -1, 1
Suppose -17690 = -646*m + 656*m. Let y = m - -22999/13. Find r 