k.
-1, 1/3
Let i(k) be the second derivative of -k**4/42 + 19*k**3/3 + 8015*k. Solve i(w) = 0.
0, 133
Let f(h) be the third derivative of 2/39*h**3 + 52*h**2 - 7/780*h**6 + 8/195*h**5 - 11/156*h**4 + 0 - h. Factor f(r).
-2*(r - 1)**2*(7*r - 2)/13
Let h(m) be the third derivative of 9*m + 7/144*m**4 + 1/360*m**5 + 3*m**2 + 0 + 1/3*m**3. Factor h(o).
(o + 3)*(o + 4)/6
Let d(a) be the first derivative of a**4/4 + 18*a**3 + 52*a**2 + 663. Factor d(n).
n*(n + 2)*(n + 52)
Let i be (915/(-2))/((-88)/(-176)). Let t = i + 917. Solve 0*g - 4/5*g**3 + 0 - 2/5*g**4 - 2/5*g**t = 0 for g.
-1, 0
Let h(m) be the first derivative of 2*m**3/9 - 139*m**2/3 + 92*m + 86. Find q, given that h(q) = 0.
1, 138
Let l = -13464 + 13464. Let z(x) be the third derivative of -x**2 + 1/80*x**5 + 1/480*x**6 + l + 0*x - 1/6*x**3 + 0*x**4. Determine r, given that z(r) = 0.
-2, 1
Let p = -1214 + 1214. Let m be (-14)/(7/(21/(-27))). Factor p + 4/9*x - m*x**3 - 10/9*x**2.
-2*x*(x + 1)*(7*x - 2)/9
Let n = -2413 + 2418. Let q(w) be the second derivative of 1/5*w**2 + 1/5*w**4 + 0 + 4/15*w**3 + 2/25*w**n + 1/75*w**6 + 12*w. Solve q(v) = 0 for v.
-1
Let s be (85/50)/((-2)/(-12)). Let w be 1306/80 + (324/36 - (-292)/(-32)). Suppose s*o - 6/5 + 81/5*o**4 + w*o**3 - 27*o**2 = 0. Calculate o.
-2, 1/3
Let v be (-25 + -5)/(9*9/54). Let y be 20*((-21)/108 + (-5)/v). Factor -y*w + 2/9*w**2 - 4/3.
2*(w - 6)*(w + 1)/9
Let g(c) be the first derivative of -9 - 1/20*c**5 + 0*c + 0*c**2 + 3/8*c**4 + 0*c**3. Factor g(s).
-s**3*(s - 6)/4
Suppose -8*l = -12*l - q - 2088, 0 = 3*q. Let y = l + 522. Let -12/5 + y*h + 3/5*h**3 + 9/5*h**2 = 0. Calculate h.
-2, 1
Let c be 7/2 - (29/50 + 568/(-7100)). Factor -24 - 28/9*n**c + 38/3*n**2 - 8*n + 2/9*n**4.
2*(n - 6)**2*(n - 3)*(n + 1)/9
Let m(w) = -46*w**2 - 311*w - 29. Let d(p) = -28*p**2 - 207*p - 19. Let v(b) = -7*d(b) + 5*m(b). Find f, given that v(f) = 0.
-3, -2/17
Let q(l) = -2*l**3 - 30*l**2 + 33*l - 7. Let m(x) = 17*x - 3 - 63*x**3 + 100*x**3 - 38*x**3 - 14*x**2. Let o(t) = 7*m(t) - 3*q(t). Factor o(j).
-j*(j - 2)*(j + 10)
Let j = -193103/38 + 5081. Let l = 41/19 + j. Factor l - 7/4*m + 1/4*m**2.
(m - 6)*(m - 1)/4
Let g(w) = 3*w**4 + 294*w**3 + 290*w**2 - 294*w - 277. Let k(f) = 8*f**4 + 589*f**3 + 578*f**2 - 589*f - 546. Let v(b) = -5*g(b) + 2*k(b). Factor v(p).
(p - 293)*(p - 1)*(p + 1)**2
Suppose -2*w + 140 = 108. Let q be (-2)/w - (-187)/88. Solve -a**2 + 31*a + 3*a**3 - 50 + a**4 + 14*a**q - 12*a**3 + 14*a = 0 for a.
-2, 1, 5
Let c = 61 + -61. Let x be (c*(-1)/(-4))/(-2). Suppose 46*g**2 - 38*g**2 - 4 - 14*g + x = 0. What is g?
-1/4, 2
Let r(l) be the first derivative of -l**6/9 + 14*l**5/5 - 151*l**4/6 + 290*l**3/3 - 496*l**2/3 + 128*l - 10695. Suppose r(n) = 0. Calculate n.
1, 3, 8
Suppose 76/13 + 4/13*t**4 - 70/13*t**3 + 110/13*t - 120/13*t**2 = 0. What is t?
-2, -1/2, 1, 19
Let d(l) be the second derivative of -l**7/28 + 31*l**6/20 - 87*l**5/20 - 854*l + 6. Solve d(z) = 0 for z.
0, 2, 29
Suppose 18*o - 14*o = 8. Suppose o*g**2 - 2*g**3 - 2278 + 2278 = 0. Calculate g.
0, 1
Let k(q) = -3*q**2 - 18382*q - 10524877. Let n(v) = 2*v**2 + 9188*v + 5262438. Let o(c) = -2*k(c) - 5*n(c). Factor o(t).
-4*(t + 1147)**2
Let x(c) be the second derivative of c**6/180 - 7*c**4/36 + 2*c**3/3 - 6*c**2 + 15*c + 2. Let q(n) be the first derivative of x(n). Factor q(p).
2*(p - 2)*(p - 1)*(p + 3)/3
Let f(r) = 190*r**3 - 120*r**2 - 135*r - 955. Let u(i) = 3*i**3 - i**2 + i - 11. Let l(d) = -f(d) + 65*u(d). Factor l(h).
5*(h + 3)*(h + 4)**2
Let y(r) = -9*r**2 + 229*r - 2496. Let b(j) = 100*j**2 - 2520*j + 27455. Let l(p) = 4*b(p) + 45*y(p). What is h in l(h) = 0?
20, 25
Factor 2/5*m**3 + 12 - 12/5*m**2 - 2/5*m.
2*(m - 5)*(m - 3)*(m + 2)/5
Let a be 342/12 + (14007/(-58))/69. Factor -a - 5*l - 1/4*l**2.
-(l + 10)**2/4
Let t = 13669 + -13667. Factor 1/2*g**t - 4*g + 6.
(g - 6)*(g - 2)/2
Suppose y = 3*i - 5, -y - i = y - 25. Suppose 0 = y*g - 6*g - 20. Find r such that 2*r**5 - 42*r - r**g - 2*r**5 + 5*r**3 + 38*r = 0.
-2, -1, 0, 1, 2
Suppose -16*d + 134 = 4614. Let k be 336/d - (-77)/10. Find s such that 0 - 2*s**5 - 12*s**3 + k*s**2 - s + 17/2*s**4 = 0.
0, 1/4, 1, 2
Let g(x) be the second derivative of 5*x**4/6 - 2*x**3 - 1670*x. Suppose g(y) = 0. What is y?
0, 6/5
Let f(a) be the first derivative of -8/3*a**3 + 0*a + 50 + 1/24*a**6 - 1/2*a**5 + 2*a**4 + 0*a**2. Suppose f(l) = 0. Calculate l.
0, 2, 4
Let p(c) be the second derivative of c**5/150 + c**4/5 + 56*c**3/45 + 918*c. Factor p(x).
2*x*(x + 4)*(x + 14)/15
Suppose 899 = -2*v + 3*l - 2377, v + 1639 = 2*l. Let u = 1638 + v. Factor 1/5*w + 1/5*w**4 + 0 - 1/5*w**u - 1/5*w**2.
w*(w - 1)**2*(w + 1)/5
Let f be (435/90 - 3) + (-27)/(-162). Factor -2/5*g**2 + f*g - 8/5.
-2*(g - 4)*(g - 1)/5
Let g(q) be the first derivative of -q**3/9 - 83*q**2/6 + 86*q + 122. Factor g(z).
-(z - 3)*(z + 86)/3
Let a(i) = -7*i**3 + 471*i**2 - 26875*i - 27373. Let y(c) = 48*c**3 - 3296*c**2 + 188132*c + 191612. Let v(z) = 68*a(z) + 10*y(z). Solve v(r) = 0 for r.
-1, 117
Let m(a) = a**4 - 300*a**3 - 21910*a**2 - 2. Let w(x) = 4*x**4 - 902*x**3 - 65733*x**2 - 7. Let s(y) = -7*m(y) + 2*w(y). Let s(g) = 0. What is g?
-148, 0
Let o(n) be the second derivative of -n**4 + 0*n**2 - 23/12*n**3 - 1/40*n**5 - 1 - 62*n. Factor o(k).
-k*(k + 1)*(k + 23)/2
Let b be 1/2 + (-15)/(-10). Suppose -n = b*t - 0*n - 3, 5*n = -4*t + 3. Factor -19*d - 6 - 3*d**t + 5*d + 5*d.
-3*(d + 1)*(d + 2)
Let y(x) = -2*x**2 - x + 10. Let q(i) = 14*i**2 + 486*i + 418. Let u(r) = q(r) + 6*y(r). Suppose u(n) = 0. What is n?
-239, -1
Factor 930*r**2 + 814*r**2 - 12705*r + 13519 - 64*r**3 - 2494.
-(r - 1)*(8*r - 105)**2
Let h(j) be the second derivative of 2*j**7/105 + 4*j**6/15 + 6*j**5/5 - 18*j**3 + 7*j**2/2 - 24*j - 2. Let z(o) be the first derivative of h(o). Factor z(d).
4*(d - 1)*(d + 3)**3
Let -572/5*y - 38 + 184/5*y**2 + 572/5*y**3 + 6/5*y**4 = 0. Calculate y.
-95, -1, -1/3, 1
Let x be (-7 + 4)/((-332)/200*4). Let j = x - -4/83. Factor 3/2*d - 2 + j*d**2.
(d - 1)*(d + 4)/2
Suppose -68*a - 4/3*a**2 + 2440/3 = 0. Calculate a.
-61, 10
Factor -709/7*k**2 - 432*k - 54/7*k**3 - 1/7*k**4 - 2368/7.
-(k + 1)*(k + 8)**2*(k + 37)/7
Let d(n) = -n**2 + 82*n - 1673. Let u(g) = 2*g**2 - 15*g - 14. Let y be u(-1). Let a(r) = r**2 - 82*r + 1675. Let k(z) = y*d(z) + 4*a(z). Factor k(h).
(h - 41)**2
Let v(i) be the second derivative of -i**7/98 + 2*i**6/35 - 3*i**5/28 + i**4/14 + 58*i. Let v(w) = 0. What is w?
0, 1, 2
Let 235*a**3 + 144*a + 106 - 251*a**3 - 2*a**4 + 74*a**2 + 164 - 86*a**2 = 0. Calculate a.
-5, -3, 3
Let b(z) = -z**4 + z**3 + 2*z**2 + z + 1. Let s(q) = 44*q**4 + 8*q**3 - 376*q**2 + 198*q - 42. Let h(w) = -84*b(w) - 2*s(w). What is p in h(p) = 0?
-30, 0, 1, 4
Let y = 183/62 - 425/186. Let n(o) be the first derivative of -2/5*o**5 - 1/2*o**4 + 1/3*o**6 + y*o**3 + 0*o**2 - 27 + 0*o. Factor n(k).
2*k**2*(k - 1)**2*(k + 1)
Let c(k) be the third derivative of -k**7/42 - 491*k**6/6 - 241081*k**5/2 - 591853855*k**4/6 - 290600242805*k**3/6 - 9*k**2 + 109*k. Factor c(d).
-5*(d + 491)**4
Let a be 3408/1065*((-670)/(-40) - 13). Let y = 5/11 + 23/22. Let y*c**2 - a + 3*c = 0. Calculate c.
-4, 2
Let y(w) be the first derivative of -2*w**3/9 - 136*w**2 - 27744*w + 646. Factor y(m).
-2*(m + 204)**2/3
Let i(k) = 18*k**3 + 3886*k**2 + 1263605*k + 1259717. Let l(n) = -3*n**3 + n**2 - n - 1. Let h(a) = -i(a) - 5*l(a). Suppose h(j) = 0. Calculate j.
-648, -1
Let n(q) be the first derivative of -2*q**5/7 - 62*q**4/7 + 1510*q**3/21 - 746*q**2/7 + 240*q/7 + 59. Determine o so that n(o) = 0.
-30, 1/5, 1, 4
Suppose -512*x - 45*x = 746*x - 6515. Solve 21*f**2 - 5/2*f**4 + 1/2*f**x - 63/2*f + 27/2 - f**3 = 0.
-3, 1, 3
Let v = -59 + 64. Suppose -v*i - 35 = -4*b, -2 = -b - i + 9. Factor -7*c + 5*c**2 + 2*c - b + 0.
5*(c - 2)*(c + 1)
Let n be (36/(-234))/(-2) + 31/(-403). Factor -4*k**2 - 1/4*k**3 + n + 17/4*k.
-k*(k - 1)*(k + 17)/4
Let 2/15*j**2 - 96/5 - 4/3*j = 0. What is j?
-8, 18
Let d(n) be the third derivative of n**7/210 - 13*n**6/24 + 383*n**5/20 - 3007*n**4/24 + 961*n**3/3 - 2*n**2 + 2134. Determine j, given that d(j) = 0.
1, 2, 31
Suppose 139*u - 352*u + 80 = -173*u. Determine o so that 1/2*o**3 - o**u - 15/2*o + 18 = 0.
-4, 3
Let q = -75 - -90. Let b = q - 13. Find n, given that -124*n**2 + 1