+ 1/72*q**4 - 11/4*q**2 - 2. Factor s(i).
(i - 33)*(i + 1)/6
Let u = 13039/68182 + 5402112203/1605890646. Let y = u - -1/2617. Solve 76/9*w**2 - 28/9*w**3 + 136/9*w + y = 0 for w.
-1, -2/7, 4
Let v be 1/(-3) - ((-42)/(-9))/(-2). Suppose -v*q = -3*q + z + 3, -5*q = -z - 15. Let 162*f - 162*f + q*f**3 + 3*f**2 = 0. Calculate f.
-1, 0
Let p(o) be the second derivative of 3/5*o**4 - 30*o + 8*o**2 + 16/5*o**3 + 1/25*o**5 + 0. Factor p(d).
4*(d + 2)**2*(d + 5)/5
Let w(g) be the first derivative of g**8/1680 - g**7/280 + g**6/180 - 2*g**3/3 + g**2 + 36. Let j(c) be the third derivative of w(c). Factor j(r).
r**2*(r - 2)*(r - 1)
Let j = 125 - 46. Factor 5*p**2 - j - 4*p**2 + 11*p**2 + 220*p - 73.
4*(p + 19)*(3*p - 2)
Find b such that -794976 - 2/3*b**2 + 1456*b = 0.
1092
Determine v so that 1/3*v**3 + 323761 - 1135/3*v**2 + 320347/3*v = 0.
-3, 569
Let z(r) = -r**2 - 4663*r + 107780. Let c be z(23). Let 3 + 1/2*s**c + 7/2*s = 0. What is s?
-6, -1
Let n(v) be the first derivative of -25*v**5/3 - 33475*v**4/3 - 11934940*v**3/3 + 14354080*v**2/3 - 5745920*v/3 + 3166. Find p, given that n(p) = 0.
-536, 2/5
Find n such that 74*n**2 + 21*n**2 - 95*n**2 + 28*n**2 - 72 + 20*n = 0.
-2, 9/7
Let u be (-11)/(-55*(-39)/(-390)). Factor 1682/11 + 2/11*w**u + 116/11*w.
2*(w + 29)**2/11
Let o be (-24)/(-18) + 2*(-1)/(-3). Let v(t) be the first derivative of -24 - 3*t**2 + 3*t**2 + t**3 - 3*t**o. Factor v(c).
3*c*(c - 2)
Let u be ((-2)/10)/((5 + (-17)/3)/(68 - 58)). Solve -22*a**2 + 2/3*a**u - 512/3 + 192*a = 0 for a.
1, 16
Let r(y) be the first derivative of y**5/35 - 11*y**4/14 - 8*y**3/7 + 11*y**2/7 + 23*y/7 - 6802. Let r(m) = 0. Calculate m.
-1, 1, 23
Let r be (-2)/(-96)*4192/2620. Let f(j) be the third derivative of -10*j**2 + 0 + 1/84*j**4 + r*j**6 + 0*j**3 + 0*j - 13/1470*j**7 - 17/420*j**5. Factor f(g).
-g*(g - 1)**2*(13*g - 2)/7
Let a be (-18)/(-15)*1/(6/20). Factor 8*z**2 + 6*z**3 - 6*z - 2*z**5 - 4*z**a - 9*z + 4*z + 3*z.
-2*z*(z - 1)**2*(z + 2)**2
Let v = 30 + -366. Let b = v - -516. Factor -20 + b*u**2 + 145 + 44*u - 344*u.
5*(6*u - 5)**2
Suppose -3*r - 3 = -b, -3*b + 2*r = 2*b - 15. Let n(v) = v**3 + 2*v**2 - 4*v. Let h be n(-3). Factor -15*o**2 + 5*o**h + 4*o**3 + 10*o - 4*o**b.
5*o*(o - 2)*(o - 1)
Find x such that 24336 + 1/9*x**2 + 104*x = 0.
-468
Suppose -20*t + 32 = -18*t. Factor 142 + 24*r + t*r - 97 - 5*r**2.
-5*(r - 9)*(r + 1)
Let d(a) = 54*a - 58. Let f be d(1). Let w be 270/(-2808) - 1/f. Let 4/13*i + 0*i**2 - 4/13*i**3 - 2/13*i**4 + w = 0. Calculate i.
-1, 1
Let k(x) be the first derivative of 0*x + 7 + x**6 + 5*x**3 + 39/5*x**5 + 0*x**2 + 12*x**4. Let k(m) = 0. Calculate m.
-5, -1, -1/2, 0
Let t(z) = 34*z**3 + 192*z**2 - 13*z - 178. Let g(x) = -24*x**3 - 128*x**2 + 9*x + 118. Let n(s) = -7*g(s) - 5*t(s). Determine a so that n(a) = 0.
-32, -1, 1
Let r(v) be the first derivative of -v**5/5 - 523*v**4/18 + 821*v**3/27 + 13*v**2 - 4373. Let r(y) = 0. What is y?
-117, -2/9, 0, 1
Suppose 148 + 72 = -20*l. Let q(r) = 3*r**3 + 2*r**2 - r + 4. Let x(n) = -16*n**3 - 11*n**2 + 4*n - 21. Let z(t) = l*q(t) - 2*x(t). Factor z(k).
-(k - 1)**2*(k + 2)
Suppose 0 = -y - s - 8 + 13, -4*y + 24 = 2*s. Find f such that 31*f**3 + 0*f**2 - 32*f**3 + y*f + 0*f**2 - 6*f**2 = 0.
-7, 0, 1
Let y(t) be the second derivative of -8/3*t**3 - t**4 - 1/10*t**5 + 0*t**2 + 62*t + 0. Suppose y(b) = 0. What is b?
-4, -2, 0
Let d(f) be the third derivative of 0 - 6*f**2 + 0*f - 1/90*f**5 + 5/12*f**3 - 17/144*f**4. Suppose d(g) = 0. What is g?
-5, 3/4
Suppose -3*r + 6 = 0, -170*r + 175*r = -4*z + 10. Let y(t) be the first derivative of 0*t + 12 - 2/35*t**5 + z*t**3 + 1/14*t**4 + 0*t**2. What is o in y(o) = 0?
0, 1
Determine w so that -7/5*w**3 - 27/5 - 93/5*w - 73/5*w**2 = 0.
-9, -1, -3/7
Let i(w) be the second derivative of w**7/42 + 17*w**6/30 - 25*w**5/4 + 287*w**4/12 - 136*w**3/3 + 46*w**2 - 8*w - 94. Solve i(u) = 0 for u.
-23, 1, 2
Determine d, given that 2198/3*d + 1207801/3 + 1/3*d**2 = 0.
-1099
Suppose 0 = -2*j - 2*j + 124. Suppose -45 = -40*w + j*w. What is z in 8 - 3*z**2 - 8*z + w*z**2 + 0*z**2 = 0?
2
Let b(x) be the second derivative of -5/12*x**3 + 1/48*x**4 + 0 - 3*x**2 + 43*x. Let b(g) = 0. Calculate g.
-2, 12
Suppose -3*s + k = -3, 869*s - 873*s - 5*k + 23 = 0. Let g(n) be the second derivative of 10/3*n**3 - 15/2*n**s - 5/12*n**4 + 0 - 12*n. Factor g(r).
-5*(r - 3)*(r - 1)
Let y(c) be the second derivative of -c**5/100 - 17*c**4/60 + 43*c**3/10 - 207*c**2/10 - 1738*c. Find n such that y(n) = 0.
-23, 3
Find z such that 0 + 317*z + 321/4*z**3 + 318*z**2 + 1/4*z**4 = 0.
-317, -2, 0
Suppose 16*m - 40 = -8. Factor -104*b**2 + 14*b - 105*b**m + 210*b**2.
b*(b + 14)
Let s be 704/224*-4 + 36. Factor -2*m**3 + 48/7*m + 0 - s*m**2.
-2*m*(m + 12)*(7*m - 2)/7
Determine i so that 21/4*i + 23/2 + 51/4*i**3 - 29*i**2 - 1/2*i**4 = 0.
-1/2, 1, 2, 23
Let r(d) be the first derivative of 5*d**4/4 - 22440*d**3 + 151066080*d**2 - 451989711360*d - 4697. Factor r(n).
5*(n - 4488)**3
Let q(g) = 27*g + 170. Let c be q(-14). Let b be 1/4 + (-13)/(c/44). Factor -42/17*k - 2/17*k**5 + 10/17 + 4*k**2 + 18/17*k**4 - 52/17*k**b.
-2*(k - 5)*(k - 1)**4/17
Let q(j) be the third derivative of -j**5/90 - 95*j**4/36 - 94*j**3/9 + j**2 - 1827. Factor q(n).
-2*(n + 1)*(n + 94)/3
Let z(o) be the second derivative of -o**6/720 - 7*o**5/40 - 147*o**4/16 - 6*o**3 - o - 36. Let r(s) be the second derivative of z(s). Factor r(n).
-(n + 21)**2/2
Suppose 103/2*r - 10*r**2 + 1/2*r**3 - 78 = 0. What is r?
3, 4, 13
Let c(w) = 7*w + 518. Let v(n) = -3*n**2 - 47*n - 244. Let f be v(-10). Let y be c(f). Suppose m**3 - m**5 + 0 + 1/2*m**4 + y*m - 1/2*m**2 = 0. What is m?
-1, 0, 1/2, 1
Let b(d) be the first derivative of d**5/5 - 5*d**4/9 + 2*d**3/9 + 2*d**2/3 + 2*d + 43. Let a(g) be the first derivative of b(g). Suppose a(i) = 0. Calculate i.
-1/3, 1
Let u be 4/52 - ((-132512)/2665 - -39). Factor 0 + 6/5*p**3 + u*p + 36/5*p**2.
6*p*(p + 3)**2/5
Suppose s = -2*q - 6, -3*q - 19 = -s - 0*s. Let o be 12/(-153)*3060/(-180). Factor -o*v**s - 20/3*v**3 + 16/3*v + 32/3 - 8*v**2.
-4*(v - 1)*(v + 2)**3/3
Factor 114921 - 116277/2*l - 1/2*l**3 + 340*l**2.
-(l - 339)**2*(l - 2)/2
Suppose -345*h = -349*h + 16. Let b(t) = 2*t**3 + 8*t**2 - 42*t - 68. Let l(p) = 2*p**3 + 7*p**2 - 39*p - 69. Let y(k) = h*l(k) - 3*b(k). Factor y(n).
2*(n - 4)*(n + 3)**2
Let n(z) be the third derivative of -z**6/30 - 3*z**5 - 383*z**4/6 + 286*z**3 - 9*z**2 + 121*z. Solve n(x) = 0.
-33, -13, 1
Suppose -64722*y - 484 = -64964*y. Factor -1/4*g**4 - 45/4*g**y + 0 + 27/2*g + 3*g**3.
-g*(g - 6)*(g - 3)**2/4
Let l(d) = d**3 - 8*d**2 + 10*d. Let s be ((-5)/20)/(1/(-28)). Let b be l(s). Factor -b*i**2 - 21*i**3 - 9*i + 6 + 15*i**4 + 16*i**3 + 14*i**3.
3*(i - 1)*(i + 1)**2*(5*i - 2)
Factor 0 - 2/5*g**4 + 44/5*g**3 + 0*g - 42/5*g**2.
-2*g**2*(g - 21)*(g - 1)/5
Suppose 45 - 114 = -2*k + 5*i, 4*i + 56 = 2*k. Factor -10/9*y - 4/9 + 14/9*y**k.
2*(y - 1)*(7*y + 2)/9
Let o(i) be the second derivative of i**5/50 - 11*i**4/30 + 8*i**3/5 - 3*i - 3. Solve o(c) = 0 for c.
0, 3, 8
Let c = -885 - -933. Let 0*u**3 - 81 - 336*u - 2*u**4 - 2*u**4 - 88*u**2 + c*u**3 - 115 = 0. What is u?
-1, 7
Let x(g) be the third derivative of g**5/20 + 41*g**4/8 - g**2 + 34. Factor x(j).
3*j*(j + 41)
Suppose -5*p = 2*m + 2 - 15, -4*p + 2*m + 14 = 0. Determine o, given that -4*o**4 + 4*o**2 + o**5 - 11*o + 8*o - o + 3*o**p = 0.
-1, 0, 1, 2
Let l(a) = -5*a**3 + 2*a**2 + a. Let h(s) = -3*s**4 - 6*s**3 + 24*s**2 - 90*s. Let f(p) = -h(p) + 6*l(p). Factor f(m).
3*m*(m - 8)*(m - 2)*(m + 2)
Let d = -678 + 681. Determine q, given that -2*q**3 + d - q**3 - 2*q**3 + 5*q**3 - 9*q - 3*q**3 + 9*q**2 = 0.
1
Factor -8*a**2 + 46/5*a - 12/5.
-2*(4*a - 3)*(5*a - 2)/5
Let g = -11493 - -11496. Solve 31/4*a**g - 32 + 71/2*a**2 + 1/4*a**5 - 7/2*a**4 - 8*a = 0 for a.
-2, -1, 1, 8
Suppose 5 = 5*h - 3*d, -5*d + d + 2 = 2*h. Suppose -r = -3 - h. Solve r*w**5 + 12*w**3 - 13*w**3 - 5*w**5 + 2*w**4 = 0 for w.
0, 1
Let c(a) be the second derivative of 2 - 32768/11*a**2 - 16/11*a**4 - 1024/11*a**3 - 1/110*a**5 - 15*a. Factor c(m).
-2*(m + 32)**3/11
Let d(j) be the third derivative of 23*j**5/540 + 5*j**4/108 + 33*j**2 - 17. Factor d(p).
p*(23*p + 10)/9
Suppose 110 = 5*c - 4*i - i, 0 = 2*c + 2*i - 32. Suppose -c*m + 461 = -52