(i). Suppose c(r) = 0. Calculate r.
-119, -1
Factor -3*b**3 - 18*b**2 - 30*b**3 - 10*b**4 + 21*b - 3*b**3 - 21*b.
-2*b**2*(b + 3)*(5*b + 3)
Suppose l + 48 = 5*l. Let q(o) = 32*o**4 + 388*o**3 + 2036*o**2 - 12. Let r(n) = 13*n**4 + 155*n**3 + 815*n**2 - 5. Let j(t) = l*r(t) - 5*q(t). Factor j(v).
-4*v**2*(v + 10)**2
Let h(w) be the first derivative of -w**4/6 + 172*w**3/9 - 1053. Factor h(a).
-2*a**2*(a - 86)/3
Let k = -609106 + 4263752/7. Factor k*l + 2/7*l**2 + 0.
2*l*(l + 5)/7
Factor -585/2 + 3/4*g**2 + 87/4*g.
3*(g - 10)*(g + 39)/4
Let k = 1318/11 - 2625/22. Let w(g) be the first derivative of 0*g + 3/16*g**4 - k*g**3 + 3/8*g**2 + 30. Factor w(s).
3*s*(s - 1)**2/4
Let l be 38*19/(171/(-252)). Let p = l + 1064. Solve 8/7*r + 2/7*r**3 + p + 8/7*r**2 = 0 for r.
-2, 0
Let n(z) = -3649*z**4 - 6067*z**3 + 2299*z**2 - 265*z + 10. Let x(g) = g**4 - 2*g**3 - g**2. Let h(a) = n(a) + 4*x(a). Solve h(o) = 0.
-2, 1/9
Let d = 3097 - 3097. Let r(c) be the third derivative of -c**2 + d + 0*c**4 + 0*c - 1/45*c**5 + 8/9*c**3. Let r(l) = 0. Calculate l.
-2, 2
Let s(g) be the second derivative of -g**4/20 - 26*g**3/5 - 30*g**2 - 2974*g. Factor s(m).
-3*(m + 2)*(m + 50)/5
Let v(b) be the third derivative of b**8/336 - 3*b**7/10 + 341*b**6/40 - 961*b**5/60 + 2*b**2 + 317*b. Determine h, given that v(h) = 0.
0, 1, 31
Let x(r) be the third derivative of -1/160*r**6 + 3/8*r**3 + 8*r**2 + 1/80*r**5 + 0*r + 0 + 5/32*r**4. Determine c so that x(c) = 0.
-1, 3
Let d be (-432)/(-42) - 3/((-42)/(-4)). Let h = -8 + d. What is x in -4 - 24*x - 12*x**h + 36*x - x**4 - x**2 + 6*x**3 = 0?
1, 2
Let f(a) be the first derivative of -a**3/3 + 309*a**2 + 1863*a - 6860. Solve f(i) = 0 for i.
-3, 621
Let h be 2/4 + (-19)/(608/(-48)). Let l(g) be the first derivative of 0*g**4 + 0*g + 0*g**3 + 1/20*g**5 + 1/24*g**6 + 4 + 0*g**h. Factor l(o).
o**4*(o + 1)/4
Let f be -3*1*4/(-42). Let u = 407 + -405. Factor 3/7*i + 2/7 - f*i**u.
-(i - 2)*(2*i + 1)/7
Let a(q) be the first derivative of -16 - 1/36*q**4 - 1/3*q**3 + 0*q**2 - 2*q. Let s(l) be the first derivative of a(l). Solve s(w) = 0 for w.
-6, 0
Let w(r) be the first derivative of -r**4/2 + 220*r**3/3 + 456*r**2 - 4438. Suppose w(v) = 0. Calculate v.
-4, 0, 114
Suppose 1/3*s**3 + 64/3 + 20/3*s**2 + 68/3*s = 0. What is s?
-16, -2
Let j(a) be the second derivative of -81*a**5/20 + 13*a**4 + 2*a**3 + a + 95. Factor j(r).
-3*r*(r - 2)*(27*r + 2)
Let s(q) = 2*q + 5. Let l be s(-1). Determine c, given that 7*c**2 - 4*c - 3*c**4 + 9*c**4 + 7*c**2 - 16*c**l = 0.
0, 2/3, 1
Let q(d) = 9*d**2 - 137*d + 156. Let l be q(14). Suppose p = 3*i - 7, -2 = -4*i + 10. Find g such that p*g**2 + 4*g + 2 + 4 + l - 14*g = 0.
1, 4
Suppose -2*p - 60 + 68 = 4*z, 0 = z - 4*p + 16. Let k(m) be the third derivative of -2/3*m**4 + z*m + 0*m**3 - 12*m**2 - 1/5*m**5 + 7/30*m**6 + 0. Factor k(h).
4*h*(h - 1)*(7*h + 4)
Solve 0 - 8/11*a**2 - 2/11*a**3 - 8/11*a = 0 for a.
-2, 0
Suppose -111/4*m**3 + 0 - 759/4*m**2 - 645/4*m + 3/4*m**4 = 0. What is m?
-5, -1, 0, 43
Let y be 200/22 - -11*26/(-3146). Let k(b) be the first derivative of -1/6*b**3 + 3/4*b**2 - y + 0*b. Determine a, given that k(a) = 0.
0, 3
Let q(k) be the second derivative of 55/3*k**4 + 2*k + 5*k**2 - 49/3*k**3 - 43/5*k**5 - 2 + 1/3*k**7 + 13/15*k**6. Determine h, given that q(h) = 0.
-5, 1/7, 1
Let c(u) be the third derivative of u**8/392 - u**7/245 - 3*u**6/140 + u**5/14 - u**4/14 - 1105*u**2. Determine g, given that c(g) = 0.
-2, 0, 1
Suppose -3*q + 33 = 3*h, -2*q + 3*h - 8*h = -37. Factor -2*c**3 - c**3 - 4*c**3 - 3*c + 4*c**3 - 24 + 15*c + q*c**2.
-3*(c - 2)**2*(c + 2)
Suppose 0 = -7366*o + 7338*o. Let a(z) be the second derivative of 0 + o*z**4 + 0*z**2 + 1/240*z**6 + 0*z**3 - 1/80*z**5 - 21*z. Factor a(w).
w**3*(w - 2)/8
Let q(a) be the third derivative of -a**8/40320 - a**7/480 - 11*a**5/12 - 49*a**2. Let w(f) be the third derivative of q(f). Factor w(c).
-c*(c + 21)/2
Suppose 10*z = -4*t + 8*z + 22, 3*t + 2*z - 19 = 0. Suppose -5*x - 4 = -4*y - 2, -x + 11 = t*y. What is o in 0 + 0*o + 2/13*o**y - 6/13*o**2 = 0?
0, 3
Let u be (-244)/1220 - 46*(-3)/240. Factor 27/8*q - u*q**2 + 0.
-3*q*(q - 9)/8
Let s be (-5100)/72*(-15)/50. Let g = s + -843/44. Factor 20/11*z + g*z**2 + 7/11*z**3 + 4/11.
(z + 1)*(z + 2)*(7*z + 2)/11
Let l(k) be the third derivative of -k**6/180 + 17*k**5/45 + 565*k**4/12 + 1600*k**3 + 334*k**2 - k. Factor l(w).
-2*(w - 64)*(w + 15)**2/3
Let z(n) be the third derivative of -n**7/945 - 17*n**6/540 + 22*n**5/27 - 91*n**4/27 - 7802*n**2. What is k in z(k) = 0?
-26, 0, 2, 7
Solve -70*f**2 - 1/3*f**3 - 623/3*f - 138 = 0.
-207, -2, -1
Let o(z) be the third derivative of z**6/420 + z**5/5 + 39*z**4/28 - 1390*z**2. Let o(b) = 0. Calculate b.
-39, -3, 0
Suppose 13*k + 2*k = 3 - 3. Let p(z) be the third derivative of -1/300*z**6 - 12*z**2 + 1/60*z**4 + k*z + 1/75*z**5 - 2/15*z**3 + 0. Factor p(h).
-2*(h - 2)*(h - 1)*(h + 1)/5
Let f(v) = 72*v**3 + 83*v**2 - 29*v - 212. Let h(z) = 10*z**3 + 12*z**2 - 4*z - 30. Let o(g) = 6*f(g) - 43*h(g). Factor o(a).
2*(a - 9)*(a - 1)*(a + 1)
Suppose 16*q + 50 = -46. Let i be (-34)/q - (7 + -13 + 9). Factor 4/9*x**2 + i - 20/9*x.
4*(x - 3)*(x - 2)/9
Let s(a) be the third derivative of a**6/45 - 31*a**5/90 - 11*a**4/9 - a**3 - a**2 + 2*a - 8. What is v in s(v) = 0?
-1, -1/4, 9
Let c(k) be the third derivative of 8/51*k**3 + 0 - 146*k**2 + 21/17*k**4 + 0*k + 3087/340*k**6 + 441/85*k**5. Solve c(n) = 0 for n.
-2/21
Let d(n) be the first derivative of n**5 + 25*n**4/4 - 10*n**3 + 851. Solve d(l) = 0.
-6, 0, 1
Let k be (6/(-5))/(54/(-1485)). Factor k*c - 13*c**2 + 4 + 2 - 4 - 18*c**2 - 4.
-(c - 1)*(31*c - 2)
Factor -98*x - 3*x**4 - 118*x + 351742*x**3 + 351759*x**3 - 703561*x**3 + 279*x**2.
-3*x*(x - 3)*(x - 1)*(x + 24)
Let b(z) be the first derivative of -z**5/25 - 3*z**4/4 - 19*z**3/5 - 73*z**2/10 - 6*z + 16189. Find c, given that b(c) = 0.
-10, -3, -1
Suppose -6*v**2 + 12 + 2/9*v**4 + 2/9*v**3 + 6*v = 0. Calculate v.
-6, -1, 3
Let t be (-2 + (-24)/(-10))/(12/(-60)). Let i be t/(-21) + (-56)/(-294). Factor 30/7*m**2 + i*m**3 + 250/7 + 150/7*m.
2*(m + 5)**3/7
Let k be 44815/(-45) - 2/18. Let v = k - -999. Let n**v - 1/4*n**4 + 0 + 1/4*n**2 - n = 0. Calculate n.
-1, 0, 1, 4
Let t(i) = -3*i**4 - 96*i**3 - 642*i**2 - 1563*i - 1002. Let b(a) = -2*a**3 - a**2 - a + 2. Let m(n) = 3*b(n) - t(n). Suppose m(p) = 0. What is p?
-21, -4, -1
Let w(j) be the first derivative of -8*j**4 + 52*j**3 - 90*j**2 + 3789. Determine i, given that w(i) = 0.
0, 15/8, 3
Let v = 10674 - 672454/63. Let y(m) be the second derivative of 0*m**3 - 1/4*m**4 + 27*m + 0*m**2 - 4/9*m**6 + 11/20*m**5 + 0 + v*m**7. Factor y(w).
w**2*(w - 1)*(4*w - 3)**2/3
Let v = -113 - -149. Suppose -v*d - 3 = -37*d. What is z in -2 + 11*z**2 - 3*z**2 - 3*z**d - 5*z + 8*z**2 - 6*z**3 = 0?
-2/9, 1
Suppose -9/2*b**3 - 31*b**2 + 1/2*b**4 - 28 - 54*b = 0. Calculate b.
-2, -1, 14
Let z(t) be the first derivative of -3*t**4/20 + 34*t**3/5 - 336*t**2/5 + 1248*t/5 - 490. Solve z(f) = 0 for f.
4, 26
Suppose 11*s = 1650 + 1210. Factor 5*c**2 + 15 - 70 + 7*c**2 - s*c - 33.
4*(c - 22)*(3*c + 1)
Let c = -1166 - -1171. Let n(p) be the second derivative of 0 + 5*p - 2/7*p**3 + 2/7*p**2 - 1/21*p**4 + 3/35*p**c. Factor n(y).
4*(y - 1)*(y + 1)*(3*y - 1)/7
Suppose 90*i + 36*i - 792 = -138*i. Suppose 8/7*y - 36/7*y**2 + 40/7*y**i + 0 - 12/7*y**4 = 0. Calculate y.
0, 1/3, 1, 2
Let b = -458660/7 - -65523. Factor 24/7*d - 23/7 - b*d**2.
-(d - 23)*(d - 1)/7
Suppose 4*d = -2*n + 64, 0 = -0*d + d. Let q(u) = 7*u - 222. Let f be q(n). Factor 8/3*h**f + 4/3 + 2/3*h**3 + 10/3*h.
2*(h + 1)**2*(h + 2)/3
Let z(o) be the first derivative of -5*o**4/4 - 265*o**3 - 1560*o**2 - 3100*o - 2238. Factor z(i).
-5*(i + 2)**2*(i + 155)
Let o(m) be the first derivative of -2*m**3/15 + 19*m**2 + 588*m/5 + 7631. Determine f, given that o(f) = 0.
-3, 98
Let z(r) be the second derivative of 31*r**7/21 - 184*r**6/15 + 267*r**5/10 + 3*r**4 - 6200*r. Suppose z(x) = 0. What is x?
-2/31, 0, 3
Let x(a) = -5*a**3 + 430*a**2 + 1305*a + 868. Let r(k) = 6*k**3 - 432*k**2 - 1308*k - 867. Let g(b) = 2*r(b) + 3*x(b). Factor g(h).
-3*(h - 145)*(h + 1)*(h + 2)
Let z be 8/308*165 - (-13 - -17). Factor z*u**2 - 10/7 - 8/7*u.
2*(u - 5)*(u + 1)/7
Let b(s) = s**3 + 51*s**2 + 221*s +