97. Let b(s) = -5*s**3 - 2*s**2 + 1. Let l(f) = -3*b(f) - x(f). Determine k, given that l(k) = 0.
-120, 1
Let u be (-377125)/(-214375) + 4/98. Factor 3/5*f**3 - 6/5 - 3*f + 3/5*f**4 - u*f**2.
3*(f - 2)*(f + 1)**3/5
Let c = -77398 - -53946325/697. Let m = 1/697 - c. Factor 6/17 - 4/17*t - m*t**2.
-2*(t - 1)*(t + 3)/17
Let j = 242 - 239. Factor 18 + 8*y**3 - 6*y - 10*y**2 + 14*y**3 - 24*y**j.
-2*(y - 1)*(y + 3)**2
Let g(s) = -s**3 + 273*s**2 + 782*s + 396. Let f(a) = a**3 + 819*a**2 + 2347*a + 1188. Let b(p) = -2*f(p) + 7*g(p). Let b(u) = 0. Calculate u.
-2, -2/3, 33
Suppose 207*f - 5*f - 465 = -133*f + 205. Let 200 - 1/2*b**3 - 180*b - 39/2*b**f = 0. Calculate b.
-20, 1
Suppose 0 = -m + 22*o - 18*o - 361, -m - 3*o - 389 = 0. Let j = 378 + m. Factor 7/4*i**3 - 23/4*i**2 + 5*i - j.
(i - 2)*(i - 1)*(7*i - 2)/4
Let k(x) = 2*x**2 - 10*x - 69. Let t be k(9). Let l(a) be the first derivative of -9 + 0*a**2 - 2/5*a**4 - 2/5*a**t + 0*a. Factor l(w).
-2*w**2*(4*w + 3)/5
Solve 12/5 + 253368/5*z**3 - 78732/5*z**5 + 26888/5*z**2 + 148716/5*z**4 + 196*z = 0.
-1, -1/27, 3
Let h(t) be the second derivative of t**7/147 - 17*t**6/35 - 109*t**5/70 + 155*t**4/42 + 72*t**3/7 - 212*t**2/7 + 6003*t. Let h(g) = 0. What is g?
-2, 1, 53
Factor 92*j**2 - 12739*j**3 - 110 + 12711*j**3 + 399*j + 79*j**2.
-(j + 2)*(4*j - 1)*(7*j - 55)
Let k(p) = -2*p**2 + 123*p + 146. Let s be k(62). Let n be 1/(-2) - (-161)/2. Factor s*c - 3*c**2 - 164*c + n*c.
-3*c**2
Let b(m) be the third derivative of 2*m**7/105 + 49*m**6/30 + 51*m**5 + 3179*m**4/6 - 19652*m**3/3 - 1990*m**2. Factor b(y).
4*(y - 2)*(y + 17)**3
Let h(l) = -3*l**3 - 2*l**2 + 19*l + 16. Let c(n) = n**2 + n + 1. Let m = 4 + -3. Let t(d) = m*h(d) + 2*c(d). Find b such that t(b) = 0.
-2, -1, 3
Let d(s) be the third derivative of 0*s - 1/8*s**6 + 25/12*s**4 + 1/12*s**5 + 3 + 0*s**3 - 51*s**2. Let d(r) = 0. What is r?
-5/3, 0, 2
Solve 39/5*t**2 - 38/5 + 17/5*t - 1/5*t**4 - 17/5*t**3 = 0 for t.
-19, -1, 1, 2
Let j(p) be the third derivative of 2/9*p**3 + p + 7/180*p**5 - 5/18*p**4 + 1/40*p**6 - 6*p**2 + 0. Determine m so that j(m) = 0.
-2, 2/9, 1
Let x(j) be the third derivative of j**7/105 + 17*j**6/75 - 11*j**5/50 - 17*j**4/15 + 28*j**3/15 + 1463*j**2. Let x(k) = 0. Calculate k.
-14, -1, 2/5, 1
Let l be -17 - (0 - (4 - 6)). Let i = l + 21. Solve -y - 2*y**2 + 3*y**2 + 7*y + i*y**2 = 0.
-2, 0
Let r = 3642583/6070955 + -2/1214191. Factor 0 + 3/5*p**3 + 0*p + 3/5*p**4 - r*p**5 - 3/5*p**2.
-3*p**2*(p - 1)**2*(p + 1)/5
Let y(z) be the first derivative of -z**4/20 + 22*z**3/15 - 21*z**2/2 + 144*z/5 + 9556. Determine f, given that y(f) = 0.
3, 16
Let p(m) = 23*m**3 - 329*m**2 + 4408*m - 14440. Let s(i) = 11*i**3 - 165*i**2 + 2204*i - 7220. Let n(t) = -7*p(t) + 15*s(t). Determine h, given that n(h) = 0.
5, 19
Let b = -56 + 53. Let d be (b - (-2 - 1)) + 5. What is v in 16*v**4 - 11*v**2 - 3*v**5 + d*v**3 - 4*v**2 - 10*v + 8*v**5 - v**4 = 0?
-2, -1, 0, 1
Let g = -1217446/5403 - 10/1801. Let k = g - -227. Solve -k*t - 5*t**2 + 5/3*t**3 + 10/3 + 5/3*t**4 = 0 for t.
-2, -1, 1
Suppose -2*o + 8*o = 8274. Factor -5*u**2 - o + 4*u**2 + 331 + 18*u - 1353 + 80*u.
-(u - 49)**2
Let q be 11 - -1555*(-39)/5525. Let u(p) be the first derivative of 6 - 4/51*p**3 + q*p**5 + 0*p + 0*p**2 + 1/34*p**4. Let u(j) = 0. Calculate j.
-2, 0, 1
Let o(y) = -y**3 - 17*y**2 + 15*y - 38. Let u be o(-18). Factor -15*w**2 - u - 18*w + 2*w + 11*w**2.
-4*(w + 2)**2
Let n = -596 - -673. Determine s, given that -n - 92*s - 8*s**2 - 73 + 27*s + 3*s**2 = 0.
-10, -3
Let b(a) = 19*a**2 + 2143*a - 2012. Let t(w) = 11*w**2 + 1071*w - 992. Let p(d) = 6*b(d) - 10*t(d). Factor p(v).
4*(v - 1)*(v + 538)
Let h(s) be the first derivative of 38 + 441/2*s + 21/2*s**2 + 1/6*s**3. Factor h(c).
(c + 21)**2/2
Find a such that 0*a - 3/8*a**3 + 0 - 231/4*a**2 = 0.
-154, 0
Let u(f) = f**2 - 11*f - 12. Suppose -w - 12 = -5*w. Let z(n) = 4 - 3 - 4*n + 2*n + w*n. Let g(p) = 4*u(p) + 44*z(p). Factor g(c).
4*(c - 1)*(c + 1)
Let y(s) be the second derivative of s**7/84 - 2*s**6/15 - 33*s**5/40 - s**4/6 + 11*s**3/3 + 154*s - 2. Suppose y(f) = 0. Calculate f.
-2, 0, 1, 11
Suppose 63/2*t + 33/2*t**4 - 1/2*t**5 - 31*t**3 - t**2 - 31/2 = 0. Calculate t.
-1, 1, 31
Suppose -64 - 203 + 115*v - 5*v**2 - 113 = 0. What is v?
4, 19
Let d(z) = -21*z**2 + 38*z - 1213. Let f(m) = -48*m**2 + 72*m - 2427. Let y(t) = 9*d(t) - 4*f(t). Factor y(n).
3*(n - 13)*(n + 31)
Find d such that -5*d**2 + 1040*d - 9*d**2 - 15*d**2 - 48321 - 5759 + 24*d**2 = 0.
104
Let y be (1/(-8) - (-252)/480)*5. Factor -a**y - 45*a + 2*a**2 + 49*a + 4.
(a + 2)**2
Suppose -3*y + r + 41 - 13 = 0, 3*y = -5*r + 4. Suppose -4*s + y*s - 1200 = 0. Suppose -7*v - s*v**3 + 125*v**4 + 105*v**2 + 0*v - 3*v = 0. Calculate v.
0, 1/5, 2
Let l(w) be the second derivative of 14/5*w**3 - 36/5*w**2 + 6/25*w**6 - 30 - 141/100*w**5 + 19/10*w**4 - w. Determine a so that l(a) = 0.
-3/4, 2/3, 2
Let o(n) = 4*n**4 - 120*n**3 - 130*n**2 + 606*n - 359. Let g(r) = -2*r**4 + 2*r**3 - 1. Let j(a) = -2*g(a) - 2*o(a). Factor j(c).
-4*(c - 60)*(c - 1)**2*(c + 3)
Let s = -10643/420 + 355/14. Let i(k) be the third derivative of 0*k - 8*k**2 + 0*k**3 + s*k**6 + 1/6*k**4 - 1/10*k**5 + 0. Factor i(l).
2*l*(l - 2)*(l - 1)
Suppose 14*q - 12*q - 1144 = 0. Suppose -4*c + 449 = 2*x + 173, -4*x - 4*c + q = 0. Suppose x*d - 148*d + 0*d**3 - d**3 + d**2 = 0. Calculate d.
0, 1
Let x(b) be the first derivative of -b**5/150 - 3*b**4/5 - 108*b**3/5 + 104*b**2 - 218. Let q(i) be the second derivative of x(i). Let q(d) = 0. What is d?
-18
Let o(y) be the second derivative of y**7/168 + y**6/8 + 31*y**5/40 + y**4/3 - 12*y**3 - 32*y**2 + 4*y + 271. Suppose o(i) = 0. Calculate i.
-8, -4, -1, 2
Suppose -15*a = -16*a + 5. Suppose 5 = -a*z + 25. Factor n**4 + 10*n + 11*n**4 + 45*n**2 + 13*n**z + 84*n**3 - 24*n**3.
5*n*(n + 1)**2*(5*n + 2)
Suppose -12*w = 32*w. Let c(k) = -2*k**2 + 11*k + 26. Let t be c(7). Factor 0*d - 3/5*d**3 - 12/5*d**4 - 7/5*d**t + w + 2/5*d**2.
-d**2*(d + 1)**2*(7*d - 2)/5
Suppose -f + 3210 - 3180 = 4*f. Let x(w) = w**3 + 10*w**2 + 9*w + 3. Let t be x(-9). Suppose 0*l + 0 + 4/5*l**2 + f*l**t = 0. What is l?
-2/15, 0
Find o, given that -1089 + 3*o**2 - 232*o - 938 + 568*o + 635 = 0.
-116, 4
Let k(c) = -5*c**2 - 700*c - 24488. Let p(n) = -66 + 32 + 32. Let i(s) = k(s) + 6*p(s). Factor i(h).
-5*(h + 70)**2
Suppose -22*v + 122 = 43*v - 4*v. Let x(a) be the first derivative of 51/2*a**v - 10*a**3 + 16 + 3/4*a**4 - 24*a. Suppose x(h) = 0. Calculate h.
1, 8
Let k = -52810 - -52812. Factor 0 + 0*u + 7/6*u**3 - 5/6*u**4 - 1/3*u**k.
-u**2*(u - 1)*(5*u - 2)/6
Factor 6/5*q**3 + 384/5*q - 288/5 - 102/5*q**2.
6*(q - 12)*(q - 4)*(q - 1)/5
Let i(c) = 5*c**2 - 624*c - 1370. Let q(a) = -a**2 + 21. Let x(l) = 2*i(l) + 12*q(l). Factor x(d).
-2*(d + 2)*(d + 622)
Let r(h) be the first derivative of -h**6/40 + h**5/20 + 21*h**4/8 - 45*h**3/2 + h**2/2 + 7*h + 75. Let k(o) be the second derivative of r(o). Factor k(x).
-3*(x - 3)**2*(x + 5)
Let h(y) = y**4 + y**3 + y + 2. Let f(k) = -6*k - 5*k**4 - 3 - 4*k**3 + 18 - 13 - 14. Let o(w) = -5*f(w) - 30*h(w). Factor o(t).
-5*t**3*(t + 2)
Let x = 290 + -255. Find q such that 61*q**2 - x - q - 26*q**2 + 2*q + 5*q**3 - 6*q = 0.
-7, -1, 1
Factor 964299*c - 23983*c + 28169 + 131079601*c**4 - 2209 + 63702236*c**3 + 2601 + 11609286*c**2.
(107*c + 13)**4
Let q be (5 + -4)/(51/204). Let n(c) be the third derivative of -1/8*c**3 - 1/48*c**q + 0 + 0*c + 1/240*c**5 - 3*c**2. Find m, given that n(m) = 0.
-1, 3
Factor 0*z + 0 - 2/5*z**3 + 1334/5*z**2.
-2*z**2*(z - 667)/5
Let f(k) = 7*k**3 - 5*k**2 - 19*k + 7. Let h(t) = -3*t**3 + 2*t**2 + 9*t - 4. Suppose -4*z = -5*q - 6, 4*q + 0*z = 2*z. Let s(g) = q*f(g) + 5*h(g). Factor s(i).
-(i - 2)*(i - 1)*(i + 3)
Let r(f) be the first derivative of 11/9*f**3 - 2*f**2 - 1/6*f**4 - 2 + 10*f. Let s(b) be the first derivative of r(b). Let s(n) = 0. Calculate n.
2/3, 3
Let p(d) be the second derivative of -2*d**7/21 + 2*d**6/15 + 3*d**5/5 - 5*d**4/3 + 4*d**3/3 + 2737*d - 2. Factor p(t).
-4*t*(t - 1)**3*(t + 2)
Let a(r) = 5*r**2 - 65*r + 180. Let l(f) = 0*f + 0*f - f. Let o(g) = -7*g**2 + 166*g - 164. Let n be o(1). Let z(s) = n*l(s) + a(s). Factor z(y).
5*(y - 6)**2
Suppose 59*k - 61*k + 13 = -2*i - 11, -2*k = -28. Determine d, giv